as are terminated by Planes , &c. 281 
These fluents being exactly similar to the one in Prop. 24, if 
we put A = arc (tang. == y x V 2k (1 +r*) x— rV) 
A'= arc (tang. = ( i-f r' a ) x — r'V) 
it is easy to see that 
A = -J“ 2 (/2 — x)} (tt — 2A) — — ( 1 4- r 2 ) x—rod 
4~ 27 Z\T 
+ {p? + 2 (£ — x)} (tt— 2A') — y ^(l + r^ i-rV 
4- corr. 
If the fluent is to begin when x = 0, no correction is necessary ; 
for at that term A == A' = - . 
When x = zk, A = arc (tang. — -7), A'=s arc (tang. =y] 
and 
A [ir— 2 arc (tang. = ~) } — ~ r + 
+ {— » arc (tang. = £) } - £ 
If we thought proper, this might still be put under a different 
form ; for r’ = and the arcs the complements of each other; 
and 7T — 2 arc (tang. == -7) = 2 arc (tang. = r) ; also tt— 2 
arc (tang. = 7) = 2 arc (tang. = /). 
Cor. 1. When the rhombus is a square, r = r = 1; and the 
action becomes A = 4&r — 8£, as we found in Prop. 24. 
Cor. 2. Let r' be infinite, then r — o, and the solid becomes 
an infinitely long circular cylinder ; and it is easy to see that 
the value of A is reduced to 2&?r, as we found before in a dif- 
ferent manner. 
The foregoing problems, which I have chosen from a great 
