W. A. Norton on Comets. 87 
of the head, the error will be slight if we regard it as a mere 
int, and conceive the nebulous matter to be repelled in all 
irections from this point. At the same time it must be observed 
that, for each expelled particle, the central eee of repulsion is 
ow the point of emission a distance equal to the radius of the 
nucleus. Again, as the rectilinear dimensions of the head of a 
comet are small as compared with its distance from the sun, we 
may, without material error for our present purpose, regard the 
repulsive force of the sun as constant. 
et N (fig. 1) be the nucleus, regarded as a point, NS the 
direction of the sun, and AB a line perpendicular to NS, which 
hi 
we will regard as the line of demarcation between the head and 
the surface of the nucleus; &= opposing acceleration, from sun’s 
repulsive force; and r= radius of nucleus, or the distance of 
the point of emission from the centre of repulsion, wherever this 
Y be. We will first undertake an approximate investigation, 
by disregarding the effect of the recess of the particle from the 
line NZ upon the repulsive force of the nucleus. This amounts 
to Supposing that the centre of repulsion moves along a line 
> ae to NZ, at the same rate that the particle recedes 
m 
Decompose the sun’s repulsive force into two components,— 
the one ong NZ, and the other perpendicular to it. former 
Will be ksina, and the latter keosa. Denoting by = the dis- 
tance passed over by the receding particle, in the direction NZ, 
many interval of time; and by v the velocity at that distance, 
we have, 
(= —& sin a)de =vdy. 
2 , 
