October 20, 1873. 
THE PRESIDENT (PROFESSOR HUMPHRY) in the Chair. 
Communications were made to the Society : 
(1) On the Mechanical Means for obtaining the real 
roots of Algebraical Equations. By J.C. W. Huts. 
The general equation 
Axe” + Ax"? + &.+A,_,0 +A" =0 
having been converted (by putting cos @ or for x) into 
B,+B,_, 00s 0+ B,, cos 20... +B, cos n0 = 0, 
various methods were shewn and illustrated by means of models 
for finding the values of 0. 
I. Wheels whose diameters were as 1 : 2: 3, &., were con- 
nected together by cogs or straps. Long arms were fixed 
diametrically on their faces, which carried sliding weights. The 
values of @ corresponding to positions of equilibrium were read 
off on a dial and gave the roots of the second equation. 
II. Another method was by hingeing a number of rods 
together of variable lengths and causing them to revolve through 
angles in the ratio of 1: 2:3, &., round a fixed point in the 
first rod. This was effected by means of an arrangement of 
fixed and moveable pullies, when a pencil in the last rod passed 
through a fixed line determined by the constant in the given 
equation. The angle revolved through by the first rod was a 
root of the equation. 
In the discussion that followed, Mr GiatsHER, of Trinity 
College, went briefly into the history of this class of mechanical 
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