ON MATHEMATICAL TABLES. 99 



These cards correspond to the fixed and movable portions of a slide-rule 

 100 inches long. A few small tables of cube roots, sines, &c. are printed on 

 one of the cards. Prof. Everett (to whom we applied for information with re- 

 gard to the date of the table) gives the following brief description — " Two 

 cards, one of them cut like a grating, equivalent to the two pieces of a slide- 

 rule;" and adds "that in the first edition [which is the one we have 

 described] one of the cards had a pair of folding leaves attached to it, 

 but these merely contained subsidiary tables and directions, and were quite 

 unessential. In the next impression the two essential cards and the two 

 cards with subsidiary tables and directions were all detached from each 

 other." A description of the table is given in the Phil. Mag. for November 

 18G6. 



Parley, 1840. [T. I.] Six-figure logarithms to 10,000 (the line is 

 broken when the change occurs in the third figure) ; followed by the loga- 

 rithms of numbers from 1001 to 1200, to 7 places. 



[T. II.] Log sines and tangents for every minute of the quadrant, to 6 

 places, with difi^erences for 100". 



[T. III.] Log sines from 0° to 2° at intervals of 6". 



There are also a few constants and some formulae. 



Parley, 1856. This very fine table of versed sines contains : — [T. I.] 

 Natural versed sines from 0° to 125° at intervals of 10", to 7 places, with 

 proportional parts throughout. 



[T. II.] Log versed sines from 0° to 135° at intervals of 15", to 7 places, 

 with difi"erences throughout. The arguments are also given in time, the 

 range being from 0*" to 9^ to every second. 



A short preface by Mr. Hind states that the table was prepared by Mr. 

 Farley, of the Nautical- Almanac Office, in 1831, and the manuscript pre- 

 sented by him to Lieut. Stratford, the then superintendent. The manuscript 

 having been in use for 25 years, and having become dilapidated, it was 

 *' deemed the most economical course to print it." It is added that the last 

 figure cannot be relied on, though it is probably very rarely in error by more 

 than a unit. 



These, the most complete tables of versed sines we have seen, are beauti- 

 fully printed, in the same type as the Nautical Almanac. 



Faulliaber, 1G30 (' Ingeuieurs-Schul '). The copy we have seen of this 

 book (viz. that in the British Museum) contains no logarithms, though it must 

 evidently have been intended to accompany some tables. In the Brit- Mug. 

 copy the work is bound up (in a volume containing four tracts) after the two 

 described below and attributed by us to Faulhaber. Murhard gives the 

 full titles of this work and of the next two, and marks them as having come 

 under his eye ; he does not, however, assign the two tables to Faulhaber. 

 Hogg, who also gives the titles of the three works, attributes them all to Faul- 

 haber. He adds, speaking of the tables, that they are also contained in the 

 ' Ingenicurs-SchuL' This is no doubt correct; for, as noted below, some errors 

 in the latter work are given at the end of the Canon. It seems therefore 

 certain that Faulhaber was the editor of the tables. It may be mentioned 

 that both Eogg and Murhard agree in describing the ' Logarithmi ' and the 

 ' Canon ' as parts of the same work, so that most likely they were never issued 

 separately. Hogg gives the date of the ' Ingenieurs-Schur as 1731, which 

 must be "a misprint for 1631; the copy before us is dated 1630, agree- 

 ing with Murhard. A lengthy account of Faulhaber and his works wiU 

 be found in Kiistner's ' Geschichte.' Sec also Schcibel, ' Math. Biicherk.' B. 2. 

 p. 39. 



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