642 Royal Society : — 



ively A!/^_,, A-m,_i, AX-2. an<^ ^V«-2' ^^' ^^^^ ^^^^ ''^^ digits 

 by which these numbers are represented run from left to right, as in 

 print. The mechanism is such, that by turning a handle continuously 

 in one direction an indefinite succession of movements is produced 

 M'hich are alternately backwards and forwards. The effect of the 

 forward motion is, that the numbers on the third and the fifth tiers 

 (or as they may conveniently be called the A" and A^ tiers) add them- 

 selves respectively to those on the tiers above, altering thereby the 

 positions of the wheels of the A' and A^ tiers, while the wheels of 

 the A- and A'* tiers remain at rest ; and the backward motion ^does 

 for the A' and A^ tiers what the forward motion does for the A= and 

 A^ tiers. Thus the numbers on the several tiers will be as follows : — 



At first M., ^Ux-\ ^""..-i ^X-3 ^\v-i ; 



After the forward motion .... m,. A«,, ^'Ux-\ ^^r-i ^X-2 » 



After the complete motion . . w^+, Am^. A-'mj^, A^m^_i A''m^._i' 



A*M^_j in the last term being written instead of A^«,_j, which is 



allowable, since the fourth differences are supposed to be constant. 

 Hence the effect of the complete motion, consisting of one forward 

 and one backward motion, is to make all the numbers advance one 

 stage ; and therefore by continuing to turn the handle the numbers 

 «j,+ i, «,.+3, Ux+3 ^^•' 'W'^1 ^^ calculated in succession. According 

 as these numbers are calculated they are impressed, by the action of 

 the machine itself, on a plate of lead, by means of steel punche.«, while 

 a numerator at the same time impresses beside them the values of 

 the argument .r. These plates are afterwards taken out, and stamped 

 on an easily fusible alloy just on the point of solidifying, and thus 

 are obtained stereotype plates of the calculated results, fit for 

 printing from. 



In retaining a given number of decimals, it is usual to add one to 

 'the last figure if the first digit left out be 5 or a higher number. 

 This is effected in the machine in the simplest possible manner, 

 namely by placing the cog which occasions the carriages from the 

 ninth to the eighth place in the highest tier in such a position that 

 the carriage takes place when the ninth wheel changes from 4 to 5, 

 instead of from 9 to 0. 



The principle of the machine is not of course dependent upon the 

 circumstance that the radix of the scale of notation commonly em- 

 ployed has the particular value 10 ; and it would be as easy to con- 

 struct a machine adapted to the senary or duodenary as to the denary 

 scale. Not only so, but the machine actually constructed admits 

 of being changed very readily from the denary to the senary scale, 

 or rather to a mixture of the denary and senary scales, which is 

 required in tabulating degrees, minutes, and seconds. For this 

 purpose it is sufficient to take oft' the ordinary figure-wheels from 

 those spindles which are to count by sixes, and put on spare wheels 

 which are provided, adapted to the senary scale. 

 '■ The machine works with the greatest freedom and smoothness. 



