Fate eee [Sep mt ees a Ae Lee EE Pre a ge pe et a Caan Se SIC So eT erat eee 
Gk cee, wae ier goer et Rn RR ee te eet So eres 
Prof. Norton on the Dimensions of Donati’s Comet. 385 
* 
any point of the curve followed by the particle, to the radius- 
- vector of the orbit of the comet; v= the velocity of the par- 
ticle at the vertex of its parabolic path; and‘v’= its velocity 
at any other point of the curve; 
HH ya 
ead on ts 
vee See ~ sin 2a (5) 
aon c ny Hsin2acota_ |p, (6.) 
——=CO, a. ang parsed “Tag — og!" eee re . 
—Vkp, : fit ais, os Sele 
v Bpyae ss GZ v ae (8.) 
Wig Je(2.4%). ae es 
. a accurately, we may obtain the velocity v” at right angles 
e radius-vector, for any point of the actual curve, from the 
ion: 
following equatio 
7 cos a\ 
v= cose fepr (1). oa oe ae 
i which x= distance of the point from the radius-vector. The 
tance from the nucleus to any point of the trajectory of the 
icle, whose codrdinates are known, may be readily obtained 
the polar equation of the curve. 
Egus. (1) to (92) have been obtained on the supposition that the 
hucleus is at rest; or, in other words, they refer to the relative 
— Motion of the cometary particle and nucleus, on the supposition 
that the two have the same velocity, and a constant direction of 
Motion through space. Strictly speaking, there is not a perfect 
accordance between the two motions, even during the short inter- 
Val of time that the particle remains within the limits of the en- 
Yelope; but no material modifications of the theoretical results 
4 required on this account, in investigating the form and dimen- 
‘ions of the envelope. But when we undertake to follow the 
‘ometary particle, after it has left the region of the envelope, 
on is receding from both the nucleus and the sun, under the in- 
aah of the solar repulsion, it will no longer answer to neglect 
© orbitual motion of the nucleus 
dependent] irce; who has sh 
y, and solved anew by Prof. Peirce; who Has shown 
a the orbit of the repelled sianiels is a hyperbola convex to- 
Se the sun, and has verified the supposed law of variation of 
Sun’s force of repulsion. In pursuing the line of investiga- 
=cOND SERIES, Vor. XXIX, No. 87.—MAY, 1860. 
49 
