414 
MINUTES OF PROCEEDINGS OE 
represents the generating line drawn from a 
point P of the helix to touch the cylinder PC). 
Now the equations to the helix being 
x — r cos<£, y — r sin<£, z = #/<£,... (17) 
while that to the cylinder is 
x 2 + y 2 = cos 77 j = rp suppose,...(18) 
if we draw from the point P (x, y, z ) of the helix 
a tangent in the plane z = to (18), the 
co-ordinates of the point of contact (see fig. 3) 
will be 
Eig. 3. 
x 
(19) 
Now, the equation to the tangent drawn through the point x x y L of the 
circle x 2 + y 2 = r x 2 is 
xx i + m = r i ...( 20 ) 
And substituting in this equation the values of x l and y x derived from 
(19), we obtain as the equations of the generator, 
xr 1 cosL-^+ yr x sin^ (j> — ^ = r ± 2 } z — &r<p, . (21) 
and as the equation to the driving-surface, 
* cos ft _ 3 +2 ' sin fe _ 3 = 
r cos - 
n 
( 22 ) 
Now 
(^r) ~ cos (t — 3 (tt) = sin (t " j 
\ax/ \Jcr n) \dy ) \Jcr n) 
(?) = \ {f cos fe - d - 7 sin (^ ~ 3} > 
or, since P, {x } y } z) is a point at once in the helix and the skew surface, 
/ dF\ 1 . 7T 
Also 
