720 
MATHEMATICAL CORRESPONDENCE. 

' For the Monthly Magazine. 
| Concluded from our laft.] 
Waa ® the magnitude of a comet, as 
weil as of a planet, bears. a 
very {mall proportion to that of the fun, 
the preceding rule will ferve to deter- 
‘ine the heat communicated to the 
comet of 1680, which Sir Ifaac Newton 
has calculated upon a different hypo- 
thefis. . 
Ei & 2 

ig. IT.) Let E be the earth, C the 
comet, in its perihelion, and HSG_ the 
fun-: draw ECO through the earth, the 
comet, and the centre of the fun, O; 
and let E, G be the points where the 
right line EO meets the furface.. Then 
hy the rule (§ VIJ) the heat communi- 
cated to the earth, at E, is to the heat 
communicated to the comet, at C, as 

pxoOG BG Sapo er sere 
=x . : — to ———- X H. L 
mage © Pe ye 
: ; ‘EG Ze 
CL. that as, as CO Log. aa to EO 
CG 
Log. ———?6 
CH 
Now on December :8th, when- the 
comet was 1m its perihelion, the diftance 
thereof from the centre of the fun was 
to the diftance of the earth from the 
fame, as 6 to 1000 nearly ; therefore, if 
E@=100000, GG, the fun’s femidi- 
er, will be == 467-6; and CO, the 
liftance = 6oo. 
it) 
¢ 
i 
pee 
t 
Om ct 
ch om 
~ 
25h 
Hence, EG=100467.6. CG=1067.6 
EH= 99532.4 CH= 132.4 
2 H = 7 : Poti ti 
and the heat at E to the heat at C, as 






foo X Log. —— to roec0o X Log, 
99534-4- 
1067.6 
132.4. 
But Log. EG =Log.100467.6==8.002026 
Log. EHi=Log. 99532-4=4 997965 
Ene ez 
Og: =—= =o0.004061 
EH 
CO = . 600 
EG 
Co Log. —_—_ = 2 4366 
EH 

Fleat of the Comet of 1680; of Planets, re 
“FO. 
Log. CG = Log. 1067. 3.028409 
Log. CH = Log.. 132-4=2.121888 

Log. Gi = 0906522 
EO = 100000 
Cee r 
Cu = Ganga = 
IX. Therefore, the heat of the fun: 
on the earth was at that time to the heat 
of the fun on the comet, as 2.4366 to 
90652.15 that is, as 1 to 37204. But. 
according to the obferwations of Sir_lfaac 
Newton, the heat of boiling water is about 
three * times greater than the heat which 
dry earth acquires from the fummer fun ; 
and the heat of red-hot iron about three 
times greater than the heat of boiling 
Water: therefore, the heat which dry 
earth cn the comet, while in its perihe- 
lion, might have received from the rays 
of the fun, was about 4000 times greater 
than red-hot iron, which is one-third 
greater than the deduétien frem New- 
ton’s hypothefis. ‘ 
From this calculation is derived one of 
the many ftrong arguments to prove that 
the bodies of comets are folid, compaét, 

EO Lag. 

. fixed, and durable, like the bodies of 
the planets: for if they were nothing 
elfe but vapours or exhalations, in its 
pafiage by the neighbourhcod of the fun, 
it weuld have been immediately diffipat- 
ed. Ina‘fimilar manner may the com- 
‘parative heats of the pianets be deter-~ 
mined, which will differ confiderably 
from Newton’s computations+. 
X. Let us now fuppofe both the bodies 
to be regular folids, generated by the 
rotation of given curves about their axes. 
Let P be the'centre of gravity of the 
body which communicates the heat ; ” 
-HFG (Fig. I) the generating curve of 
the other body; HG its axis; A ahy 
point in its circumference ; AD a per. 
pendicular on the axis; and ler AP, CP, 
and CA be joined. Then if the whole 
body be fuppofed to aét in communicat- 
ing the heat, its aétion upon the point 
A will be given by § EFI; and, confe- 
quently, its aétion upon the convex fu- 
perficies of a fegment of a {phere, whofe 
axis (or thicknefs) =DE, and centre P, 
Let this a€tion =, and 9X dAP will be 
$n 
* This proportion is probably too great, as it- 
is the equatorial heat we fhould reckon as the 
fun’s true heat at our orbit. 
sun 
f Frncp. HI. Prop, 8, Com 4. 

equal "4 | 
