Ae 
Log. + 
4796.) 
equal to the differential of the agtion on 
_ the part AHBA of the folid. 
_ XI. For example, let the two folids 
be fpheres, whereof the radii are R, 1, 
(R being that of the fiery folid); and 
Jet a=CP, the diftance of their centres, 
and AP. Oo. hen cil pS 
(2 pe Oe ed ae —), 



a r—R 
~ 0 aban KDE 
and 9X Ape am (22 Ree ae 
| p(4?—R?) wR 
—— aig 
; therefore, pXdAP=a4j2R 
p22 dn (72#—R25 
ROS ) 4 
204 Ag? 
PER fades “RNa =) 
a—R-> A x 
a Se an een ; 
| 


bas DE 
ages rer 
mae 

2a 
G?—(a—«)?) de 

Hyp. Log. 
23 
Vda per2du(x?—R?) 


ey i Oe ie ‘ 
eo MR: pide (?—R?*)(a--1)? 
Ober =a ges Chale ner eerie seen aed 
: £—R 1G joe A x 
#+R 


» the integral of which, when 
ia— < 4 3 5 
#—A--y, will give the whole action of 
the fiery globe upon the other. 
MII. But if the furface only be fup- 
pofed to communicate the heat, the effeét 
upon the point A will be given by § V; 
and if this effe&t =o, the action upon 
‘the circumference of a circle whofe radius 
=AD, will be =ox2sX AD, and the 
action upon the furface of the fegment 
AHBA=f2pox AD x dAH. : 
Let the two bodies be {pheres, then 




Bi] 
will i x Hyp. Log. a and 
eM ete 
2pPX AD xdAH =~ x 2p XAD x -- 
PARDIT sica 4 Get Re cap eRe 
pat Olle aT 
dPD x Hyp. Log. a but by the 
} : VI 
nature of the circle, PD —---.------ 
CP2_CA2_ Ap: AP xdAP 
| p = —— 
Tere ae , and dPD marae 
==. Therefore, 2pax AD x dAH= 
Rid: a 
ox Hyp. Log. ae he vin 
tegral of this expreffion is evidently = 
Rr ak 87 Rer veda 
nf ie 

_ Mathematical Correfpondence. 
- x H. 
. between - the 




OG y i v-+-R « 4/2Rar 
7a aoe x Hyp. Lo ae Ror e 
Xx Hyp. Log. (47—R?*)-1C. But when 
#—A—r, this integral ought to. be =o; 
therefore the complete integral is equal 
apr 
—— [(@@+R) Hyp. Log. (#+R)+ 
(R—«) Hyp. Log. (a—R)—(a+R—7) 

Log. (Aa-r—R)}. 
If we fuppofe that part only of the 
furface of the fiery globe, contained be« 
tween the tangents drawn from any point 
in the furtace of the other globe, to a& 
upon that point, the whole aétion upon 
the fegment AHBA will be ju one< 
fourth of the aétion on the other hy po- 
thefis: that is, its aétion will be equal 
Dea sue 
_ [(@+R) Hyp. Log. (#+R)+4 
(R—«) Hyp. Log. (w—R)—(a+R—)9 
Hyp. Log. (a+R—r)—(R—a-+r) B, 
Log. (a—r—R)]. 
Aberdeen, Fine 24. Bb. Cyewr 
Ee Se ee aon 
Question XVI (No WV). — Anfwered by 
i LMr. H.Cox. je 
Let x denote the firft man’s money; then will 
w-f4 be the fecond man’s; 3v-t1 the third 
man’s; and 2¥-+-4 the fouith man’s, The 
fum of thefe, by the queftion, is equal to G05 
that is, 43x-+-9==90, or gx-+-1°=180; hence 
x—+2==20, and x==181. the frft man’s monicy, 
confeq.ently, r2-L-4==22, the fecond man’s $ 
--i=ic,thethirdman’s; and 18 % 2-}-4=10, 
the fourth man’s. 

This Qucftion qwas allo anfwered by Meffrs... 
George Hox, Liverpool; Wm. Adams 3. Academ 
micus; N. Bofwor:4, L—t C—r; W. Clavery 3 
Oe 4 Dp - 
yi ae : : Laycey 5 
Chriflophcr Dann; Fohn Richier, jun. 5, Wr 
Roufe; T. S—_—h 3 T. Salmon; and FW, 
Pee 
poe Juv AIS, 

New MatHemaTicar QuESTIONS. 
QuEsTION XX.—By F. F. r, 
‘Treornem. If throaghany point of a great 
circle two other great circles be defcribed, at right 
angles to eacn other 3 and from two other pointe 
of the firft mentioned great circle, one on each 
fide of the point of interfe€tion, perpendiculars 
be raifed to meet the interlefting circles ; the 
the reCtangle of the tangents of the perpen- 
diculars will be equal to the rettangle of the 
fines gf the fegments of the arc intercepted 
perpendiculars.—-Required, a 

demontftration. 
QuEsTIon XXI.—Py L. WD. 
What is that nimber, whofe fquare root is 
equal to the fum of the two digits of which it~ 
is compofed; ana if from. the faid numbeis 
be fubtracted the produ& of the fum and diffe- 
rence of its digits, they will be inverted, and 
reprefegt my age in years? 
Hyp. Log. (a+R—r)—(R—4-++7) H.: 



i 
| 
| 
