W. A. Norton on Comets. 89 
supposition the formula gives nearly the same value, as when z 
is made equal to zero. Therefore let t=0, when z=0, and we 
have C= Z ; and 
ksin a 
1 oer java 28% F (6) 
ksin a pr 
V/ 2pr 
For the point X, z—-—?” Er da =e ge 
ts k sing ae ksina (8) 
_ To verify this value of T, I have made another calculation, by 
dividing the time into two intervals. The first extends to the 
instant of time when the distance becomes equal to the € part 
P 
of the whole distance, Z; during which the motion may be 
regarded as very nearly uniform, with an average velocity 
equal to V pr, The calculation for the remaining interval was 
made by the above equation (a). The result obtained is T= 
2 or 1 ik a 
Vopr(L4t 3 This differs from the above determination, by 
k sina Sal p 
Es 
only z, in the case of the comet of 1811, and about = in the 
instance of Donati’s Comet. 
2. 
To find ZX=X, we have X=$hceosa.T?=4hc0s a fa. 
Prcosa _ pr 
hia, bana oe 
But ZX=ZN x cot ZXN= * — - cot ZXN; hence ZXN=a= 
ZNB=NSZ. (Fig. 1.) Thus NX=NS; and the point of tan- 
a Fi of the path of any particle to the line ZR, lies ina 
parabola, which has N for its focus, and V for its vertex. 
As the orbits of all the particles are tangent to this parabola, 
the paraboloid generated by revolving it about its axis will be, 
approximately, the bounding surface of the head of the comet. 
(O ascertain the form of the orbit traced, on the present sup- 
tion, by any particle, resume the value of ¢, as given by equ. 
5); also take the value of ¢ given by equation x=4k cos a.t?, 
e thus get 
raat me) = 22 
ksin a ive pr 2) ~ alk cosa 
: 2g seo Qn 
tre (1 iP min) 
SECOND SERIES, Vor. XXVII, No. 79.—JAN., 1859. 
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