and printing Mathematical and Astronomical Tables. i!6 J 



they may, or let them be dependent on any given law what- 

 ever, are dedticible with equal ease, expedition and accuracy 

 by the help of the machine. So that, in fact, there is no limit 

 to the application of it, in the computation of astronomical 

 tables of every kind. 



I might now direct your attention to those other subjects of 

 a particular nature, to which the machine is applicable ; such 

 as tables of Interest, Annuities, &c. &c. : all of which are re- 

 ducible to the same general principles, and will be found to 

 be capable of being computed by the machine with equal fa- 

 cility and safety. But, I trust that enough has been said to 

 show the utility and importance of the invention ; an invention 

 inferior to none of the present day; and which, when fol- 

 lowed up by the construction of a machine of larger dimen- 

 sions now in progress (by which alone its powers and merit 

 can be duly appreciated), will tend considerably to the ad- 

 vancement of science, and add to the reputation of its distin- 

 guished inventor. 



I have omitted to state that this machine computes, in all 

 cases, to the nearest figure, whatever it may be. That is, 

 after the required number of figures are computed, if the next 

 following figure should be a 5 or upwards, the last figure is 

 increased by unity, without any attention on the part of the 

 operator. 



But, it is not in these mechanical contrivances alone, that 

 the beauty and utility of the machine consist. Mr. Babbage, 

 who stands deservedly high in the mathematical world, con- 

 siders these but of a secondary kind, and has met with many 

 curious and interesting results, which may ultimately lead to 

 the advancement of the science. The machine which he is at 

 present constructing will tabulate the equation /^ti z =c: con- 

 sequently there must be a means of representing the given 

 constant c, and also the four arbitrary ones introduced in the 

 integration. There are five axes in the machine, in each of 

 which one of these may be placed. It is evident that the ar- 

 bitrary constant must be given numerically, although the num- 

 bers may be any whatever. The multiplication is not like 

 that of all other machines with which I am acquainted, viz. 

 a repeated addition — but is an actual multiplication : and the 

 multiplier as well as the multiplicand may be decimal. A 

 machine possessing five axes (similar to the one now con- 

 structing) would tabulate, according to the peculiar arrange- 

 ment, any of the following equations : 



A 5 «* = au x + i A*u x = au x + 2 



A 5 «, + i «= au x + A J «x A s m» + i= flA*M*+i -I- A 4 u x . 



If 



