384 Prof. Norton on the Dimensions of Donati's Comet. 
ing by H the distance of the vertex of the cometary envelope 
from the nucleus ( — ie 
a’? 9H sin 2a.a’= +2Hsin2Qacota.z’, . . . . (2) 
), we have # . 
Putting Hsin 2a=K, “oe 
* 
: PPK = — 2K cota. te ee 
Let 2’=0, and we obtain for the half-breadth of the envelope, 
ga2k ; and thence, for the cdordinates of the vertex of the 
ae 3 b K 
curve described by the particle, X’=7= KX, and 7=h=>. tangs 
Transferring the codrdinates to this point, we get for the equ 
tion of the curve; referred to its vertex, 
an WON eet a 2 eS ee 
ee ‘ : : 
This is the equation of a parabola, of which the 
2p, =2K ~ a=4h cot 2a; “and the distance from the focus to the 
vertex = cot a=h cot 7a. 
parabolic projectory becomes materially modified by its repulsi? 
action, and equations (8 and (4) are inapplicable. - ae 
We may conclude from the result just obtained that, 80 far 
the form and dimensions ofthe nebulous envelope 4 “ 
cerned, the theory of a repulsion exerted by the amass of t 
nucleus does not differ materially from that of the project” 
the cometary matter by an instantaneous force from 
surfice; which, it appears, has been advocated and diseussel 
2 ¥ met 
Other determinations relative to the envelope <2 the 
ing formulas; in wl 
greatest distance attained by a particlé, in the initial directio? 
motion; Y = the actual distance from the nueleus, of 6 Se 
cle when in this. extreme position ; 9 = the angle inel ; to 
tween Zand Y; 8 = the inclination of the tangent draw? 
= the 
ch Z= sf 
