358 Mr. F. Daily on Mr.Babbage's newrMackmeJbi' calculating 



and comprise, in one octavo volume, double the quantity of 

 the French tables. Another volume, of the same size, which 

 is announced by the same author, will render these by far the 

 most valuable of their kind, provided their accuracy can be 

 relied on. The quantity of mental labour saved, in the con- 

 struction of such tables, by the help of the machine, is literally 

 infinite : for, in fact, no previous calculation is at all requisite; 

 and it will be necessary merely to put into the machine, at the 

 end of every two pages, the number whose multiples are re- 

 quired. This number will be successively 1, 2, 3, &c. ... to 500. 



2°. Tables of Square Numbers. The squares, of all num- 

 bers, as far as 1000, were a long time ago published on the 

 continent by M. Lambert. These have been since extended 

 as far as the square of 10,000 by Mr. Barlow of the Royal 

 Military Academy at Woolwich. The Board of Longitude" 

 employed the late Dr. Hutton to calculate a similar table as 

 far as the square of 25,400. In computing a table of this kind 

 by the machine, even if extended to the most remote point 

 that could be desired, the whole of the mental labour vvould 

 be saved: and when the numbers 1, 1, 2 are once placed in 

 it, it will continue to produce all the square numbers in suc- 

 cession without interruption. This is, in fact, one of those 

 tables which the engine already made is capable of computing, 

 as far as its limited number of wheels wiil admit. 



3°. Tables of Cube Numbers. Tables of this kind have 

 likewise been already computed by Mr. Lambert and Mr. 

 Barlow ; and also by the late Dr. Hutton, by order of the 

 Board of Longitude. In computing such a table by the ma- 

 chine, the whole of the mental labour would be in this case 

 also saved: since it would be merely necessary to place in the 

 machine the numbers 1, 7, 6, 6 ; and it would then produce in 

 succession all the cube numbers. 



4°. Tables of the higher Powers of Numbers. The Board 

 of Longitude employed Dr. Hutton also to construct a limited 

 table of this kind ; which should contain the first ten powers 

 of all numbers from 1 to 100. And Mr. Barlow has published, 

 in his collection, a table of the fourth and fifth powers of num- 

 bers between 100 and 1000. Should it be thought desirable 

 to re-compute or extend these tables, the whole labour may 

 be performed by the help of the machine, except the few 

 figures required to be first placed in it; and which might per- 

 haps occupy the computer about ten minutes for each power. 

 In fact, the computation of these lew fundamental figures would 

 not occupy so much time, nor be so liable to error, as the cal- 

 culation of one of the tabular numbers, according to the usual 

 method. 



5°. Tables 



