4796.) 
the places from the fun; but this hy po- 
thefis is not generally true, as the heat 
communicated by a fiery body feems to 
depend upon its figure, as well as its dif- 
tance from the other body ; and as its 
laws differ very confiderably from thofe 
of attraction; I fhall therefore, in the 
prefent paper, confider the proportional 
effects of tiery bodies of regular figures, 
“upon the moft probable,hypothefes, and 
afterwards compare the conclufions with 
thofe deduced from experiments. 
That the ation of a very {mall fiery 
Podgytipon another fmall body is nearly 
in the reciprocal duplicate ratio of their 
diflance, is a fuppofition fo agreeable to 
reafon and to general experience, that 
Wwe may fafely found our computations 
upon it: but whether in eftimating the 
effect of a fiery body, we ought to confi- 
der the aétion of the whole, or only pare 
of the hody ; or of the whole, or only part 
ef the furface > are queftions which have 
mot yet been determined: we {hall 
therefore give the refulrs upon each of 
thefe fuppolitions.—It is likewife necef- 
Mathematical Correfpondences 
639 
pofed of an indefinite number of fphe- 
rical. furfaces, 
centre is P, the effeét of one of thefe 
iat DE 
furfaces (§ II) willbe equal 2px 7p 
and the differential of the whole aétion 
But as CD is 
: dAP 
alee 2px DEX AP. 
given, and from the mature of the gene- 
rating curve the relation between CD 
and AD, PD will be given, in terms of 
AP; and, confequently, the integral of 
AP 
‘AP’ 
action of the part of the folid AHBE 
upon the point 2. 
CARRS 
the expreflion 2px DEx or the 

Fig. 
| 
IV. Suppofe, for example, the fiery boa 
tary toremark, that the compofition and 4Y to be a fphere, whofe centre is C and 
refolution of forcés can no where take 
place in eftimating effeéts produced by 
heat; in this refpedt, it differs materially — 
from atttaétion. 
I]. Let P be the centre, and AP 
(Fig. ©) the radius of a fphere, and let 
it be required to find the heat communi- dAP — 
AP 
eated to the point P by the convex fue 
Pperficies of a fegment, whofe axis equals 
DE HE p= 3) tar so equal the circum- 
, ference of a circle, whofe diameter is 
unity, 26x AP will be = the cirey nfe- 
rence of the generating circle, and there- 
fore 24x APXDE equals the fuperfi-, 
cies of the fegments; and as every p(CP?—CA?) 
point in this fuperficies is equally dif- 
tant from P, the effect of the whole 1S pXAP» 
a) 2PX AP MDT DE 

rive ap : 
IIL. + Now let HFGBH reprefent a 
folid, generated by the rotation of the 
_ curve HFG about its axis HG, and let 
ADB be perpendicular to MG, meeting 
‘the furface in the points A, B; alfo let P; 
fituate in the axis GH produced, be the 
point which receives the heat from the 
body ; and from the centre P and radius 
PA deferibe the arc PEB, meeting HG 
in EF. Then fuppofing the folid com- 
px AP xdAP 
radius CA ; then will 2PCxPD ayes 
7P2- A P»—C Az 
CAtL AP pp tiene aie 
CAz—(CP-—AP)2 
2CP 
CA: (CPAP), 
CPx AP 
: p(CP2—CA2) 
ike WC 
op , and the effect of the 
part AHBE of the fphere =2p x AP— 
x Hyp. Log. AP—---- 
Hence, 2px DEX 
ae 
xdAP=ap 
x dAP—----- 




CP 
2C0P i 
But when AP=PH=CP—CA, the 
effect thould be =o ; therefore, C=— 

CP2—C A? 
2px PH ~ iw geas ei CUAT x Hyp. Log. 
a PH? 
pepe ae and the foregoing value 
2G s é 
A - p(CP2—CA?2 
equal 2p(AP—PH) Op 
~.PH?—AP? 

AG a | 2 
Hyp. Log. oq PR a5: There- 
2p 
fore, if we put AP=PG, we will have 
+ This problem may be refolved in feveral dif. 
ferent ways, but the one we have given is pro- 
bably the fimpleft, 7 ax, 
the action of the whole globe =2p(PG 
: pxPHxPG PG 
—PH)—’— Gp — x Hyp. Log. PH 

= 
= 
of which the common- 



