542 
Proceedings of the Royal Society 
We may introduce 
( =7 = 
| jd = y = —ft) + he) . 
When the equations become for y and y , 
S 2 yp + $ 2 jp = c 2 , 
which leaves the component of p parallel to S, or to S', indeter- 
minate. 
These two cylinders intersect in the planes (j, k) and (i, j). In 
the first of these planes the equations become 
< 41) *-o« and © 2 + (v) 2=1 ’ 
an ellipse which in the next section we will meet again as Minding’ s 
Ellipse. The second intersection 
= 0 
\ac : b J 
has not received, as yet, any physical signification. 
In the case of h = 5 2 , or, as we will put it 
h - b 2 = an infinitely small value, 
the values of Y in the expression (39) of z will be real for values of 
y 2 which do not outpass the limit 
. ^ 
and therefore the “tore-surface” represented by p — p' + p " will 
shrink into an infinitesimally narrow canal embracing the hyperbola 
represented by 
p = ix + kz ' , 
where we have 
(42) y = 0 , and (L J _ (fj = 1 . 
This tore-surface, like all others represented by (39), contains 
at every one of its points one point of the single resultants of the 
system (generally four of which are passing through every point of 
space) ; and the different points of the surface represent the corre- 
