119 
of Edinburgh, Session 1875-76. 
My arrangement consists of a combination of two equal modifica- 
tions of Ammsler’s Planimeter, ABC, AB'C', the wheels of which 
are attached at the joints B, B'. O' slides along AC, and the length 
of AC can be altered by turning either of the heads I), D', of coaxal 
screws of equal pitch. Now, if we suppose D connected with the 
wheel at B, and D' with that at B', by means of universal flexure 
joints (Thomson & Tait’s “ Natural Philosophy,” § 109), it is obvious 
that the length of AC will depend upon its angular position, and 
upon the motion of C' along AC. 
Let AB = AB' = a, BC = B'C'=6, AC = r, AC' = r 15 / ABC = £, 
and let 0 denote the position of AC. Then, if the whole turn through 
an angle dO , the motion of B perpendicular to CB is the same as 
if it had rotated about 0, where [_ AOB is a right angle. Hence, 
if p be the radius of the wheel at B, dif/ the angle through which it 
rotates, 
^2 ^ 
pd if/ = — a cos </> dO — ^ dO 
A similar expression holds, of course, for B'. Now, if a be the 
inclination of the threads of the screws, one right, the other left, 
handed, 
dr = p (dif/ — dif/f tan a , 
Now C' may be made to move along any curve we choose, so that 
r 1 may be any assigned function of 0. Hence, by introducing the 
constant factor 
tan a 
~w 
for r, we may give the equation the form 
dr 
dO 
r 2 — © 
