ON MATHEMATICAL TABLES. 97 



[T. II.] Log sines, tangents, and secants for every minute of the quadrant^, 

 to 7 places (without difl'ereuces). 



[T. III.] 2^atural sines, tangents, and secants for every minute of the 

 quadrant, to 7 places (without differences). 



[T. IV.] Natural and log versed sines to every minute, from 0° to 180°, to 

 7 places (without differences). 



T. III. Supplement. Table to convert sexagesimals into decimals. It 

 gives 1", 2", 4" . . . 58", 1', 1' 1", 1' 2", 1' 4". . . 1' 58", 2' ... 2' 58", &c. to 

 60', expressed as decimals of 60', to 4 places. 



T, IV. Supplement. Logarithms of numbers from 1 to 180, to 15 places. 



Ducom, 1820. T. VII. Proportional logarithms for every second to 3°, 

 to 4 places ; same as T. 74 of IIapee. 



T. IX. Log sines and tangents for every second to 2° ; then follow log 

 cosines and cotangents for every 10" to 2^; and then log sines, cosines, 

 tangents, and cotangents from 2^ to 4-5°, at intervals of 10", to 6 places. 

 Proportional parts are added for the portion where the intervals are 10". 



T. XIX. Natural sines for every minute of the quadrant, to 6 places. 



T. XX, Parties proportionnelles for interpolating when the tabular result 



is given for intervals of 24'', viz. g^*( (expressed in hours, minutes, and 



seconds), where x is 1™, 2™, . . . . 60™, and, in the first table, y is 1'', 2", 



24\ and in the second 1"", 2™, 60'". 



T. XXI. Six-figure logarithms of numbers to 10,800, with corresponding 

 minutes and seconds : logarithms printed at full length ; no differences. 

 The other tables are nautical &c. 



The tables form the second part of the work. It may be noticed that, in 

 the remarks on T. XIX. (p. xiv), the versed sine of x is erroneously defined 

 as if it were 1 — sin .r. 



Dunn, 1784. [T. I.] Six -figure logarithms to 10,000. The arrangement 

 is the same as is usual in seven-figure tables ; only instead of the numbers 

 0, 1, 2, . . . . 9 running along the top line, they are printed 0-00, 100, 2-00, .... 

 9-00, which gives the table the appearance of being arranged differently. 



[T. II.] Log sines, tangents, and secants to every minute of the quadrant, 

 to 6 places. At the foot of each page is a small table, giving the differences 

 (for the sine and tangent) for an interval of 60" in the middle of the page, 

 and their proportional parts for 50", 40", 30", 20", 10", 9", 8", 7", 6", 5", 4", 

 3", 2", 1". At the end is a table of the differences of the log sines, tangents, 

 and secants for every 10'. 



Dupuis, 1868. T. I. & II. Seven-figure logarithms from 1 to 1000, and 

 from 10,000 to 100,000. Proportional parts to tenths, viz. multiples with 

 the last figure separated by a comma, are added. (The separation of the last 

 figure is an improvement on the simple multiples given in Sang, 1871, and 

 others, as the table can be more readil}'- used by those accustomed only to 

 proportional parts true to the nearest unit.) S and T (§ 3, art. 13) arc given 

 at the bottom of the pages at intervals of 10". Dupuis states in the preface 

 that his intention had been that the table should extend to 120,000, and 

 that accordingly he had calculated the last 12,000 logarithms by differences, 

 but at the request of a number of professors he stopped at 100,000. "\Vc 

 venture to think he would have acted more wisely if he had not listened to 

 the professors*; but the matter is of no consequence now, as Sang, 1871, 

 extends to 200,000, 



* Several of tbe ordinary seven-figure tables (Babbage, Callet, Hulsse's Vega, and 

 many otliers) extend to 108,000, and the last 8U00 logarithms are given to eight places. 

 1873. H 



