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A TABLE

OF

ANTI -LOGARITHMS:

CONTAINING TO

SEVEN PLACES OF DECIMALS, NATURAL NUMBERS

ANSWERING TO ALL

LOGAKITHMS FROM -00001 TO -99999;

AND AN IMPROVED

TABLE OF GAUSS'S LOGARITHMS,

BY WHICH MAY BE FOUND

THE LOGARITHM TO THE SUM OR DIFFERENCE OF TWO QUANTITIES WHOSE LOGARITHMS ARE GIVEN.

PRECEDED BY

AN INTRODUCTION,

CONTAINING ALSO THE HISTORY OF LOGARITHMS, THEIR CONSTRUCTION, AND THE VARIOUS IMPROVEMENTS MADE THEREON SINCE THEIR INVENTION.

WITH

AN APPENDIX,

ONTAIN1NG A TABLE OF ANNUITIES FOR THREE JOINT LIVES AT THREE PER CENT, CARLISLE.

BY HERSCHELL E. FILIPOWSKL

"

sr&ttU e&Won, UrtfsrlJ anU ®ormt*&. 0 / -

LONDON: BELL AND DALDY, 186 FLEET STREET.

MDCCCLXI.

5 JT

INTRODUCTION.

N introducing the present table of Anti-Logarithms to the public, it is deemed xpedient to give a brief account of Logarithms in general, and of Anti- arithms in particular, — independent of the numerous treatises on the same ubject by various authors — with a view of sparing its possessor the trouble f consulting other works wherein such treatises might be found.

The laborious and irksome processes of raising powers and extracting roots f natural numbers in common arithmetic, principally requisite in Astronomical nd trigonometrical calculations; as also the tedious working of multiplication nd division in general, gave rise to the idea of the immortal Lord JOHN APIER, Baron of Merchiston, in Scotland, to devise a plan for facilitating such rorking, and which he successfully carried through, by means of arranging a sries of numbers in arithmetical progression, opposite another series of num- >ers in geometrical progression. Thus

0, 1, 2, 3, 4, 5, Indices, or logarithms.

1, 2, 4, 8, 16, 32, Geometric progression.

0, 1, 2, 3, 4, 5, Indices, or logarithms.

1, 3, 9, 27, 81, 243, Geometric progression. Dr,

0, 1, 2, 3, 4, 5, Indices, or logarithms.

1, 10, 100, 1000, 10000, 100,000 Geometrical progression. Where it is evident that the same indices serve equally for any geometric eries ; and consequently, there may be an endless variety of systems of Loga- •ithms to the same common numbers, by only changing the second term, 2, 3, Dr 10, etc. of the geometrical series.

It is also apparent, from the nature of these series, that if any two indices be added together, their sums will be the index of that number which is equal to the product of the two terms, in the geometric progression, to which those indices belong.

Thus, the indices 2 and 3, being added together are = 5, and the numbers and 8, the terms corresponding with those indices being multiplied together, are 32, which is also the number answering to the index 5.

And, in like manner, if any one index be subtracted from another, the difference will be the index of that number, which is equal to the quotient of the two terms to which those indices belong.

. )

Thus, the index 5, minus the index 2, is 3 ; which is the index of the numbe 8, the quotient obtained by dividing the term 32, corresponding to the index by the term 4, corresponding to the index 2.

In order to illustrate our subject the better, we shall take the geometric •eric* 1, 10, 100, 1000, etc., as our criterion, by which the reader will be ena bfod to comprehend more easily the immense advantage derived from this! admirable invention.

Let 10 be called 10', 100 = 103, 1000 = 10s, 10,000 = 10', and so on, the indices or logarithms being always subjoined to the number 10, the basis, to] indicate the number of zeros which otherwise are to be affixed to 1, in Older to express the several values in the geometrical progression ; it will be manifest that if 10' be multiplied by 104, the product will be 105; namely, its] index trill equal the sum of the indices of the two factors. Or, in like man- ner, if 10* be multiplied by 10s, their product will also be 10', equal to 103+8, Whence we infer that multiplication and division are respectively reduced tc addition and subtraction, and consequently, the raising of powers and extract- ing of roots, to multiplication and division.

From all that has hitherto been said, we may conclude, that, instead; of multiplying any two or more terms of a given geometrical series, by one another, in the common arithmetical way, we have simply to add together the indices of the two or more factors, and the sum will indicate that term in th< series which will answer to the required product. The question now becomes | how are we to act with the intermediate numbers, the indices to which are to be readily found in the corresponding arithmetical series ? Here the subj( becomes rather complicated ; and, we may justly say, it is this which entit the grand inventor to endless praise and merit

We shall now point out the method which Napier employed in constructh logarithms for the intermediate numbers. After he had applied the geometric eeriea, 1, 10, 100, 1000, 10000, etc., to the arithmetical series, 1, 2, 3, 4, as rithnu, he had to find a geometric mean between 1 and 10, 10 and 100, or an] other two adjacent terms of the series between which the number proposed lied

-Between the mean thus found, and the nearest extreme, he had to fine]

another geometrical mean, in the same manner, and so on, till he had arrivec

within the proposed limit of the number whose logarithm was sought. 3.— He

iltimately had to find as many arithmetical means in the same order that hi

we geometrical ones, — and the last of this was the logarithm answering

to the Dumber required.

fTeeBijifii.— According to the above method, let it be required to find tin of 9.

Here the numbers between which 9 lies are 1 and 10.

FfaH, then— the log. of 10 is 1, and the log. of 1 is 0; therefore, ^" = °'<

( V. >

b the arithmetical mean, and V (1 X 10) = V 10 = 3-1622777 = geometrical [mean, whence the logarithm of 3-1622777 is 0-5.

Secondly— the log. of 10 is 1, and the log. of 3-1622777 is 0-5 ; therefore, L? = 0-75=i arithmetical mean, and V (10 X 3-1622777) = 5-6234132 is 0-75.

Thirdly— the log. of 10 is 1, and the log. of 5-6234132 is 0-75; therefore, L+07_5 _ 0.875 _ arithmetical mean, and V (10X5-6234132) = 7-4989421 = Geometrical mean; whence the log of 7-4989421 is 0-875.

Lastly, if we proceed in like manner with as many processes, till we obtain m arithmetical mean sufficiently near to 9, the ultimate geometrical mean is its ogarithm.

The results of this extraordinary idea were first published by the original inventor, the Lord Napier himself, at Edinburgh, 1614, under the title of MirificusLogarithmorum Canon, which contains a table of natural and logarithmic dnes for ever}' minute of the quadrant. He died the 3rd of April, 1618.

"Whereas it was at his choice to give the logarithm 0, to any number he >leased, whether to proceed by way of increase or decrease, he chose to make 0 the logarithm of the whole sine 10,000,000 so that the multiplication or division >y the whole sine — frequent in trigonometrical calculations — might be dis- mtched by mere inspection, requiring only the addition or subtraction of 0.

Henry Briggs, a contemporary of Napier, on consulting the original inven- tor, introduced a different system of Logarithms, to which he gave 10 as the )asis, agreeably with our current numeration, by which system the number of ilaces of any natural number, can easily be ascertained by the index or charac- .eristic of its corresponding logarithm ; thus, log. 3'OGOO . . , represents the lumber 1000 = 103, having three zeros annexed to 1 ; log. 4-000 . . . repre- ents 10000 = 10«, having four zeros : or log. 3/, (/, denoting the fractions ubjoined to the characteristic) indicates a number lying between 1000 and 0000 ; log. 4 /, expresses a number that is contained between 10,000 and 00,000 ; and so on, whilst this advantage could not be derived from Napier's jr any other system. From this motive, our common logarithms, also having 0 as their basis, are called Briggs' logarithms, for, it is by him that they were rst introduced.

Mr. Briggs originally calculated logarithms with 14 decimals, to 31 chiliads f absolute numbers, from 1 to 20,000, and from 90,000 to 101,000; preceded >y an extensive discourse on the nature, properties, and the use of logarithms, published (London 1624) under the title of Arithmetical Logarithmica. Adrian Vlacq, a native of Holland, completed the great gap of 70 chiliads vhich Briggs omitted, and among others, he calculated logarithms, with ten lecimals, to sines, tangents, and secants, for every minute of the quadrant. His grand tables appeared at Gouda, 1628.

About the beginning of the last century, when the use of logarithms had

in all branches of mathematics, and the scarcity of Briggs' an Vlacq's tablet had begun to be felt, Mr. Sherwin published (London 1724) al table of logarithms, with seven decimals, to all numbers from 1 to 101,000, the] jfr^ tangents, and secants, preceded by a discourse on the construction of logft^ and in which he compares the several methods as were employed by Drs. j Wallis, Halley, and Mr. Sharp. The first two editions having been exhausted, j Mr. Gardiner published a third edition of the same (London 1742) ; and in order to supply the want of Vlacq's tables, which had become rare, he published in the same year his grand tables in 4to, in which the logs, of the sines are ni|ii«s<iil with seven decimals, for every ten seconds of the quadrant: these tables are now also rare like those of Vlacq.

John Aubert, a native of France, in the year 1770, published a new edition. of Gardiner's tables, in grand 4to. ; this edition was revised by M. Pezenas ; the principal augmentation that may be remarked therein, consists of the logarithmic . sines from second to second for the first four degrees, calculated by M. Mouton, and communicated to M. Pezenas by M. Lalande. This edition, though well executed and more complete than that published at London, is inferior in its correctness.

At the suggestion of astronomers, and more particularly at that of mariners, to whom the utility of Gardiner's tables was indispensable, but very incom- modious as regards size, M. Didot, was induced to publish a new edition of the same in a portable size, Paris, 1783. Another edition, more correct than the preceding one, was published by the same, from stereotype, 1789.

In 1795 another edition of logarithms appeared by the above, edited by F. Callet, in which the logs, with seven decimals, (from 1 to 1200, and fro: 100,000 to 108,000, with eight decimals), are given, from 1 to 108,000, the number of seconds contained in an arch of thirty degrees ; 2. The vulgar and hyperbolic (Napier's) logarithms, with twenty decimals, for all numbers from 1 to 1200, and from 100,000 to 101,180; 3. The same, with sixty-one decimal*, for numbers from 1 to 1097 ; 4. Anti-Logarithms or natural numbers, »iih twenty decimals to vulgar and hyperbolic logarithms from -00001 to -00180; and a variety of similar tables, which, though rarely, maybe found serviceable.

The astronomical part of Callet's tables, is furnished with logarithms to •my second for the first five degrees, and from thence for every ten seconds for the remaining pert of the quadrant These tables may truly be said to be the most perfect and most convenient of the kind : they are repeatedly re- ariaUd from time to time according to demand.

Tfce principal tablet of logarithms next to those already mentioned, deserv- taf notice on account of their extent and accuracy, are the following :—

Vega's Tattsf of logarithm*, in folio, Leipzic, 1794,— the basis of which was the table of fTsoy, as printed at Gouda, as early as 1628 ;— and Vega's Octavo

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(vii. )

Logarithms, Leipsic 1797, with an additional table of prime numbers, and a variety of astronomical tables, etc. These tables are the best and completest extant.

Hutton's Mathematical Tables, containing common, hyperbolic, logistic logarithms, etc., and much valuable information respecting the history of loga- rithms and other branches of mathematics connected with them.

Taylor's Tables of Logarithmic Sines and Tangents for every secondof the quadrant, in a large 4to. volume ; to which is prefixed an introduction by Dr. Maskelyne, and a table of logarithms from 1 to 100,000, etc. This is a most valuable work.

Babbage's Tables of Logarithms, which probably are the most accurate of all : for, by the aid of his ingenious calculating machine, he was enabled to detect a variety of errors in former tables. But what is rather amusing, — on examining a set of tables in the Chinese characters, and which, like every Chinese inven- tion, were older than the deluge, Mr. Babbage found they contained precisely the same errors as those of Vlacq did ; thus proving, as had long been suspected, from what source those original inventors had derived their logarithms.

There are various smaller sets of tables, which, indeed, are too numerous to be catalogued here. It will suffice to say, that care must be taken to choose such tables, whose figures are distinct — rather the ancient figures — and particu- larly that that line of figures in which a change of the three or more leading figures takes place, be sufficiently marked, so as to enable the computer to avoid errors, which he cannot escape in the absence of such. It is for this reason that some prefer to use Callet's Tables, for, there, all logarithms changing by 1 in the third or fourth place, are separated by a blank line from the preceding logarithms, — though others might object to the typographical appearance thereof.

There is, however, in all tables of logarithms to seven places, without excep- tion, one principal defect, to which no remedy has as yet been procured. Since a table of logarithms to numbers of five places requires 200 pages, allowing 500 logarithmic values in a page, a similar table to numbers of seven places, therefore, would necessarily require 20,000 pages, — too voluminous to be brought into practice ; consequently, in order to find logarithms to seven places of numbers, it is requisite to consult the proportional parts of the tabular differ- ences, which are generally observed at the side of each column, given for this purpose. Now, as these auxiliary tables furnish only with tenths parts of the tabular differences, sufficient to obtain in the numbers a sixth place only, it is obvious that, to obtain a seventh place, a second entry in the same auxiliary table is necessary. This process is both troublesome, and at the same time attended with considerable risk of error, which, in a series of operations, is likelv to follow.

( viii.)

the finding of seven places in numbers is more requisite than the _ of seven places in logarithms, must be indisputable to all; since the former expresses the required value in nature, whilst the latter merely expresses its character, by which the working of the computer is facilitated. For, in all logarithmic calculations, the ultimate results must finally be re-converted into natural numbers, with which the computer originally started. It is therefore manifest, that the easier two extra places of numbers be obtained, the more valuable becomes the working by logarithms.

This defect, indeed, has long been felt ; and actually a table of natural numbers (undoubtedly to seven or more places) answering to all logarithms from 1 to 100,000, or rather from -00001 to 0-99999, following in natural order, under the title of Anti-Logarithmic Canon, was prepared, about 1620-30,— so that a number might be found readily by inspection, in the same manner as logarithms are found to numbers, — yet it was never published ; as will be seen from the following extract made of Dr. Wallis' Works, Vol. II. " But," says he, * there seems to be wanting one thing, for the more convenient use of the loga- rithmic canon ; since, in the common logarithmic canon for numbers in a continued order from 1 to 100,000, though the logarithms are found there by inspection only, yet it is not with the same facility that a number corresponding to a given logarithm is found : in that case, the next logarithms on both sides, and their numbers, must be taken, and the intermediate number corrected by a proportional part, in order to find the number required.

" That the inconveniency may be remedied, an Anti-Logarithmic Canon, is wanting, in which the logarithms being put in a continual order from 0 to 100,000, and their corresponding numbers put down answering to each ; so that the number to a given logarithm is had by this Anti-Logarithmic Canon, with the same facility that the logarithm to a given number is had by the common

•

"And, indeed, we have had this canon formed many years ago, but not yet lished. I am not sure but that it was Mr. Thomas Harriot that began to calculate that canon ; for his papers came into the hands of Mr. Walter Warner, who, from those published the Algebra in the year 1631 ; and the same Mr. Warner soon afterwards, (if he was not the first who begun it,) finished that on, and prepared it for the press about fifty years ago, if not more : this I iformcd of by Dr. Pell, who was familiarly acquainted with Mr. Warner, ttafated him in pan of the calculation. I remember I saw that work, (and only taw it) amongst some of Harriot's or Warner's Papers, now above « ago. I knew not what became of them afterwards, until lately I was I again by Dr. Pell, that they were in the hands of Dr. Busby, and he hopes likewise that they should soon be made public, and that by his caw (Dr. Pall,) especially, if I would, (which I readily consented to) promise to

(be.)

see the work finished, in case he should die before it was done. But Dr. Pell died, very old, in the year 1685 ; and the printing of the canon, not as much as begun : and I fear, lest by Dr. Busby's death, the whole will be laid aside; especially as there is no one that will defray the expenses of the edition."

The next that has anything relating to tables of this kind, is Mr. Long, Fellow of Corpus Christi College, Oxford, who in the Philosophical Transactions No. 339, A. 1714, has given a small table for finding the logarithm of any num- ber proposed ; and vice versa, which indeed is a very short specimen, only of seventy-two logarithms. (This account relating to Anti-Logarithms, has been copied from Dodson's Anti-Logarithmic Canon.)

James Dodson, animated with a desire of seeing a similar table done, under- took and completed this laborious task, and in the year 1742 (the year of Gardiner's publication) he printed, in folio, his Anti-Logarithmic Canon, with eleven places of decimals in the natural numbers, answering to logarithms of five places, namely, from -00001 to -99999.

Since no human invention can, by the first experiment, be expected to be carried to perfection, it is not surprising that room was yet left for improvement. Any one acquainted with the nature and arrangement of Dodson's Anti-Loga- rithmic Canon, must at once acknowledge that it is unavailable. As a proof thereof, we venture to state that, to our best knowledge, none has as yet made mention of the numberless errors found therein, in addition to those which the author himself has corrected with his own hand, as will be demonstrated here- after,—which shews that the work has never been brought into practical use. In the first place, the natural numbers therein are given to 11 places, which necessarily require at least a quarto page in width ; and as he introduced also the tabular differences close below each number respectively, thus double the number of lines in each page; he consequently, found it suitable, according to his own notion, to place 200 lines in every three pages, — giving in fact, results to 1000 logarithms only, which, in modern tables, are con- veniently found in two pages — 50 of every 100 being constantly given on page b, and 50 more on the opposite page a, without variation. This circumstance renders his table at once inconvenient, both in size and arrangement; for, the eye frequently is dazzled with the appearance of two sets of figures, opposite one argument. In addition to these double lines, the table of proportional parts is placed at the foot of each page, and thus, the table growing in depth according as the variety of tabular differences grows in the course of the natural numbers, makes the depth of the pages increase, the further they are off from the beginning of the table (contrary to the order of ordinary logarithmic tables;) for which reason, the author was compelled to print his table in folio. — Secondly. The proportional parts in his table are likewise defective, in the same manner as are those of all modern tables, as mentioned above, inasmuch as they are

(*•)

only of ttnth* of the tabular differences ; wherefore, his table can- not be admitted as a sufficient substitute for the ordinary logarithmic tables ; •foot, to find incerstly a logarithm to a certain number, would also require a doable entry in the auxiliary table of proportional parts, thus rendered more difficult than by ordinary tables, where such may readily be found by mere in- spection. Thirdly, the leading figures, as are generally and justly given in ordi- nary tables to ikrtt places, are given in his table to four places, which begin to vary rapidly in the course of the table : and in order to make a distinction at the point of their changing, three dots thus v are placed under each number with which the change commences, leaving all the remaining numbers in the tame line to depend upon that only mark, a sufficient opportunity to commit an error, particularly in the latter part of the table, where such marks are naturally distributed in almost every line, and rather than to caution the com- pater against an error, cause more confusion to his eye.

All these imperfections having come under our notice, it is hardly necessary to £ive an additional motive for our present undertaking. All such obstacles, w» 'jare endeavoured to remove from our table.

Pint, in every page, as in most of the ordinary tables, are contained 500 results, which being distributed in ten columns, form fifty lines in depth, so that the first fifty of every hundred in each four places of the argument, are placed on page 6, facing the second fifty results on page a. The natural numbers go to to the nearest unit efficient for all intricate calculations ; and the last figure was an mweased 5, in consequence of the 8th place having been 5, or above 5, it has been printed with a Roman v, so that in case the seven places of number are required to be reduced to six places, such 6 is to be rejected. It has been done so with 5 only, as it is this figure alone, that makes such reduction uncertain ; we therefore, consider, the int«2* dofltion of marks, in Mr. Babbage's tables, to all last figures if incre//ind, Uft

flafMitfy, the tabular differences are proportionally divided into himdredths of parts, also to the nearest unit, and equally arranged into twice fifty lines corresponding to the other lines of the page ; so that by one single entry into thk auxiliary table, the computer is enabled to find the portion that is to be ^ to a number, if required to answer to a logarithm of seven places, and vice 11>eae tables, as well as the headings of their respective columns, have one or two leading figures, which must be subjoined to their respective and at the point of their changing, the unit is marked with two dots it, to signify that to such unit, the next leading figures are to be taken. «iw mlaane of these tables are easily ascertained, by subtracting the tabular '"l •*** otbar. There are some other trivial improvements which wi?) be obrioos to the ttunpilef when using the table. As to its size and typogrx-

(xi. )

phical appearance in general, we need hardly speak ; the ancient figures have been cast anew for the purpose of this work, on account of their neatness and distinctness, so much preferable to the modern figures, of which the figures 6, 9, and 0, or 3 and 8, resemble each other so much in their appearance, that any one is apt to err in consequence.

Some examples of the use and application of this table may not be super- fluous. To all logarithms consisting of five places of decimals, the numbers to seven places are readily found by mere inspection ; but, if the given logarithm consist also of seven places, namely, two more than in the table, which can be no others than from 1 to 99, they must be found in column D of the propor- tional parts, and the portion answering to them opposite, in either of the columns of the tabular difference, must be added to the tabular number.

EXAMPLES.

I. It is required to find the number to seven places, to log. '35684,63. To the number 2274259 —log. -35684 (page 73), add 33, as found in column 3 (53) of the tabular differences, opposite the two extra figures 63, the sum 2274292 is the number required.

II. To the number 4548976 find its corresponding logarithm to seven places. The next smaller number in the table is 4548938, which answers to the logarithm '65791 ; the unit of the tabular difference of the next smaller and the next greater numbers, is 5 ; the difference of the next smaller number and the one given, is 38, which, in column 5 of the proportional parts, has 36 as its corresponding value in col. D ; affix the same to the loga- rithm previously found, and these seven figures 6579136, form the logarithm required.

ILL To log. 2-3564896, find the number. The number answering to log. -35648 is 2272375; the unit of the tabular difference is 2, add 50 to the number found, as given in col. 2 (52) opposite 96 of col. D, the sum 2272425 is the number sought ; and since the index of the logarithm is 2-, the number must be written thus : • 227-2425.

IV. Required to find the sum of two numbers corresponding to log. 1-45896, and log. 3'49547. The number to log. -45896=2877133, that of log. -49547 = 3129464 ; consequently, as the former has 1 as its characteristic, and the latter 3, their respective numbers must be written thus : 28-77133, 3129-464; their sum, therefore, is 3158-235.

V. Log. 1-56794 and 2-23495 being given, to find the difference of their numbers. The number of log. -56794 = 3697771, that of log. '23495 = 1717711; now, as the characteristic of the one logarithm is minus 1, and that

(xii.)

of the Moond, pirn* 2, their numbers must be written thus : -3697771 and 171-7711 ; their difference, therefore, is = 171-4013.

Hot*.— In all CMC* where the index is plus, the figures to be separated as whole number*, mu»t be one mart than the index ; and if minus, they must be one less, than the index. Indeed, the terms pha and minus sufficiently indicate this change.

VI. To find mean proportional* between any two numbers. Subtract the logarithm of the least term from the logarithm of the greatest, and divide the remainder by a number more by one than the number of means desired; then add the quotient to the logarithm of the least term (or subtract it from the logarithm of the greatest) continually, and it will give the logarithms of all die mean proportionals required.

Let three mean proportionals be sought, between 106 and 100.

Log. of 106 = 2-0253059 Log. of 100 = 2-0000000

Divide by 4) <M)253059 (0-0063264-75

100 added 200000-00

101-4673846 2-0063264-75

102-9563014 2-0126529-5

104-4670483 2-0189794-25

106-0000000 2-0253059

Log. of the least term Log. of the 1st mean Log. of the 2nd mean Log. of the 3rd mean Log. of the greatest mean

As it is not our intention here, to enter into the extensive knowledge of mathematics, but merely to supply the mathematician and astronomer with a convenient instrument, which may ease his mental labour, and at the same time enable him to attain his object in less time, we confine ourselves to the above few examples, which, we trust, will be sufficient to indicate the application of t table. And as for the entire study and utility of logarithms in general, we

t refer the reader to such works, as may treat exclusively on this subject.

The following is a list of errors as detected, by means of our table, in the •rst 8 placet of Dodson's Anti-Logarithmic Canon, in addition to those corrected with the author's own hand.

il

US] •,

•10706

•II

toaif

For

10795128 11224853 11603576 11834591 ISWMN 11796139 15240176 15832U3 16149554

Read 10795182 11224835 11603526 11834502 12579691 12796169 15240176 15832153 16149534 ItMMM

Log. •30488 •32995 •33338 •33339 •33453 •36043 •41164 •41584 •41799 •42019

For

20178187 21377659 21546562 21547058 21603392 22931569 25801265 26051735 26181237 26314129

Read 20178087 21377159 21546662 21547158 21603792 22931369 25801205 26051935 26181227 26314189

Lay.

•42084 •43161 •58643 •62163 •66088 •67461 •68088 •75472

For

26356303 27015512 38586621 41843992 45801513 47272855 47960081 56849629

Read 26356603 27015312 38586021 41843692 45801531 47272655 47960091 56848629

Log. •78737 •78955 •78956 •78957 •78958 79089 •91679 •91845

For

61289230 61595743 61597162 61598580 61599998 61785088 82563962 82880649

Read 61287230 61595643 61597062 61598480 61599898 61785988 82563862 82880049

OF TABLE H.

By means of this table, the working of various calculations, principally in trigonometry and astronomy, is materially abridged. Especially in such equations as have the sign of plus or ?nmus, combined with those of multi- plication and division, when the mode of solving them is intricate and much complicated. This table, originally constructed by Professor GAUSS, of Gottingen, in Germany, was first published by Mr. Von Zach, in his Monthly Correspondence, part XXVI., of the year 1812, to five places of decimals. It gives logarithms to the differences of logarithms, that is to say, by the difference of two logarithms answering to a and b, another logarithm may be found in the table, which, if added to the less logarithm of the two, is either the logarithm of a -j- b, or of a — b j as will be shown hereafter. In other words, since, a + b = a (1 -f ~), and a — b = a (1 — |), this table may be con- sidered to contain the double logarithms of the tangents, co-secants, and secants of the angles from 45° to 90° . For, as the tangent to the secant bears the same proportion, as does the radius to the co-secant, it follows that the co-secant is equal to 1 (i-±-*) = (L±J) — log. (1 + 6) -f co-log, a. (1, denotes the radius, which is assumed to be = 1 j b = secant — radius ; a = tangent. These signs have been preferred here, to give them resemblance to the former expression.)

In introducing this table to the public, the author says : " The object of this table is to facilitate the processesof a variety of calculations of frequent occurrence in astronomy ; for, in lieu of a triple or at least a double entry in the ordinary tables of logarithms, the same results may be obtained by one single inspection in this table. This idea, according to my knowledge, originated from LEONELLI ; yet, as his design was to compute such a table to fourteen places of decimals, it appeared to me inappropriate. It would be desirable, that a similar table of a tenfold or a hundredfold extent, to seven places of decimals, be constructed, which, indeed, might be considered as a valuable supplement, if appended to the ordinary tables of logarithms."

This table may also successfully be applied in calculating annuities, and instead of converting the logarithm of a certain annuity into a number, and then adding one to the results, before another annuity can be obtained, we

this differential table, where, by mere inspection, we readily find the logarithm of the required annuity.

Gauss' table consists of three columns headed respectively A, B, C. The first goes from <M) to 2-0 to three places, from 2-0 to 3-4 to two places, and from 3*4 to 5-0 to one place of decimals. Supposing the first column A to be = log. *, then the column B =log. (1 +;•), and column C = log. (1 + ro), so that C always equals A + B. The application of them is as follows :

L To fad ike logarithm of the sum of two quantities, a, b, whose logarithms

<;-<• <;i ' f, .

Let a denote the greater logarithm ; then enter column A with the differ- of the two logarithms, and take its corresponding logarithm either of the id column B, or of the 3rd column C. Then, Log. (a + 6) = log. a 4- JJ; or, log. (a + 6)= log. 6 + C.

tt To find the logarithm of the difference of two quantities whose logarithms

Here the method of solution depends upon the value of the difference of the two logarithms: if it be greater than 0-30103, it must be sought for in column C, whereby it is obtained :

Log. (a — 6) = log.a — B; or, log. (a — b} =log. b + A. And if the difference be under 0-30103, it must be looked for in column B, whereby

Log. (a — 6) =log. a — C; or, log. (a — b) = log. b — A.

Hence it follows : that there are two methods for the case of log. (a -f- 6), and f*ar methods for the case of (a — 6). Although each two methods might be reduced to one, there still remain three methods which are unavoidable. In- deed, the two methods for (a — 6), differ so materially, that great caution is required to escape an error.

A similar table to the above, has been recomputed to seven places, by E. A. Matthiessen, and published in the year 1817, at Altona. Another table of this description to six places, was published this year by Peter Gray, of In this latter publication, the whole table of Gauss has been remo- In the first place, the column headed log. x, answering to column A in that of Gauss, goes only to 2*0 altogether, consequently, confined to such two numbers, whose difference must not exceed 100. Secondly, it has been divided into two separate tablet, the one intended for (a -f 6) and (a — 6), and tbt other for (a — 6) only, by which re-arrangement was gained nothing. Instead of reducing the three methods of Gauss to two, they were left unaltered ; the ptouass by nAtroctton not being avoided. Nor has there been removed the obstacle which, in the application of his table, will occasionally cause an r, as In that of Gauss ; especially where the ratio of a to b approaches a

(XT.)

ratio of equality, namely, where the difference of the two given logarithms is near 0-30103, as was mentioned above. The author himself, page 11 of his work, after giving three methods for the case of (a — b) alone, says : " We have thus three modes of solution of Problem II. (alluding to the case of a — b ;) but all are not applicable throughout the same limits. That is to say, in many of the cases that arise in practice, some one or more of the methods may not admit of being applied, in consequence of the argument being beyond the limits of the series in which, in the use of those methods, it has to be sought. The second method applies to all the cases to which the first applies ; and it is generally to be preferred, as being at least as correct as the others, and also somewhat easier. The results of the third method, where it alone is applicable, namely, towards the commencement of the table, where the ratio of a to 6 approaches a ratio of equality, must be used with caution. The deviation from the truth, in the results arising from the inverse use of that part of the table, will often be very considerable."

To remedy this great inconvenience, an entirely new arrangement of the above table has been introduced, by which the three modes of solution for both cases of (a -f- 6) and (a — b} are reduced to ttuo only, and both, without ex- ception, are effected by addition. These two methods form, throughout the table, the headings of each page, so that whenever there is occasion to consult them, they are constantly at sight. In both cases the less logarithm of the two must be subtracted from the greater, and, in case of (a -{- &), the difference is to be sought directly in col. A, and its corresponding logarithm added to the less logarithm; whilst in case of (a — b ), that difference is to be sought in- versely among the tabular logarithms, and its corresponding value, in col. A, must likewise be added to the less logarithm. In fact, these two methods may be considered as only one, their only difference consisting in the last term, which, in the former case, is X A, signifying either of the logarithms correspond- ing to column A ; and in the latter, it is A X, meaning the reversed application of the table ; namely, the value of column A answering to either of the tabular loga- rithms. The condition made in the former tables, namely, if the difference of the two logarithms be above or below 0-30103, is entirely removed from our table. The use and application of this table, more clearly demonstrated, will be found in page 202, close to its commencement. It must be remembered that all logarithms of this Table II., are placed perpendicularly, to be read down- wards instead of the horizontal reading, as is the case in ordinary tables as well as in Table I. of our own. This too, cannot be considered as a disadvan- tage to the computer, inasmuch as it affords facility in solving the case of (a — bj. Indeed, if such arrangement could conveniently be introduced in all ordinary tables, they would by far have surpassed those with the present mode of arrangement ; as it is always easier to compare one set of tabulated figures

with the next following, if arranged perpendicularly, than in a horizontal direction. And instead of placing the leading figures in a horizontal line, we placed them in our table, at the top and bottom of each column, another slight advantage which ia felt on perceiving the mark that hints to a change in the leading figures, which in that case, those of the top differ in 1 from those at the foot of the column. We have especially introduced this new arrangement in Table IL, on account of the many differences occurring in the greater part of itt pages, and which accordingly are tabulated on each page with their proportional parts, as they run. From this very motive, several of its pages have been halved, in order to place their corresponding tabular differences into the same pages, also to hundredths of parts. There is another advantage ofiered by our table, not to be derived from similar tables extant, as it extends to the index 4, withyJtv decimals, thus serviceable to solve all problems in which the difference of the two numbers answering to the two given logarithms does not exceed 10,000=10*.

Wilton Street, Fintbury, Ilk December, 1849.

TABLE

OF

ANTI-LOGARITHMS;

OR

NATURAL NUMBERS,

TO SEVEN PLACES OF DECIMALS,

OF ALL LOGARITHMS,

FROM -00001, TO -99999.

Ltf. '00000— '00490.

<*>

Num. 100.0000—101.15


1 !•<>*	0	1	a						8	9	D	23
0000	100 0000	ooz-	0046	0069	009	0115	0138	0161	0184	020	oo	0 0
0001	0210	0251	0276	0299	032	0345	0368	0392	04. i v	043 H	0	o
ooos		0484	0507	0530	<>55	0576	0599	0622	0649	ooo	02	0
0003 0004	069! 0921	0714 094*	0737 0968	0760 0991	078 101	0806 1037	0829 1060	fcl	0875 I KM	089 112	03	I
0005	1152	"75	1198	1221	i*44	1267	1290	131	1336	135	05	I
0006	1383	uoi	1429	1452		1498	1521	1544	1567	'59	• 06	I
0007	1613	1636	1659	1682	1705	17*8	1751	177	1798	182	07	2
0008	1844	1867	1890	1913	1936	'959	1982	200	2028	205	08	2
:0009		2098	2111	2144	2167	2190	2*13	2236	2259	228	09	2
0010 001 1 1 0012	too 2305 2536 2767	1318 *559 2790	2351 2582 2813	2605 2836	2398 2628 2859	2421 2651 2882	2444 2&7V 2905	246 269 2929	2490 272 95	251 2744 297V	o	2 3 3
0013	2998	3021	3044	3067	3090	3"3	3136	3160	3183	320	\	3
0014	3229	35	3*75	3298	33*'	3344	3367	339	34H	343	4	3
0015	3460	3483	3506	35*9	355*	3575	3598	3622	364v	3668	15	3
0016 0017	3691 39**	37 14 3945		3760 3991	3783 40iv	3806 4038	3830 4061	til	3876 4107	3899 4*3°	16 17	4 4
' 0018	4'53	4176	4199	4223	4246	4269	49	43*5	4338	436	18	4
0019	4384	4408	443 «	4454	4477	4500	45*3	4546	4570	4593	19	4
0020	too 4616	4639	4662	4685	4708	473 *	475v	4778	4801	48*4	20	5
002)	4847		4893	4917	4940	4963	4986	5009	5032	5055	21	5
0022	5079	5102	5I2V	5148	5171	5J9-i	5*17	5241	5*6^	5*87	22	5
0023	5310	5333	5356	5379	5403	54*6	5449	547*	5495	5518	*3
0024	554*	556v	5588	56n	5634	5657	5680		57*7	5750	24	6
0025	5773	5796	5819	5843	5866	5889	5912	5935	5958	5982	*5	6
••si	6oov	6028	6051	6074	6097	)I2I	6144	6167	6190	6213	26	6
0027	6236	>26o	6283	6306	6329	6352	6375	6399	6422	644v	27	6 (
••si	6468	6491	6514		6561	6584	6607	6630	6653	6677	28	6 •
0029	6700	6723	6746	6769	6793	68l6	6839	6862	6885	6908	,*9
0030	oo 6932	695v	6978	7001	7024	7048	7071	7094	7117	7140	30
0031	7164	7if7	7210	7*33	7256	7280	73°3	73*6	7349	737*	3*
•••s 0033	7395 7627	7419 7651	744* 7674	7465 7697	7488 77*o	75" 7743	753v 7767	7558 7790	7581 7813	7604 7836	3* 33
0034	7860	7883	7906	79*9	795*	7976	7999	8022	8045	8068	34
0035 •••\| •••) N II	8092 87588 9021	8uv {J47 S >~9 8811	8138 8370 8602 883v 9067	8161 8393 8626 8858 9090	8184 8417 8649 8881 9113	8208 440 672 904 137	8231 8463 8695 8928 9160	8*54 8486 8719 8951 9183	877 8510 874 8974 9206	5301 8533 8997 9*3°	35 36 37 38 39
0040 0041 ••41 ••41 0044	01 0183	9176 95<>9 974» sa	999 953 9764 9997 0129	93*3 9555 v-xx 0020 0253	9346 9S78 9811 6043 0276	& aj 299	939* 9857 6090 0322	9416 9648 9881 6113 0346	9439 9671 9904 0136 0369	9462 169? 99*7 >i6o 0392	40 4* 43 44	o
0045 ••41 '"•47 ••41	as 0881 1)49	an 0904 »»J7 l$70	0462 069, 0927 1160 Iff]	0485 0718 095, 1184 I4l6	0509 c-4i 1207 1440	53* 76v 997 230 463	°555 0788 1021 \in	0578 0811 1044 1*77 1510	0602 0834 067 300 533	062V 0858 1090 1323 1556	-7 48 49	o I I
Lo*. — — —	0 — — -	1	a	3	4	S •	e	7'	8	9	D	23

•00500— '00999.

(3)

Num. 101.1579 — 102 '3 26 9.

Log.	0	1	2	3	4	5	6	7	8	9	D	23	4
D050	101 1579	1603	1626	1649	1673	1696	1719	1743	1766	1789	5°	I 2	2
D051	1812	1836	1859	1882	1906	1929	1952	1976	1999	2022	51	2	2
,)052	2045	2069	2092	2115	2139	2162	2185	2209	2232	2255	52	2	2
3053	2278	2302	2325	2348	2372	2495	2418	2442	246 v	2488	53	2	3
)054	2512	253v	2558	2582	26ov	2628	2651	267v	2698	272I	54	2	3
)055	274v	2768	2791	28lV	2838	2861	288v	2908	2931	295v	55	3	3
)056	2978	3001	3O2V	3048	3071	309v	3118	3Hi	3i6v	3188	56	3	3
)057	3211	323v	3258	3281	33ov	3328	335i	337v	3398	3421	57	3	4
)058	344v	3468	3491	35iv	3538	356i	358v	3608	3631	365v	58	3	4
)059	3678	3701	372v	3748	3771	379v	3818	3841	386v	3888	59	4	4
»060	101 3911	393v	3958	3981	40ov	4028	4051	4°7v	4098	4122	60	4	4
(061	4i4v	4168	4192	42 iv	4238	4262	428v	4308	4332	4355	61	4	5
>062	4378	4402	4425	4448	4472	4495	4519	4542	4565	4589	62	4	5
• 063	4612	4635	4659	4682	4705	4729	4752	4776	4799	4822	63	4	5
• 064	4846	4869	4892	4916	4939	4963	4986	5009	5033	5056	64	5	5
065	5079	5^3	5126	5T49	5173	5196	5220	5243	5266	5290	65	5	6
• 066	5313	5337	5360	5383	5407	5430	5453	5477	55°°	5524	66	5	6
'067	5547	557°	5594	5617	5640	5664	5687	5711	5734	5757	67		6
068	578i	5804	5828	5851	5874	5898	592i	594v	5968	5991	68	6	6
069	6oiv	6038	6062	6o8v	6108	6132	6i55	6178	6202	6225	69	6	7
070	01 6249	6272	6295	6319	6342	6366	6389	6413	6436	6459	70	6	7
071	6483	6506	6530	6553	6576	6600	6623	6647	6670	6693	7i	6	7
072	6717	6740	6764	6787	6816*	6834	6857	6881	6904	6928	72	7	7
073	695i	6974	6998	7021	7o4v	7068	7091	7iiv	7x38	7162	73	7	8
074	7185	7209	7232	7255	7279	7302	7326	7349	7373	7396	74	7	8
075	7419	7443	7466	7490	75'3	7537	7560	7583	7607	7630	75	7	8
076	7654	7677	7701	7724	7747	7771	7794	7818	7841	786v	76	7	8
077	7888	7911	793v	7958	7982	8005	8029	8052	8076	8099	77	8	8
078	8122	8146	8169	8i93	8216	8240	8263	8287	8310	8333	78	8	9
079	8357	8380	8404	8427	8451	8474	8498	8521	8544	8568	79	8	9
080	01 8591	86iv	8638	8662	8685	8709	8732	8756	8779	8802	80	8	9
081	8826	8849	8873	8896	8920	8943	8967	8990	9014	9°37	81	9	9
082	9061	9084	9108	9J3!	9X54	9178	9201	922V	9248	9272	82	9	6
083	9295	9319	9342	9366	9389	9413	9436	9460	9483	9507	83	9	6
084	9530	9553	9577	9600	9624	9647	9671	9694	9718	9741	84	9	6
085	976v	9788	9812	9835	9859	9882	9906	9929	9953	9976	85	2 0	0
086	K)2 OOOO	0023	0047	0070	0094	0117	0141	0164	0188	02 1 1	86	0	i
087	02H	0258	0281	O3ov	0328	0352	0375	0399	0422	0446	87	0	i
088	0469	0493	0516	0540	0563	0587	0610	0634	0657	0681	88	0	i
089	0704	0728	0751	077Y	0798	0822	0845	0869	0892	0916	89	0	i
090	02 0939	0963	0987	1010	1034	1057	1081	1104	1128	II5I	9°	I	2
091	II7V	1198	1222	1245	1269	1292	1316	1339	1363	1386	91	I	2
092	1410	H33	H57	1480	1504	1527	i55i	J574	1598	l62I	92	I	2
093	1 64v	1668	1692	1716	J739	1763	1786	1810	1833	1857	93	I	2
094	1880	1904	1927	1951	1974	1998	2021	204V	2068	2092	94	*	3
095	2116	2139	2163	2186	2210	2233	2257	2280	2304	2327	95	2	3
096	2351	2374	2398	2422	2445	2469	2492	2516	2539	2563	96	2	3
097	2586	2610	2633	2657	268l	2704	2728	2751	277v	2798	97	2	3
098	2822	2845	2869	2893	2916	2940	2963	2987	3010	3°34	98	3	4
099	3057	3081	3iov	3128	3152	3175	3'99	3222	3246	3269	99	3	4
,og.	o	1	2	3	4	5	6	7	8	9	D	23	4

Log. -01000— -01499.

CO

Num. 102.3293 — 103.5HJ

-— ' Lo*.		•^•^•1		=^=				7	8	9
oioo 0101 0102 0103	io» 393 359 37*4 4000	33*7 4024	3340 3576 3811 4047	3364 3599 3835 4071	3387 3623 3859 4094	34" 3646 3882 4118	3434 3670 3906 4142	3458 3694 39*9 4165	3482 3717 3953 4189	35°5 3977 4212
0104	£36	4*59	4*83	4307	433°	4354	4377	4401	442v	4448
0105 0106	447* 4708	4495 473*	459 475	4543 4778	4566 4802	459° 4826	4613 4849	4637 4873	4661 4896	4684 4920
0107	4944	4967	499*	5014	5038	5062	5085	5109	5132	5156
0108	» 5180	5203	5227	55	5*74	5*98	53*i	534v	5369	539* £. O
0109		5439	5463	5487	5510	5534	5557	5581	56ov	5628
01 10 Oil 1 0112	loi 5652 5888 6114	5676 591* 6148	5699 5935 6172	57*3 5959 6195	5746 5983 6219	5770 6006 6243	5794 6030 6266	5817 6053 6290	5841 6077 6313	5864 6101 6337
0113 0114	636, 6597	6384 6621	«	mi	6692	6479 6715	6502 6739	6526 6763	6786	6573 6810
0115	6833	6857	6881	6904	6928	6952	6975	6999	7023	7046
01 16	7070	7094	7117	7141	7164	7188	7212	7*35	7*59	7283
01 17	7306	7330	7354	7377	7401	742v	7448	747*	7496	75*9
01 18	7543	7567	759°	7614	7638	7661	768v	7709	773*	7756
01 19	7780	7803	7827	7851	7874	7898	7922	7945	7969	7993
0120	02 8016	8040	8064	8087	8111	8i3v	8158	8182	8206	8229
0121 0122	8253 8490	8*77 8514	{300 8537	83*4 8561	8348 858v	8371 8608	8395 8632	8419 8656	8442 8679	8466 8703
0123		8750	8774	8798	8821	8845	8869	8892	8916	8940
0124	8964	8987	9011	9o3v	9058	9082	9106	9129	9'53	9177
0125	9201	9224	9*48	97	9*95	9319	9343	9366	9390	9414
0126	9438	9461	948v	9509	953*	9556		9603	9627	9651
0127	967*	9698	97**	9746	9769	9793	9817	9841	9864	9888
0128	9912	9935	9959	9983	0007	6030	6054	0078	OIOI	0125
0129	103 0149	o*73	0196	022O	0244	0267	0291	O3iv	0339	0362
0130	103 0386	0410	0434	0457	0481	o5ov	0528	0552	0576	0600
0131	0613	0647	0671	J 069*	0718	0742	0766	0790	0813	0837
0182	0861	0884	0008	nmt	f\f\ rf\		IOO7	IOZ7	IOC I	IO7A
0183	.098	1122	1146	0932 1169	°95° 1193	1217	1241	1264	HJ} 1 1288	1312
0134	• 336	'359	1383	1407	1431	*454	1478	1502	1526	'549
0135	•573	»597	1621	1644	1668	1692	1716	'739	1763	1787
0136	1811	»«34	1858	1882	1906	1929	'953	1977	2001	2024
Olt7	1048	2072	2096	2I2O	2143	2167	2191	22IV	2238	2262
0138	1286	2310	*333	*357	2381	24OV	2429	2452	2476	2500
0139	»S»4	»547	*57«		2619	2643	2666	2690	2714	2738
0140	loj 1761	»7*S	1809	2833	2857	2880	2904	2928	2952	2975
! 0141	»999	3023	3°47	3071	3094	3118	3142	3166	3190	3*'3
	I2 J"	3161	38	3308	333*	3356	3380	3404	34*7	345'
0143	347$	M99	JS*3	3546	3570	3594	3618	3642	3665	3689
0144	37']	3737	3761	37«4	3808	3832	3856	3880	3903	39*7
0145	I9$i	397*	3999	4013	4046	4070	4094	4Il8	4142	4165
0146	4119	4«i3	4*37	4*61	4*84	4308	433*	4356	4380	4404
0147	44*7	44$'	H7 J	•491	45*3	4546	4570	4594	4618	4642
0148 A • M A	4666	V •">	4713	4737	4761	478v	4809	4832	4856	4880
O 1 49	49°4	4918 •t /		4Q7C		CCil -9				• * w O
				•« / ^	•»>»	5°*3	5°47	5071	5094	5115
	0 I	1	2					==	8	9

•01500— '01999.

(5)

Num. 103.5142 — 104.7104,

Log.	0	1	2	3	4	5	6	7	8	9	D	23	i 5
0150	103 5142	5166	5190	5214	5238	526	5285	530	533	535	5o	I 2	2 3
0151	538i	5404	5428	5452	5476	5500	55^4	554	557	559	5		2 3
0152	5619	5643	5667	569	57H	5738	5762	578	5810	583	52		z 3
0153 0154	6096	5881 6120	59°5 6144	5929 6168	5953 619	5977 6215	6001 6239	602^ 626	604! 6287	607 631	53 54		3 3 3 4
9155	653v	6358	6382	6406	6430	6454	6478	6502	6526	654	5		3 4
0156	6573	6597	6621	664v	6669	6693	6716	6740	6764	678	56		3 4
0157	6812	6836	6860	6884	6907	6931	6955	6979	7003	7027	57		\ 4
3158	7051	707v	7098	7122	7146	7170	7194	7218	7242	7266	58		4- 5
)159	7290	7313	7337	7361	7385	7409	7433	7457	7481	75ov	59		4- 5
)160	103 7528	755*	7576	7600	7624	7648	7672	7696	7720	7743	60		4- 5
)16 1 )162	7767 8006	7791 8030	7815 8054	7839 8078	7863 8102	7887 8126	7911 8150	793v 8174	7959 8198	7982 822	6 62	<	M
)163	8245	8269	8293	8317	8341	836v	8389	8413	8437	846	63	t	5 6
)164	8484	8508	853*	8556	8580	8604	8628	8652	8676	8700	£	5	5 6
)165	8724	8748	8771	8795	8819	8843	8867	8891	Sgiv	8939	65	r	6 6
)166	8963	8987	9011	9o3v	9°59	9082	9106	9130	.9J54	9178	66	(	S 7
)167	9202	9226	9250	9274	9298	9322	9346	9370	9394	9417	67	l	S 7
)168	9441	9465	9489	9513	9537	9561	958v	9605	9633	9657	68	(	5 7
)169	9681	97ov	9729	9753	9777	9800	9824	9848	9872	9896	69	6	7 7
H70	103 9920	9944	9968	9992	0016	6040	0064	0088	0112	6136	70	6	7 8
)17 1	104 0160	0184	0208	0231	°*55	0279	0303	0327	0351	0375	72	6 •	7 8
U72	0399	0423	0447	0471	0495	0519	0543	0567	0591	o6iv	72		8
H73	0639	0663	0687	0711	o73v	°7S9	0783	0807	0830	0854	73	7 !	8
>174	0878	0902	0926	0950	0974	0998	1022	1046	1070	109^	74	7 '	9
• 175	1118	1142	1 1 66	1190	1214	1238	1262	1286	1310	1334	75	7	9
•176	1358	1382	1406	1430	"454	1478	1502	1526	'55°	1574	76	7 *	9
177	1598	1622	1646	1670	1694	1718	1742	1766	1790	1814	77	8 i	9
'178	1838	1862	1886	1910	J933	'957	1981	2005	2029	2053	78	8 S	0
179	2077	2101	2125	2149	2173	2197	2221	2245	2269	2293	79	8 S	o
180	04 2317	2341	2365	2389	2413	2437	2461	2485	2509	2533	80	8 S	6
181	2557	258l	2605	2629	2653	z677	2702	2726	2750	2774	81	9 S	0
182	2798	2822	2846	2870	2894	2918	2942	2966	2990	30H	82	9 c	V
i!83	3038	3062	3086	3110	3J34	3158	3182	3206	3230	3254	83	9 c	i'
184	3278	3302	3326	335°	3374	3398	3422	3446	3470	3494	84	9 c	1
185	35i8	3542	3566	359°	3614	3638	3662	3686	3710	3734	85	2 0 C	i
186	3758	3782	3807	3831	385v	879	39°3	39*7	395i	397v	86	0 I	2
187	3999	4023	4047	4071	409v	4119	4M-3	4167	4191	4215	87	0 I	2
188	4239	4263	4287	4311	4335	4359	4383	4408	4432	4456	88	0 I	a
189	4480	4504	4528	455*	4576	4.600	4624	4648	4672	4696	!89	0 I	2
190	04 4720	4744	4768	4792	4816	4841	486v	4889	49J3	4937	90	I 2	3
191	4961	498v	5009	5033	5°57	08 1	5I05	5129	5*53	177	91	I 2	3
192	5201	5226	5250	5274	5298	322	5346	5370	394	418	92	I 2	3
193	544^	5466	5490	5SH	5538	563	5587	56n	63v	659	93	I 2	3
194	5683	5707	573i	5755	5779	803	5827	5851	876	900	94	a 3	4,
195	5924	5948	5972	5996	6020	044	6068	1092	116	140	95	2	*]
196	6i6v	6189	6213	6237	6261	285	6309	6333	357	38i	96	2	4
197	6405	6430	6454	6478	6502	526	6550	6574	598	622	97	2	4
198	6646	6671	669v	6719	6743	767	6791	6815	839	863	98	3 4	f \ 5 i
199	6887	6912	6936	6960	6984	008	7032	056	080	104	99	3 4	5
-og.	0	1	2	3	4	5	6	7	8	9	D	23 4	5

Ix*. «02000— -02499.

(6)

Num. 104.7129 —

												rt A \
Log. 0 '2 0 0 0201	104 7129 737°	7«53 •'94	7177	7201 744»	722V 7466	7*49 749°	7«73 75H	7*97 7539	8 73*i 7563	9 7346 7587	.00 01	z*± c o 0
0202 0203 0204	£ 76ll &	* 7j35 tSU	7659 7900 814*	7683 8166	7707 7949 8190	773' 7973 8214	7756 7997 8238	7780 8021 8262	7804 8045 8287	7828 8069 8311	02 °3 04	0 I I
0205 0206	»}%	!2S	8383 8624	8407 8649	8431 8673	8455 8697	8480 8721	8504 8745	8528 8769	855* 8794	05 06	I I
0207	88l8	8842	8866	8890	8914	8938	8963	8987	9011	9035	07	2
0208	9°59	9083	9108	9132	9156	9180	9204	9228	95	9*77	08	2
0209	9301	932v	9349	9373	9397	9422	9446	9470	9494	9518	°9	2
0210	104 9541	9567	9591	961%-	9639	9663	9687	9712	9736	9760	10	2
0211	9784	9808	9832	9857	9881		99*9	9953	9978	0002	ii	3
0212	IOC 0026	0050	0074	0098	0123	0147	0171	0195	0219	0243	12	3
0213	0268	0292	0316	0340	0364	0389	0413	0437	0461	0485	13	3
0214	0510	0534	0558	0582	0606	0630	o6sv	0679	0703	0727	"4	3
0215	0751	0776	0800	0824	0848	0872	0897	0921	0945	0969	15	4
0216	0993	1018	1042	1066	1090	1114	1139	1163	1187	I2II	16	4
0217	1235	1260	1284	1308	133*	1356	1381	i4Ov	1429	H53	17	4
0218	«478	1502	1526	1550	1574	1S99	1623	1647	1671	1695	18	4
0219	1720	•744	1768	1792	1817	1841	i86v	1889	1913	1938	'9	5
! 0220	105 1962	1986	2010	203V	2059	2083	2107	2!3I	2156	2180	20	5
, 0221	2204	2228	2253	2277	2301	35	2350	*374	2398	2422	21	5
, 0222	2446	2471		2519	*543	2568	59	2616	2640	266v	22
0223	Z689	2713	2737	2762	2786	^810	2834	2858	2883	2907	*3	6
0224	2931	*955	2980	3004	3028	3052	3077	3101	3125	3H9	*4	6
0225	3'74	3198	3222	3246	3271	329v	3319	3343	3368	339*	*5	6
0226	34.6	3440	346v	3489		3538	3562	3586	3610		26	6
0227	3659	3683	3707	373*	3756	3780	3804	38*9	3853	3877	*7	6
0228	3901	3926	3950	3974	3999	4023	4047	4071	4096	4120	28	7
0229	4144	4168	4193	4217	4241	4266	4290	43 H	4338	4363	*9	7
0230	•05 4387	44"	4435	4460	4484	4508	4533	4557	458i	4605	30	7
<»;:j 1	4630	4654	4678	4703	47*7	4751	4775	4goo	4824	4848		7
»S»\|	4873 S'«$	4897 5 '40	49* » 5164	4945 5.88	4970 5213	4994 5*37	5018 5261	5043 5286	5067 5310	5091 5334	32 33	8 8
0234	5358	5383	5407	543»	5456	548o	5504	55*9	5553	5577	34	8
0235	$602	$626	5650	5674	5699	57*3	5747	577*	5796	5820	35	8
0236 0237 0238 023»	ts,i «574	ffi J355 6599	S	5918 6161 6404 6647	594* 6185 6428 6672	5966 6209 6453 6696	5990 6234 6477 6720	6oiv 6258 6501	6039 6282 6526 6769	6063 6307 6550 6793	36 37 38 39	9 9 9 9
0240 0241	105 6818 7061	684* 7085	6866 7110	6891 7«34	7?58	6939 7183	6964 7207	6988 7231	7012 7256	7037 7280	40 41	I 0 0
0242 0243 0244	7304 7S4l 779«	73*9 7$7» 7816	7353 7596 7840	7377 7621 7864	7402 7645 7889	7f6 7670 79»3	745° 7694 7937	747v 7962	7499 7743 7986	75*3 7767 Son	42 43 44	0 o I
0246 0146 0247 ! 0248 O24t	S01' 8179 8766 9010	8059 8303 •547 1790 9°J4	8084 83*7 SB: 9059	8108 & 9083	8132 8376 ilk 8864 9107	8,57 8400 8644 8888 9132	8181 8669 8912 9156	8205 8449 8693 8937 9.8,	8230 8474 8717 8961 920V	854 8498 874 8985 9229	45 46 47 48 49	i 2 !
Log.								7	8	9	D	24 [l

ff. -02500— -02999.

(7)

Num. 105.9254—107.1495,

Log.	0	1	2	3	4	5	6	7	8	9	D	24	5
0250	105 9254	9278	9303	93*7	935i	9376	9400	9424	9449	9473	5°	I 2	•7
0251	9498	95"	9546	957i	9595	9620	9644	9668	9693	9717	51	2	J •7
0252	9742	9766	979°	9815	9839	9864	9888	9912	9937	9961	5*	2	} -J
0253	9986	60 10	0034	0059	0083	0108	6132	0157	6181	0205	53	3	J •7
0254	106 0230	0254	0279	0303	0327	0352	0376	0401	0425	0450	54	j 3	j 4
0255	0474	0498	0523	0547	0572	0596	0620	o64v	0669	0694	55
0256	0718	0743	0767	0791	0816	0840	0865	0889	0914	0938	'56	T
0257	0962	0987	ion	1036	1060	io8v	1109	"33	1158	1182	57	4"	4
0258	1207	1231	1256	1280	1304	1329	J353	1378	1402	1427	58	4"	e
0259	1451	1476	1500	'5*4	1549	'573	1598	1622	1647	1671	159	4	j 5
0260	106 1696	1720	1744	1769	1793	1818	1842	1867	1891	1916	;6o	4"	c
0261	1940	i96v	1989	2013	2038	2062	2087	2III	2136	2160	61	(	J
0262	2i8v	2209	2234	2258	2282	2307	2331	2356	2380	240V	62	<	6
0263	2429	2454	2478	2503	2527	2552	2576	2600	262V	2649	63	c	6
0264	2674	2698	27*3	2747	2772	2796	2821	2845	2870	2894	64	i	6
)265	2919	2943	2968	2992	3016	3041	3065	3090	3"4	3J39	65	6	6
0266	3163	3188	3212	3237	3261	3286	3310	333V	3359	3384	66	6	7
0267	3408	3433	3457	3482	3506	353i	3555	358o	3604	3629	67	6	7
0268	3653	3678	3702	37*7	375i	3776	3800	382v	3849	3874	68	6	7
0269	3898	39*3	3947	3972	3996	4021	4045	4070	4094	4119	69	7	7
0270	106 4143	4168	4192	4217	4241	4266	4290	43 iv	4339	4364	70	7	8
0271	4388	44*3	4437	4462	4486	4511	4535	4560	4584	4609	71	7	8
0272	4633	4658	4682	4707	473i	4756	478o	48ov	4829	4854	7*	7	8
0273	4878	4903	4927	4952	4976	5001	5025	5050	507v	5099	73	8	8
0274	5I24	5148	5173	5'97	5222	5246	5*7i	5*95	53*o	5344	74	g	9
0275	5369	5393	5418	5442	5467	5492	5516	554i	5565	559°	;75	8	9
0276 0277	5614 5860	5639 5884	5663 5909	5688 5933	57i2 5958	5737 5982	5761 6007	5786 6031	5811 6056	5835 6081	:76 77	8 8	9 9
0278	6105	6130	6154	6179	6203	6228	6252	6277	6301	6326	i78	9	6
0279	6351	6375	6400	6424	6449	6473	6498	6522	6547	6572	;79	9	0
0280	ic6 6596	6621	6645	6670	6694	6719	6743	6768	6793	6817	80	9	0
0281	6842	6866	6891	6915	6940	696v	6989	7014	7038	7063	81	9	o
0282	7087	7112	7137	7161	7186	7210	723v	7*59	7*84	73°9	82	2 0	i
0283	7333	7358	7382	7407	743 1	7456	7481	7505	7530	7554	83	0	i
0284	7579	7604	7628	7653	7677	7702	7726	7751	7776	7800	,84	0	i
0285	782v	7849	7874	7899	79*3	7948	7972	7997	8022	8046	85	0	i
0286	8071	8095	8120	8144	8169	8194	8218	8243	8267	8292	86	I	2
0287	8317	8341	8366	8390	8415	8440	8464	8489	8513	8538	87	I	2
0288	8563	8587	8612	8636	8661	8686	8710	873v	8760	8784	88	I	2
0289	8809	8833	8858	8883	8907	8932	8956	8981	9006	9030	;89	I	2
0290	106 905v	9079	9104	9129	9X53	9178	9203	9227	95	9276	9°	2	3
0291	9301	9326	935°	937v	9400	9424	9449	9473	9498	95*3	91	2	3
0292	9547	9572	9597	9621	9646	9670	9695	9720	9744	9769	9*	2	3
0293	9794	9818	9843	9868	9892	9917	9941	9966	9991	6015	93	2	3
0294	07 0040	oo6v	0089	0114	0139	0163	0188	0212	0237	0262	,94	3	4
0295	0286	0311	0336	0360	O3&v	0410	0434	0459	0484	0508	9f	3	4
0296	0533	0558	0582	0607	0631	0656	0681	0705	0730	o75v	196	3	4
0297	0779	0804	0829	0853	0878	0903	0927	0952	0977	1001	9l	3	4
0298	1026	1051	1075	1 100	II2V	1149	1174	1199	1223	1248	98	4	5
0299	1273	1297	1322	1347	I37I	1396	1421	1445	1470	I49v	99	4	5
Log.	0	1	2	3	4	5	6	7	8	9	D	24	5

Lof.'OSOOO— -03499

(8)

Num. 107.1519 — 108.390

1 T .-»									91 «\	s~* *
LOR II 030									1	mm	5 6
107 1519	154^	1560	'591	i6i8\| 164'	166	169	171	17411 1 oo (o o	0 o
1 030	I766	»79	1815	1840	i86v\|i88s	191	'93	196	19881 [oi\| o	0 o
1 030	»or	103^	2063	2087	211212136	216	218	221	22351 I °*	o	I I
1 030	1260	128.)	*3°9	*334	2359(2383	240	243	245	2482! :	i	I I
II 030	»5<>7	*53J	1556	2581	260512630	26*	268	270	2729\| (04	i	I 1
1 030	»754	1778	2803	2828	285212877	290	292	295	2976! (05	i	I I
1 030	3001	3015	3050	3°7V	3100(3124	3 '4	317	3'9	3223! 1 06	i	i 2
1 030	34	37	3*97	33**	33471337'	339	34*	344	3470 1 (07	2	i 2
1 0308 II 0309	349» J74*	35*o 3767	3544 379*	$1	3594h6i9 3841 386	364 389	366 39'	369 394	3717! (08 3y6vl	2 2	1 2 2 2
1 0310	107 3989	4014	4039	4064	4088(411	4'3	416	418	42121 1 10	2	3 3
1 0311	4*37	4261	4286	43"	4336(436	438	44'	443	44591 jjii	3	7 •;
1 0312	44*4	4509	4534	4558	4583(460	463	465	468	4707! I! 12		j j 3 i
1 . ! '	473*	4756		4806	4831 485	488	490	493	49541 1 '3	3	j j 3 3
1 0314	4979	5004	5029	5053	5078(510	512	5'5	5'7	5*oi j 1 14	3 '	1- 4
1 0515	5**7	5*5'	5276	5301	53*6(535	537	540	54-*	54491 1 '5	4 *	(. 4
1 03 1 6	5474	5499	55*4	5549	5573 559	562	564	567	5697\| 1 '6	4 '	L 4
1 031 7	5722	5747	577'	5796	5821 584	587	589	592	594v 1 1 17	4 '	1- 4
1 0318 1 0319	5970 6217	5994 6242	1019 6267	6044 6292	6069(609 6317(634	636	614 639	616 641	5193! 1 18 6440! 1 19	4 5 .	5 5 5 5
II 0320 0321	107 6465 6713	6490 6738	«5«» 6763	6540 6787	6564(6589 6812(6837	6614 6862	663 688	6664 691	66881 1 20 69361 ('21	5 . r	> 5
0322	6961	6986	7011	7035	7060(7085	7110	7'3V	7'59	7184! II 22	j .	6
0323	7209	7*34	7*59	7283	73o8\|7333	7358	738	7408	7431 \|3	6 i	> 6
0324	7457	7482	7507	753*	7556(7581	7606	763	7656	7680! (24! 6 e	6
0325 0326 0327	7705 7953 8202	730 97* 8226	775^ 8003 8251	77*0 8028 8276	78ov\|7829 805318075 8301(8326	7854 8102 8351	7879 {127 8375	7904 8152 8400	7929J *5	6 6 6 7 6 7	7 7 7
0329	8450	847* 8723	8500 74*	5*4 773	8549 8574 8798(8823	8599 8847	8624 8872	8649 8897	i7*5 p	7 7 7 7	7 8
0330 0331 0332 0333 0334	07 8947 9»95 9444 9692 994'	97 9220 9469 97'7 9966	996 24V 493 74* 999'	021 270 5'* 9767 6016	9046(9071 99v \|93 '9 954319568 97919817 6040(0065	9096 9344 9593 9841 0090	9121 9369 9618 9866 0115	9'45 9394 9643 891 140	170! 1 30 ?6v 3"	88 8 8 8 9	8 8 1
0335 0336 0337 0338 \| IV,	of 0190 21° SC	0214 071* 096. 1210	o*39 °737 0986 113^	0264 °5'3 0762 ion 1260	0289(0314 0538 0563 0787(0812 1036(1061 I28v\| 1309	0339 0588 0836 085 334	364 613 861 no 359	886 '35 384	4131 (35 662! I! 36 9"! 37 i6o\| 38 4°9 j 139	8 9 9 9 9 9 9\|o 9 q	1
\|\| to \|\| i ! oil* OKI	"ffl! 1911 nit 1430	»957 II », H55	14X4	1509 »75* 2007 2256 1505	'534 '558 1783(1808 2032 2057 228112306	I83 832 082 33' 580	608 106 356 6ov	633 882	658 40 907! 41 156! (42 406 43 65V\| \|\|44	100 o o 0 I O I I I	i
~ T »713 1981 1231 1480
1141 0-14.	t68o *	170* •954 ju>3 3453 370*	1730 \|47l 37»7	75 3004 353 3503 375	17791804 02913054 178 3303 58 3553 777J3*oa	829 sS 578 8*7	854 104 353 603 852	879 129 378 627 877	904) 1 45 '53 46 °3\| 47 902! J49J	I I I 2 I 2 2 2 2 2	[ 2 2 2 3
' ***	0 =5	i =	a	3	T\| 5	6	7	8	9 \ 1 DJ24 5	6

•03500— '03999.

(9)

Num. 108.3927 — 109.6453.

-og.	0	1	2	3	4	5	6	7	8	9	D	24	5	6
• 350	108 3927	395*	3977	4002	4027	4052	4077	4102	4127	4152	5	I 2	—	—
»351	4*77	4201	4226	4*5 1	4*76	43° i	43*6	43 5 1	4376	4401	c		;
(352	44*6	445 *	4476	4501	45*6		4576	4601	4626	4651	j 5	;	;
>353	4676	4701	47*6	4751	4776	4801	4826	4851	4876	4901	5		;	•
1354	4926	495i	4976	5001	5026	5051	5076	5101	5126	5I51	5		<	• 4
1355	5176	5201	5226	5*5'	5*76	5300	53*5	5350	5375	5400	5			4
)356	54*5	5450	5475	55°°	55*5	5550	5575	5600	56*5	5650	! 5
357	5675	5700	57*5	575°	5775	5800	58*5	5850	5875	5900	5			.
1358	59*5	5950	5975	6000	6025	6050	6075	6100	6l2«	6150	5			.
1359	6i75	6201	6226	6251	6276	6301	6326	6351	6376	6401	5	t	5	5
»360	108 6426	6451	6476	6501	6526	6551	6576	6601	6626	6651	6			6
»361	6676	6701	6726	6751	6776	6801	6826	6851	6876	6901	6		•	6
1362	6926	6951	6976	7001	7026	7051	7076	7101	7126	yiCI	6	•	6	6
(363	7176	7201	7226	7251	7276	7302	73*7	735*	7377	7402	6	1	6	6
"364	74*7	745*	7477	7502	75*7	755*	7577	7602	7627	7652	64	5	6	7
• 365	7677	7702	77*7	775*	7777	7802	7827	785*	7878	7903	6	i	6
• 366	79*8	7953	7978	8003	8028	8053	8078	8103	8128	8l5;	6	(	_
•367	8178	8203	8228	8*53	8278	8303	8328	8354	8379	840^	6	i	_	„
• 368	8429	8454	8479	8504	85*9	8554	8579	8604	8629	8654	6	(	_	8
»369	8679	8704	8730		8780	88ov	8830	88sv	8880	8905	6		7	8
1370	108 8930	8955	8980	9005	9030	9°55	9081	9106	9131	9156	70	_	\| j	8
1371	9181	9206	9231	9256	9281	9306	9331	9356	9382	9407	7	',	8	8
1372	943*	9457	9482	9507	953*	9557	9582	9607	9632	9657	7*	',	8	9
1373	9683	9708	9733	9758	9783	9808	0833	9858	bf3	9908	73	{	8	9
• 374	9933	9959	9984	0009	0034	0059	0084	0109		0159	74	8	9	9
375	109 0184	0210	023V	0260	028v	0310	°335	0360	0385	0410	'75	8	9	b
'376	0436	0461	0486	0511	0536	0561	0586	0611	0636	0662	76	8	9	b
377	0687	0712	0737	0762	0787	0812	0837	0862	0888	O9I'	i 77	8	9	b
378	0938	0963	0988	1013	1038	1063	1089	1114	"39	Il64	!78	9	b	b
379	1189	I2J4	1*39	1264	1290	i3iv	1340	1367	1390	1415	79	9	b	i
380	109 1440	1465	1491	1516	1541	1566	'591	1616	1641	l667	80	9	b	'i
381	1692	1717	1742	1767	1792	1817	1843	1868	1893	I9l8	81	9	b	J
382	1943	1968	1993	2019	2044	2069	2094	2119	2144	2l69	[82	2 0	i	I
383	2I9V	2220	224V	2270	2295	2320	*345	2371	2396	2421	83	0	i	2
384	2446	2471	2496	2522		2572	*597	2622	2647	2672	84	0	1	2
385	2698	2723	2748	2773	2798	2823	2849	2874	2899	2924	85	0	,	2
386	2949	2974	3000	3O2V	3050	3075	3100	3125		3I76	86	I	2	2
387	3*01	3226	3*5J	3276	3302	33*7	335*	3377	3402	34*8	87	I	2	3
388	3453	3478	3503.	35*8	3553	3579	3604	3629	3654	3679	88	I	2	3
389	37ov	373°	375V	3780	3805	3830	3856	3881	3906	3931	89	I	2	3
390	109 3956	398*	4007	4032	4057	4082	4108	4133	4158	4183	9°	2	3	3
391	4208	4*33	4*59	4284	43°9	4334	4359	438v	4410	4435	91	2	3	4
392	4460	4485	4511	4536	4561	4586	4611	4637	4662	4687	9*	2	3	4
C93	4712	4738	4763	4788	4813	4838	4864	4889	4914	4939	93	2	3	4
394	4964	4990	5oiv	5040	5065	5090	5116	5HI	5166	5191	94	3	4	4
395	5217	54	5267	59	5317	5343	5368	5393	54i8	5444	95	3	4	5
396	5469	5494		5544	557°	559V	5620	5645	5671	5696	96	3	4	1
397	57*i	5746	5771	5797	5822	5847	587*	5898	59*3	5948	97	3	\.
398	5973	5999	3024	6049	6074	6100	6l2V	6150	6175	6201	98	4	\
399	6226	6251	6276	6301	6327	6352	6377	6402	6428	6453	99	4	5
,og.	0	1	2	3	4	5	6	7	8	9	D	24	5	6

Log. -04000--04499.

(10)

Num. 109.6478 — :

LOR.	0	1	a	3	4	5	6	7	8	9	D	25 6
0400 I 0401 0402 j 0403	109 6478 6731 6983 7236	650\| 6756 7009 726l	«S*9 6781 7034 7286	6554 6806 7059 7312	6579 6832 7084 7337	6604 6857 7110 7362	6630 6882 7I3V 7387	6907 7160 74] 3	6680 6933 7185 7438	6705 6958 7211 7463	00 OI 02 03	0 0 0 0 0 I I I I
0404	7489	75'4	7539	7564	7590	;6iv	7640	7665	7691	7716	04	I I
0405	774 '	7767	779*	7817	7842	7868	7893	7918	7944	7969	05	I I
0406	7994	8019		8070	8095	8121	8146	8171	8196	8222	06	2 2
; 0407 1 0408	* wJ* 8247 8500	8272 8525	8298	83*3 8576	as	8373 8626	8399 8652	8424 8677	8449 8702	8728	07 08	2 2 2 2
0409	8753	8778	8803	8829	8854	8879	89ov	8930	8955	8981	°9	2 2
0410 ! 0411	109 9006 9*59	9031 9284	9056 9310	9082 933V	9107 9360	9132 9385	9158 9411	9183 9436	9208 9461	9*34 9487	10 : II	3 3 3 3
0412 0413	9512 9765	9537 979*	$2	9588 9841	9613 9867	9639 9892	9664 9917	9689 9943	9968	9740 9993	12	3 3 3 3
0414	no 0019	0044	0069	oo9v	0120	0145	0171	0196	0221	o*47	H	4 4
0415	0272	0297	0323	0348	0373	0399	0424	0449	O47v	0500	15	4 4
i 0416	0525	0551	0576	0601	0627	0652	0677	0703	0728	0753	16	4 4
0417	0779	0804	0829	085%-	0880	0905	0931	0956	0981	1007	17	4 4
; 0418	1032	1058	1083	1108	1134	1159	1184	I2IO	I23V	1260	18	5 5
0419	1286	1311	1336	1362	1387	1412	1438	1463	1489	'5H	*9	5 5
0420	no 1539	I56v	1590	1615	1641	1666	1692	1617	1742	1768	20	5 5
0421	"793	1818	,844	1869	1894	1920	1945	1971	1996	2021	21	5 5
0422	2047	2072	2097	2123	2148	2174	2199	2224	2250	2275	22	6 6
1 0423	2300	2326	2351	2377	2402	2427	*453	2478	2504	2529	23	6 6
0424	*554	2580	2605	2630	2656	2681	2707	273*	2757	2783	24	6 6
0425	2808	2834	2859	2884	2910	*935	2961	2986	3011	3037	*5	6?
0426	3062	3088	3113	3138	3164	3189	32IV	3240	3265	3291	26	7 7
0427	3316	3341	3367	339*	3418	3443	3469	3494	35J9		27	7 7
0428	3570	3596	3621	3647	3672	3697	37*3	3748	3774	3799	28	7 7
0429	3824	3850	3875	3901	3926	395*	3977	4002	4028	4053	29	7 8
0430	no 4079	4104	4129	4157	4180	4206	4231	4*57	4282	4307	30	8 8
0431	4333	4358	4384	4409	443V	4460	4485	4511	4536	4562	31	8 8
0432	4587	4613	4638	4663	4689	47 '4	4740	4765		4816	3*	8 8
0433	484*	4867	4892	4918	4943	4969	4994	5020	5°45	5071	33	8 9
0434	5096	5121	5»47	57	5198	5223	5*49	5*74	5300	53*5	34	9 9
0435 0436 0437 0438 0489	5350 5605 5860 6114 6369	5376 5630 ft '> 14 - «394	5401 5656 59" 6165	54*7 568, 5936 6191 6445	545* 5707 6471	5478 573* 5987 6242 6496	5503 5758 6012 6267 6522	55*9 5783 6038 6293 6 547	5554 5809 6063 6318 6573	5580 5834 6089 6344 6598	35 36 37 38 39	9 9 9 9 9 o I 0 0 0 0
*
0440 0441 0442 f\ m m m	no 6624 6879 7«J4	"49 6004	667v 6930 718*	6700 6955 7210	6726 6981 7*35	6751 7006 7261	6777 7032 7286	6802 7057 7312	6828 7083 7337	6853 7108 7363	40 4' 42	0 0 0 I
^j^^r 7»59
0443 j 0444	tOAl ™^i	7$	7439 769*	77*o	749° 7746	7416 777»	754' 7797	7567 7822	759* 7848	7618 7873	43 44	I
0445 ; 0446 0447 0448 "449	7899 8»54 Ifl)	794 •iS JJ£ 894	7950 820V 8460 8715	7975 8230 8485 8741 xr/,	8001 8256 8511 8766 9022	8026 8281 8537 879* 9047	8052 8307 8562 8817 9073	8077 8332 8588 8843 9098	8103 8358 8613 8868 9124	8128 8383. 8639 8894 9149	45 46 47 48 49	J 2 2 2 2
						=-—	_ j —		8	9	D	25

•04566— "04999.

Num. 1 10.9 1 7v — 1 12.1993,

Log.	0	1	2	3	4	5	6	7	8	9	P	25	6
• 450	no 9iyv	9200	9226	9251	9277	9303	9328	9354	9379	940v	5°	i i	3
• 451	9430	9456	9481	9507	9532	9558	9584	9609	963v	9660	51	3	3
• 452	9686	9711	9737	9/62	9788	9813	9839	986v	9890	9916	52	3	4
1453	9941	9967	9992	0018	6044	6069	oo9v	0120	6146	0171	53	3	4
1454	in 0197	0222	024$	0274	0295	032V	0350	0376	0401	0427	54	4	4
>455	0453	0478	0504	0529	O55v	0580	0606	0632	0657	0683	55	4	4
•456	0708	0734	0759	078v	0811	0836	0862	0887	0913	0938	56	4	5
457	0964	0990	1015	1041	1066	1092	1118	JI43	1169	119^	57	4	5
1458	1220	1245	1271	1297	1322	1348	1373	1399	142 v	1450	58	5	5
459	1476	1501	1527	1553	1578	1604	1629	i65v	1681	1706	59	5	5
>460	III 1732	1757	1783	1809	1834	1860	1885	1911	J937	1962	60	5	5
i46l	1988	2OI3	2039	2o6v	2090	2116	2141	2167	2193	2218	61	5	6
i462	2244	2269	2295	2321	2346	2372	2397	2423	2449	2474	62	6	6
463	2500	2526	2551	2577	2602	2628	2654	2679	270V	2731	63	6	6
i464	*756	2782	2807	2833	2859	2884	2910	2936	2961	2987	64	6	7
465	3012	3038	3064	3089	3iiv	3Hi	3166	3192	3217	3^43	«5	6	7
>466	3269	3*94	33^0	3346	337i	3397	34^3	3448	3474	3499	66	7	7
467	35*5	355i	3576	3602	3628	3653	3679	37ov	3730	3756	;67	7	7
468	3782	3807	3833	3858	3884	3910	3935	3961	3987	4012	'68	7	8
469	4038	4064	4089	4iiv	4141	4166	4192	4218	4243	4269	69	7	8
470 471	in 429v 455 J	4320 4577	4346 4602	4372 4628	4397 4654	4423 4679	AAA%	4474 473 J	4500 4756	4525 4782	70 7i	8 8	8 8
III 4705
472	4808	4833	4859	488v	4910	4936	4962	4988	5013	5039	72	8	9
473	5o6v	5090	5116	5142	5i67	5193	52I9	5244	5270	5296	73	8	9
474	53^1	5347	5373	5398	5424	545°	5475	55°i	55^7	5552	74	9	9
475	5578	5604	5630	5655	5681	5707	5732	5758	5784	5809	75	9	0
476	' 5835	5861	5886	5912	5938	5964	5989	6oiv	6041	6066	76	9	0
477	6092	6118	6l43	6169	6i9v	6221	6246	6272	6298	6323	77	9	o
478	6 349	637v	6400	6426	6452	6478	6503	6529	655v	6580	78	2 0	o
479	6606	6632	6658	6683	6709	673v	6760	6786	6812	6838	79	0	I
480	in 6863	6889	69 iv	6940	6966	6992	7018	7043	7069	7o9v	80	0	I
481	7120	7146	7172	7198	7223	7249	727V	7301	7326	7352	81	O	I
482	7378	7403	7429	745v	7481	7506	7532	7558	7584	7609	82	I	I
483	7635	7661	7686	7712	7738	7764	7789	7815	7841	7867	83	I	2
484	7892	7918	7944	7970	7995	8021	8047	8073	8098	8124	84	I	2
485	8150	8176	8201	8227	8253	8279	8304	8330	8356	8382	85	I	2
486	8407	8433	8459	848v	8510	8536	8562	8588	8613	8639	86	2	2
487	866v	8691	8716	8742	8768	8794	8819	8845	8871	8897	87	2	3
488	8922	8948	8974	9000	9026	9°5!	9077	9103	9129	9J54	00 So	2	3
489	9180	9206	9232	9257	9283	93°9	933v	9361	9386	9412	89	2	3
490	ii 9438	9464	9489	95J5	954i	9567	9593	9618	9644	9670	9°	3	3
491	9696	9721	9747	9773	9799	982v	9850	9876	9902	9928	91	3	4
492	9954	9979	6005	0031	0057	0082	0108	0134	0160	0186	92	3	4
493	12 O2II	0237	0263	0289	03iv	0340	0366	0392	0418	0444	93	3	4
494	0469	0495	0521	0547	°573	0598	0624	0650	0676	0702	94	4	4
495	0727	0753	0779	o8ov	0831	0856	0882	0908	0934	0960	95	4	5
496	0986	ion	1037	1063	1089	IIIV	1140	1166	1192	1218	96	4	5
497	1244	1269	1295	1321	1347	1373	1399	1424	1450	1476	97	4	5
498	1502	1528	1554		1605	1631	1657	1683	1708	1734	98	5	j
499	1760	1786	1812	1838	1863	1889	1915	1941	1967	1993	99	5
,og.	0	1	2	~3~	4	5	6	7	8	9	D	25	>

Lof. -05000— '05499.

Num. 112. 2018 — 113.498


Log. MM	-2 III 20l8	1044	1070	2096	2122	2148	2173	2199	2225	2251		00	25 0 O	6 o
0501 (0501	1177 1303 535 5*i	2319 1587	*\|54 1613	2380 2639	2406 z66v	2432 2690	2458 2716	2484 2742	2509 2768		01 02	0	0 I
0503	»794 2820	2845	2871	2897	2923	2949	297v	3001	3026		03		I
0504	3052	3078	3104	3130	3156	3182	3208	3*33	3*59	3285		04		I
0505 0506	S3"	3337 3596	3363 3621	3389 3647	34*4 3673	3440 3699	3466 372v	349* 375*	3777	3544 3803		°5 06		2
0507	1828	3854	3880	3906	393*	3958	3984	4010	4035	4061		°7	2	2
0508	4087	4*»3	4*39	4i6v	4191	4217	4*43	4268	4*94	4320		08	2	2
0509	4S46	437*	4398	44*4	445°	4476	4501	45*7	4553	4579		09	2	2
0510	in 46or	4631	4657	4683	4709	4734	4760	4786	4812	4838		1C	3	3
051 1	4864	4890	4916	494*	4968	4993	5019	5°45	5071	5097		ii	3	3
0512	5»*3	5*49	57	5201	5227	5*53	5278	5304	533°	5356		12	3	3
0513	5382	5408	5434	5460	5486	5512	5538	5563	5589	5615		13	3	3
0514	5641	5667	5693	57*9		5771	5797	58^3	5849	587v			4	4
0515 0516	\|9f> 6160	5926 6186	595* 6212	5978 6238	6004 6263	6030 6289	6056 63'5	6082	6108 6367	6393		:i	4 4	4 4
0517	6419	6445	6471	6497	6523	6549		6601	6627	6653		17	4	4
0518	6678	6704	6730	6756	6782	6808	6834	6860	6886	6912		18	5	5
0519	6938	6964	6990	7016	7042	7068	7094	7120	7146	7172		'9	5	5
0520	112 7*97	7223	7*49	7*75	7301	73*7	7353	7379	7405	7431		20	5	5
0521	7457	7483	7509	753v	7561	7587	7613	7639	766v	7691		21	5	5
0522	77*7	7743	7769		7821	7847	7872	7898	79*4	795°		22	6	e
0523	7976	8002	8028	8054	?o8o	8106	8132	8158	8184	8210		23	6	6
0524	8236	8262	8288	8314	8340	8366	8392	8418	8444	8470		24	6	6
0525	8496	8521	8548	8574	8600	8626	8652	8678	8704	8730		*5	6	7
0526	8756	8782	8808	8834	8860	8886	8912	8938	8964	8990		26	7	7
0527	9016	9042	9068	9094	9120	9146	9172	9198	9224	9250		*7	7	7
0528	9276	9302	93*8	9354	9380	9406	943*	9458	9484	9510		28	7	7
0529	9536	9562	9588	9614	9640	9666	9692	9718	9744	9770		29	7	8
0530	112 9796	9822	9848	9874	9900	9926	995*	9978	6004	6030		30	8	8
0531	113 0056	0082	0108	0134	0160	0186	0212	0238	0264	0290		31	8	8
0532 0533	0316 0577	0342 0603	0368 0629	0394 o6Sv	0420 0681	0446 0707	0472 °733	0498 0759	052V	0551 08 1 1		32 33	8 8	8 9
0534	0837	0863	0889	0915	0941	0967	0993	1019	1045	1071		34	9	9
0535	1097	1123	"49	1176	1202	1228	i*54	1280	1306	133*		35	9	9
0536	'358	1384	1410	1436	1462	1488	1514	1540	1566	1592		36	9	9
0537	1618	1644	1671	1697	1723	1749		1801	1827	1853		37	9	o
. . .', :t •«	1879	1905	1931	*957	1983	2009	2035	2061	2088	2114		38	I 0	0
0589	1140	2166	2192	2218	**44	2270	2296	2322	2348	*374		39	o	0
§1 i , 0541 0542 0543	1131400 1661 1922 3183 1444	2426 2687 2948 3109 3470	453 73 »974 335 3496	479 2739 3000 3261 35*	2765 3026 3287 3548	2531 2792 3052 3574	*557 2818 3079 3339 3600	2583 2844 3iov 3366 3627	2609 2870 3131 339* 3653	2635 2896 3^57 3418 3679		40 41 42 43 44	0 o I	0 I I I I
0345 0546 fl ft. 4 •	370r 3966	373* 399*	3757 4018	3783 t t ;	3809 4070	3835 4096	3861 4123	3888 4149	39H	3940 4201		45 46	I 2	2 2
T "I *f
1 • 4 , 9948 0549	44" 4749	4»53 45'4 4776	479 4540 402 — _	4567 4828	433* 4593 4854	4358 4619 4880	4384 4906	4410 4671 493*	4437 4697 4959	4462 4723 498v		47 48 49	2 2 2	2 2 3
									9		D	25	6

•05500— -05999.

(13)

Num. 113.5011 — 114.8127.

Log.	O	1	2	3	4	5	6	7	8	9	JL	25	6	7
550	113 5011	5037	5063	5089	5"5	5141	5168	5194	5220	5246	5°	I 7	?
551	57	5298	5324	5351	5377	5403	54*9	5455	5481	55°7		J	J 1
552	5534	5560	5586	5612	5638	5664	5691	57*7	5743	• + 5769	52		j
553 554	5795 6057	5821 6083	5847 6109	5874	5900 6161	5926 6187	595* 6214	5978 6240	6004 6266	603? 6292	53 54	3 4	4 4	4 5
555 556	6318 6580	6606	6371 6632	6397 6658	6423 668v	6449 6711	6475 6737	6501 6763	6528 6789	6554 6816	55 56	4 4	5 C	5
557	6842	6868	6894	6920	6946	6973	6999	7O2V	7051	7077	57		J c
558	7104	7130	7156	7182	7208	7*34	7261	7287		7339	58	c	J c	6
559	7365	739*	7418	7444	7470	7496	75*3	7549	757v	/ J J«7 7601	59	j 5	3 5	6
560	113 7627	7653	7680	7706	773*	7758	7784	7811	7837	7863	60	5	6	6
561	7889	79X5	794*	7968	7994	8020	8046	8073	8099	8125	61	c	6	6
562	8151	8178	8204	8230	8256	8282	8309		8361	8387	62	6	6	7
563	8413	8440	8466	8492	8518	8544	8571	8597	8623	8649	63	6	6	7
564	8676	8702	8728	8754	8780	8807	8833	8859	8885	8912	64	6	7	7
565	8938	8^4	8990	9016	9°43	9069	9095	9121	9148	9174	65	6	7	8
566	9200	9226	9*53	9*79	93ov		9357	9384	9410	943 6	66	7	7	8
567	9462	9489	95iv		9567	9594	9620	9646	9672	9699	67	7	7	8
568	972v	975*	9777	9804	9830	9856	9882	9909	993v	9961	68	7	8	8
569	9987	6014	6040	6066	0092	0119	6i4v	6171	0197	0224	69	7	8	9
570	114 0250	0276	0302	0329	O35v	0381	0407	0434	0460	0486	70	8	8	9
57 1	0512	0539	O56v	0591	0617	0644	0670	0696	0722	0749		8	8	9
572	0775	0801	0828	0854	0880	0906	0933	0959	0985	IOII	7*	8	9	9
573	1038	1064	1090	1117	1143	1169	"95	1222	1248	i*74	73	8	9	6
574	1300	1327	J353	1379	1406	1432	H58	1484	1511	J537	74	9	9	b
575	1S63	1590	1616	1642	1668	i69v	1721	1747	T774	1800	75	9	b	0
576	1826	1852	1879	1905	1931	1958	1984	2010	2037	2063	76	9	b	i
577	2089	2115	2142	2168	2194	2221	2247	2273	2300	2326	77	9	b	i
578	2352	2378	240V	*43i	*457	2484	2510	2536	2563	2589	78	2 O	0	i
579	2615	2642	2668	2694	2720	2747	*773	2799	2826	2852	79	0	i	i
580	114 2878	290V	2931	2957	2984	3010	3036	3063	3089	3"5	80	O	I	2
581		3168	3194	3220	3*47	3*73	3*99	3326	335*	3378	81	O	i	2
582	34ov	3431	3457	3484		3536	3563	3589	3615	3642	82	I	I	2
583	3668	3694	37*i	3747	3773	3800	3826	385*	3879	3905	83	I	2	2
584	3931	3958	3984	4010	4037	4063	4090	4Il6	4142	4169	84	I	2	3
585	4i9v	4221	4248	4*74	4300	43*7	4353	4379	4406	443*	85	I	2	3
586	4458		4511	4537	4564	459°	4616	4643	4669	4696	86	2.	2	3
587	47**	4748	477v	4801	4827	4854	4880	4906	4933	4959	87	2	3	3
588	4986	5012	5038	5o6v	5°9J	5117	5J44	5170	5*96	5223	88	£	3	4
589	5*49	5276	5302	53*8	535V	5381	54°7	5434	5460	5487	89	2	3	4
590	"4 55'3	5539	5566	559*	5618	564v	5671	5698	57*4	575°	90	3	3	4
591		5803	5830	5856	5882	5909	5935	5961	5988	6014	91	3	4	5
592	6041	6067	6093	6120	6146	6173	6199	6225	6252	6278	9*	3	4	5
593	63ov	6331	6357	6384	6410	6436	6463	6489	6516	6542	93	3	4	5
594	6568		6621	6648	6674	6700	6727	6753	6780	6806	94	4	4	5
595	6833	6859	6885	6912	6938	696v	6991	7017	7044	7070	95	4	5	6
596	7097	7123	7H9	7176	7202	7229	7*55	7282	7308	7334	96	4	5
597	7361	7387	74H	7440	7466	7493	7519	7546	757*	7599	97	4	5
598		7651	7678	7704	7731	7757	7784	7810	7836	7863	98	4	5
599	7889	7916	794*	7969	7995	8021	8048	8074	8101	8127	99	5	O	7
-og.	0	1	2	3	4	5	6	7	8	9	D	25	6	7

Log. -06000— -06499.

(14)

Num. 114.8154—116.142!

tog.	0	1	a	3	4	5	6	7	8	9	D	25
tM-,00 0601	114 8154	8180 8444	8206 847i	8*33 8497	859 8S4	8286 8550	8312 8577	8339 8603	8365 8630	839* 8656	oo OI	0 0 0
0602	8682	1709	8735	8762	8788	88iv	884,	8868	8894	8921	02	I
0603	«947	8973	9000	9026	9°53	9079	9106	9132	9*59	9185	o;	I
0604	9212	9238	920V	9291	9317	9344	9370	9397	94*3	9450	04	I
0605	947*	9503	95*9	9556	9582	9609	9635	9662	9688	97H	°5	,
0606	974'	9767	9794	9820	9847	9873	9900	9926	9953	9979	06	2
0607	115 0006	0032	0059	0085	OII2	0138	oi6v	0191	02 1 £	0244	07	2
0608	0271	0*97	0324	0350	0376	0401	0429	0456	0482	0509	08	2
0609	0535	0562	0588	06 iv	0641	0668	069^	0721	0747	0774	09	2
0610	115 0800	0827	0853	0880	0906	0933	0959	0986	IOI2	1039	10	3
0611	1065	1092	1118	ii4v	II7I	1198	1224	1251	i*77	1304	ii	3
0612 0613	1330 1596	1357 1622	1649	1410 1675	'437 1702	1463 1728	1490	1516 1781	1543 1808	1569 1834	12	3 3
0614	1861	1887	1914	1940	1967	1993	2020	2046	2073	2100	H	4
0615	2126	2153	2179	2206	2232	2259	2285	2312	2338	236v	15	4
0616	2391	2418	2444	2471	2498	2524	2551	2577	2604	2630	16	4
0617	2657	2683	2710	2736	2763	2o8v	28l6	2843	2869	2896	17	4
0618	2922	2949	2975	3002	3028		3081	3108	3i3v	3161	18	5
0619	3188	3214	3241	3267	3*94	3320	3347	3374	3400	34*7	19	5
0620	"5 3453	348o	3506	3533	3559	3586	3613	3639	3666	3692	20	5
0621	37'9	3745	377*	3799	3825	3852	3878	39ov	3931	395s	21
0622	398v	4011	4038	4064	4091	4117	4144	4171	4*97	4224	22	5
0623	4250	4*77	4303	4330	4357	4383	4410	4436	4463	449°	Z'.	6
0624	4516	4543	4569	4596	4622	4649	4676	4702	47*9	4755	24	6
0625	4782	4809	4835	4862	4888	49 iv	494*	4968	499v	5021	2<	7
0626	5048	5°7V	5101	5128	5154	5181	5208	5*34	5*6i	5*87	26	7
0627	S3H	534i	5367	5394	5420	5447	5474	5500	55*7	5553	27	7
0628	5580	5607	5633	5660	5686		574°	5766	5793	5819	28	7
0629	5846	5873	5899	5926	5953	5979	6006	•}' 0032	J / 7J 6059	6086	29
0630 0631 0632 0633 0634	115 6112 6378 664* 6911 7178	6139 6405 6671 6938 7204	6165 6432 7*3 '	6192 6458 672V 6991 7*57	6219 648 v 6751 7018 7*84	6245 6512 6778 7044 73"	6272 6538 68ov 7071 7337	6299 6831 7098 7364	6325 6592 6858 7124 7391	6352 6618 6884 7151 741?	30 31 3* 33 34	8 8 8 9 9
0635 0636 0637	7444 77" 7077	7471 7737	7497 7764 {011	75*4 779'	7551 7817 808/1	7577 7844 H I T ¥	7604 7871 0 . -_	7631 7897 O.f..	7657 79*4 o __	7684 7951 «_ , ,	35 36	9 9
0638 0689	PS	8«7	»V»J I	J3*4 8591	80»4 8617	5 I I I 8377 8644	8137 8404 8671	o 104 8431 8697	5I9I 8457 87*4	0217 8484 8751	37 38 39	I O o 0
0640	lie 8777	x y •	8811			J _ .	O . ..	O £
0641 0642 0643 0644	J / / / 9<H4 91"	<> -' 9872	0031 ) ',* [Sj 9899	9124 939' 9658 99*5	9151 9418 968v 995*	»9" 944v 9712 9979	8937 9204 9738 6005	8964 9231 9498 9765 6032	8991 9258 979* 0059	9018 9284 955' 9818 6086	40 42 43 44	0 I I I I !
0645 0646	"6 0112 0170 * '	23	0166	0192 • i)	0210 • '•it	0246	0273	0299	0326	035-?	45	2 I
0647 0648 M4I	0914 1181	•/;• r; •	>7OO ."''"	0400 0727 0994 1261	•t ^ °753 102 I 1288	0513 0780 1048 1 3 iv	0540 0807 1074 1342	0566 0834 IIOI .368	0593 0860 1128 '395	0620 0887 "54 1422	46 47 48 49	z : z \ 2 ' 3 :
						'•		7	8	9	D	26 '5

•06500— '06999.

(15)

Num. 116.1449 — 117-4871

C.og.	O	1	2	3	4	5	6	7	8	9	D	26	7
'650	116 1449	H75	1502	J5*9	1556	1582	1609	1636	1663	1689	5°	I -5
'651	1716	1743	1770	1796	1823	1850	1877	1903	1930	J957	51	* J 3	4
• 652	1984	2010	2037	2064	2091	2117	2144	2171	2198	2224	5*
653	2251	2278	230V	233i	*358	*385	2412	2439	2465	2492	53
'654	2519	2546	2572	*599	2626	2653	2679	2706	*733	2760	54	4	5
'655	2787	2813	2840	2867	2894	2920	2947	2974	3001	3028	55	4	5
'656	3°54	308l	3108	3i3v	3161	3188	3*i5	34	3269	3*95	56	5	5
657	3322	3349	3376	3403	34*9	3456	3483	35io	3536	3563	57	5	5
'658	3590	3617	3644	3670	3697	37*4	375i	3778	3804	3831	58	5	6
659	3858	388v	3912	3938	3965	399*	4019	4046	4072	4099	59	5	6
'660	116 4126	4T53	4180	4206	4*33	4260	4287	43H	434°	4367	60	6	6
661	4394	4421	4448	447v	4501	45*8	455^	4582	4609	4635	61	6	6
662	4662	4689	4716	4743	4770	4796	4823	4850	4877	4904	62	6	7
663	493°	4957	4984	5011	5038	5o6v	5091	5118	5H5	5172	63	6	7
'664	5'99	5226	55	5279	5306	5333	5360	5387	54i3	544°	64	7	7
665	5467	5494	5521	5548	5574	5601	5628	565v	5682	5709	65	7	8
666 667	5735 6004	5762 6031	5789 6058	5816 6084	5843 6111	5870 6138	5897 6i6v	59*3 6192	5950 6219	5977 6246	66 67	7 7	8 8
668	6272	6299	6326	6353	6380	6407	6434	6460	6487	6514	68	8	8
669	654i	6568	659v	6622	6648	6675	6702	6729	6756	6783	69	8	9
670	116 6810	6836	6863	6890	6917	6944	6971	6998	702V	7051	70	8	9
671	7078	7105	7132	7*59	7186	7213	7240	7266	7*93	7320	7i	8	9
672	7347	7374	7401	7428	745V	7481	7508	7535	7562	/589	7*	9	9
673	7616	7643	7670	7697	77*3	7750	7777	7804	7831	7858	73	9	0
674	788v	7912	7939	7965	7992	8019	8046	8073	8100	8127	74	9	o
675	8154	8181	8208	8234	8261	8288	8315	8342	8369	8396	75	z o	0
676	8423	8450	8477	8503	8530	8557	8584	86n	8638	866v	76	o	i
677	8692	8719	8746	8773	8799	8826	8853	8880	8907	8934	77	0	i
678	8961	8988	9oiv	9042	9069	9096	9122	9149	9176	9203	78	0	i
679	9230	9257	9284	93"	9338	936v	939*	9419	9446	947*	79	I	i
680	116 9499	9526	9553	9580	9607	9634	9661	9688	97iv	974*	80	I	2
681	9769	9796	9823	9850	9876	99°3	993°	9957	9984	OOII	81	I	2
682	117 0038	0065	0092	0119	0146	0173	0200	0227	0254	0281	82	I	2
683	0308	°334	0361	0388	0415	0442	0469	0496	°5*3	0550	83	2	2
684	°577	0604	0631	0658	o68v	0712	0739	0766	0793	0820	84	2	3
685	0847	0874	0901	0927	0954	0981	1008	1035	1062	1089	8I	2	3
686	1116	1143	1170	1197	1224	1251	1278	I3°S	133*	1359	86	2	3
687	1386	1413	1440	1467	1494	1521	1548	i57v	1602	1629	87	3	3
688	1656	1683	1710	1737	1764	1791	1818	1 84v	1872	1899	88	3	4
689	1925	1952	1979	2006	2033	2060	2087	2114	2141	2168	89	3	4
690	117 2195	2222	2249	2276	2303	2330	*357	2384	2411	2438	90	3	4
691	2465	2492	2519	2546	2573	2600	2627	2654	2681	2708	91	4	5
692	X 2735	2762	2789	2816	2843	2870	2897	2924	2951	2978	9*	4	5
«93-	3005	3032	3°59	3086	3"3	3140	3167	3194	3221	3*48	93	4	5
694	3275	3303	333°	3357	3384	3411	3438	346v	349*	3519	94	4	5
695	3546	3573	3600	3627	3654	3681	3708	373v	3762	3789	n	5	6
'696	3816	3843	3870	3897	39*4	3951	3978	4005	4032	4059	96	5	6
;697	4086	4"3	4140	4167	4194	4221	4248	4276	43°3	4330	97	5	6
•698	4357	4384	4411	4438	446 v	449*	45J9	4546	4573	4600	98	5	6
899	4627	4654	4681	4708	4735	4762	4789	4816	4843	4871	99	6	7
,og.	0	1	2	3	4	5	6	7	8	9	D	26	7

Log. '07000— -07490.

(16)

Num. 117.4898 — :

									8	9		D	27 8
0700	H7 49	1492V	495*	4979	5006	5033	5060	5087	5"4	5Hi		00	0 O O
0701	5i68 5195	5222	5*49	5276	5303	5330	5358	538v	54"		01	0 O
0702 0703 0704	5439 5709 5980	§	5493 5764 6034	\|79i 6061	5547 6088	5574 584v 6116	5601 5872 6143	5628 5899 6170	5655 59*6 6197	5682 5953 022^		02 03 04	I I I I I I
0705 0706	625, 6522	6278 6 549	6576	6603	6359 6630	6386 6657	6414 6684	6441 6712	6468 6739	6766		05 06	I I 2 a
0707	6793	6820	6847	6874	6901	692g	6955	6982	7010	7037		07	2 2
0708	m 7064	7091	7118	7H5	7172	7199	7226	7*54	7281	7308		08	2 2
0709	733»	7362	7389	7416	7443	7470	7498	752v	755*	7579		.09	* 3
0710	117 7606	7633	7660	7687	77H	774*	7769	7796	7823	7850		1C	3 3
071 1	7«77		7931	7959	7986	8013	8040	8067	8094	8121		II	3 3
0712	8148	8176	8203	8230	8257	8284	8311	8338	8365	8393		12	3 3
0713	8420	8447	8474	8501	8528	8555	8583	8610	8637	8664		13	4 4
0714	8691		8745	8773	8800	8827	8854	8881	8908	8935		H	4 4.
0715	8963	8990	9017	9044	9071	9098	9125	9'53	9180	9207		15	4 4
0716	9*34	9261	9288	9315	9343	9370	9397	94*4	945 l	9478		16	4 4
07 17	9506	9533	9560	9587	9614	9641	9669	9696	97*3	9750		17	5 5
0718	9777	9804	9832	9859	9886	9913	9940	9967	999v	0022		18	5 5
0719	118 0049	0076	0103	0130	0158	oi8v	0212	0239	0266	0291		'9	5 5
0720	118 0321	0348	°37V	0402	0429	0457	0484	0511	0538	0565		20	5 6
0721	0592	0620	0647	0674	0701	0728	0756	0783	0810	0837		2)	6 6
0722	0864	0892	0919	0946	0973	1000	1027	io5v	1082	II09		22	6 6
0723	1136	1163	1191	1218	i*45	1272	1299	1327	1354			23	6 6
0724	1408	'435	1463	1490	1517	*544	1571	1599	1626	1653		*4	67
0725	1680	1708	I73v	1762	1789	1816	1844	1871	1898	95		*5	7 7
0726	1952	1980	2007	2034	2061	2089	2116	2143	2170	2197		26	7 7
0727	222V	2252	2279	2306	2334	2361	2388	2415	2442	2470		27	7 8
0728	*497	2524	2551	2579	2606	2633	2660	2687	27IV	2742		28	8 8
0729	2769	2796	2824	2851	2878	2905	*933	2960	2987	3014		29	8 8
0730	118 3042	3069	3096	3'*3	3i5I	3178	3205	33	3260	3287		30	8 g
0731 0732 0733	33'4 3586 3859	334i 3614 3886	3368 3641 39 '4	3396 3668	3f3 3696 3968	3450 37*3 3995	3477 375° 4023	35ov 3777 4050	353* 4077	3559 3832 4104		31 3* 33	8 9 9 9 9 9
0734	4131	4'59	4186	4213	4241	4268	4*95	43*3	435°	4377		34	9 o
0735	4404	443*	4459	4486	45'3	454i	4568	4595	4623	4650		35	9 6
	4677	4704	473*	4759	4786	4814	4841	4868	4895	4923		36	I 0 0
0737	4950	4977	5oov	5032	5059	5086	51*4	5141	5168	5196		37	0 0
0738	5»*3	5250	5*77	53ov	533*	5359	5387	54H	544i	5468		38	0 I
0739	549*	55*3	5550	5578	56ov	5632	5660	5687	57H	5741		39	i i
0740 0741	'"loS	ag	%l	5851 6124	5878 6151	5905 6178	5933 6206	5960 6233	5987 6260