92 B. V. Marsh on the Distinguishing Features of Comets. 
S.—a6 a straight line passing through S and meeting the curve in the 
points a and 6, and making but a very small angle with AB. 
Let t= time occupied by the comet in passing from a to A. 
v— « “ “ “ “« 6 to B. 
= light and heat received in a given time by the comet at a. 
v= «& “ “ 6 6“ b 
Then since the angle BSd is very small we may without material 
error assume that Sb== SB, Sa=SA, and that the sectors BSd and ASa 
are to each other as the triangles BS6 and ASa. Also consider / and J’ 
constant during the times ¢ and ?¢’ respectively. 
Then since the radius vector describes equal areas in equal times, 
t: tt: sector ASa:sector BSb:: triangle ASa: triangle BSd::Sa?:Sb%. 
Therefore ¢: t”::Sa?:Sb2. But since the light and heat received in. 
& given time vary inversely as the square of the distance, | 
"20 3: Sa? : $2 
Therefore, ger PR EA 
and hence, thee TI’ 
But i! represents the total amount of light and heat received by the comet 
in passing from @ to A; and ?'l’ represents the total amount of light and 
heat received by the comet in passing from 6 to B, and since, if for AB 
nd ab we substitute any other two straight lines intersecting each other at 
a very small angle in S, the same reasoning will apply, it follows that the 
whole amount of light and heat received by the comet while passing from 
D, through its perihelion at A, to C, is equal to that which it receives 
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sae open 
during its passage from C, through the aphelion point B, to D—and 
“since the times occupied are to each other as the areas of the segments — 
DAC and CBD, the ratio which these areas bear to each other affords @ 
“@ measure of the average contrast in the amount of light and heat re 
ceived by the comet in a given time on the two sides of the line CD 7 
that is, in what we may for convenience term the aphelion and perihelios 
‘ hac 3 
rae rr 
of its orbit respectively. So that this ratio seems to furnish the fait 
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