



pxPHx?PG 
Weer 
of the fegment AHBA= 

640 
H(PG— PH) 
— 

SEP TP XE AS = - oe a 
i PG 
| x Bye E-bay: 
If the point P touch the globe, PH 
will be =o; and the heat communicated 
to P=2pxCA, or directly as the radius 
of the globe. : 
“WV. Jf the furface of the folid alone 
communicates the heat, the inveftigation 
and the refult will be different. For if 
if HAGB te the folid, and P the given 
point (Fig. T) the action of the circum- 
ference of the circle, whofe radius is 
i ; po AD 
AD, will be cqual to nae, and the 
differential of the a€tion of the furface 
2px AD 
Be 
dAH, Now in this cafe, if the folid be 
* CA»xdPD 
a {phere, dA will oe equal AD’ 
ADxdAH + 
bur PD=o ae ae ppt 
APdAp  @e2CP 
Seo therefore, 2px —-___ = 
2pxCA dAP : x 
eps > "AP? and the integral equal 
ap XC Age 
a -X Hyp. Log. AP+C.- When 



and 2p 


AP=PH, this expreffion fhould be =o; ; 
coniequently, the correct integral = 
A B 
2pXCA AP 
—ep x Hyp. Log. oa? and the ac- 
I iE 
tion of the whole fpherical furface = 

2p MICA PG rt 
cP ee Hyp. Log. DH 
Vi. Now as PG=PC+CA, and PH 
PG PU On 
- = PG = OA — : 1a} Se = 
PP. reo 
fee es one 
o CAM PG 
a, aud oa a ek lt): 7 
—— | CP 2 PH 
25x CA ‘tap a, 
“ep x lg eee oa But by the 
BCP 
Mathematical Correfpondences 
y 
[ Sept. 
nature of logarithms, the Hyp. Log? 
Pees Wi 
¥ ence ts » ‘ 
eC < 2CA iC ae & 
————_ 5s = See cr oe SRE oe é 
CA PC. ' 3PGs) eee ae 
and the a¢tion of the whole furface = 
(CA? CAs. iC AS 
~~ + =~ +——, &c. } When 
4b | Gpalt 3eRa 7 ype ) 
the radius CA bears a {mall proportion 
to the diflance PC, the whole action will 
- Az = = 
Cr ar 
ly, the heat as the fquare of theif 
tance: which is the very principle upon 
which our reafonings were grounded,--~ 
This rule will anfwer pretty accurately, 
when we want to compare the héat of 
the different planets with each other. 
When P coincides with H, the expref- 
fon becomes infinite. _ 
VII.-But there is another hypothefis. 
which appears more probable than any 
of them: that is, that the peint P re- 
ceives its heat from that part of the fur- 
face only which is contained between the 
tangents drawn from the point to the 
furtace of the fphere. In thus cafe, AP 
be nearly =46X , and, confequent 
' =P, and by the nature of the circle 
PF2=PG x PH; but the action of the 
fuperficies of the fegment FHF (§ V) 

Lape PE pxea 
is) == Cp Dae ele Log. Pa Pee 
PRAOn pa Cas 
él af oo SS >. . « 
x Hyp. Log. Pin ve x Hy. Log 
PG 
peel ghee x Hyp. Log. ——. 
co 8 rc. ee 
Ti 1s obvious that this laft expreffion! is 
juft half the preceding, where the aétion 
of the whole furface was confidered. «, 
When P coincides With Hy, this ex« 
preflion likewife becomes infinite. 
(To be continued} 
Aberdeen, Fune 24. f. CWGNI. 
** The Conclufion of this valuable Paper; 
as well as the new Quefiions, and tbe 
Anfwers 10 the former ones, are deferred, 
for want of Room, till our, Next. 
# OO; Cop KR RES PG NDE Nees. 
THE wery curious Papers relative to the Marches of Wales—The ingenious Effays on the 
Chara&erifics of Posi Anti Magione D. C. in reply to ¢ A Woman’ —Tbhe interefting 
Letter of Sarah Bockett—A Poor Northumbrian on Large Farms—N, 0. in reply to 
“« O. N.”—T.S.A.T. on Oratory—The Sonnet figned Y—the Poetry, by W. R.—the Reply 
of © A Woman’ to“ C. D.?—A Layman on Tythes—dnd fome other accepted and valuable 
Communications are unavoidably deferred—frveral of them on account of their great Lengths. 
Zs the Paper of W. T. jun. original ?—The frequent and the continued Correppondente 
of all other Literary and ingenious Friends will be thankfully accepted. 
