[Sum 
Qvestron XXKXV (No. XXII) —Anfwered by Mr. Fomes Afton, of Harringtom 
Tue furface of the given fphere is 2827 * 44, and its folidity is 14137" 2 ; and by the given 
denfities, the weight of the fame quantity of rain-water is 8181‘ 25 ounces, and that of air 
is'g' 3175 ounces. Now put a= 1728 =a cubic foot, 6 = 19640 its weigit of gold, s=the 
giobe’s furface, ¢ =the required thicknefs of the fhell, and w==<the weight in ounces; then 
aw ‘: : 
4:63. st:w, hence dst == aw, and ¢ =F; =='25458 of an inch when in water; and when 
5 x Fie 
Anfwers ta Queftions propafed. 
x ; aw - . Oc 3 . . z 
av == 9'3175, then aah eee of an inch ==the thicknefs when fwimmmg m air; 
: ee kiran sy OC an SG 
_ hence the required thicknefs is ‘254275 of an inch. 

The fame anfwered by the Rev. L. Evans, of Froxfidd. " 
- Let 30d, +5236 =m, 19640 =g, 1000 == wy 1:2 =a and x —thickaefs of the helt 
when fwimming in rain-water. Then nd? == folidity of the whole fyhere, and 2*d—2x3 = 
folidity of the cavity; therefore nd3—r.¢— 2x3 = folidity of the fhell. Whence, by hy- 
drottaties, (vd3 — 2. d —- 2x3). == wad3,, In numbers, x3—— 45x? +. 675% = I7r- 843177. 
Hence x =="2590309. And by putting y== thicknefs of the fhell fwimming in air, and pro- 
ceeding in the fame way, we have (nd3 —1.d— 2y3).g = and3. In numbers, y3 — 45)? + 
€75y = '2062118. Hence y= 00030549, and x —y =='2587255, the anfwer, 
Otherwefe thus. 
Let 30 ==d, "5236 —= 7, 19640==g, 1000== w, 1'2 == ay and <= diameter of the cavity 
when the globe is {wimming in rain-water, then md — x3 = folidity of the fhell. Now, by 
hydroftatics, (nd? —=nx3).¢—=-wnd3, Hence x= d3 saminda 29°43193; anh ae 
°2590309, the thicknefs of the fhell. Again, by making y==diameter of the cavity of the 
globe, {wimming in air, and proceeding in the fame way, we have (223 —ny3),¢ ands, 

Hence y wad fame == 29°99538, and as "00030549, the thicknefs of the fhell. The 
difference between the former thicknefs and this, is ‘2587255, the anfwer. 
Arithmitically. ; 
30)3 x *§236 X I000 
19640 
ow == 719°Srs cubic inches of gold in the fhell fwimming ic 
rain. water. . 
But 30)? x *7354 % 4 == 2327° 426, the fuperficies of ‘the globe. 
Then age” B15 = ' 254, the thicknefs, nearly, 

2827°*426 
- 30)3 + .5236'% F° 
Again, a == 863728 cubic inches of Bold in the fhell {wimming in air ; 
9649 ; 
363728 
an == *'9003054, the thicknefs ; and their difference °2.<2 is the anfwer, nearly. “ 
2827-426 3°54) x ; 253 F) . 
pe e 
Nov. 14, 1797- e Bee ~ 
This Quefion was allo anfwered by TMr. T. Hickman, * 

' Be pleafed to notice the following errata: at page 117, of this Magazine, laft line of the 
letter, inftead of *¢ infertion of it,” read ‘ infertion of this paper;’? in the exemplification of 
& 
; x : Le . 
cafe 2, fupply the denominator 4 to x?, thus, “« pees” in cafe 6, fuppiy the negative 
b ; ; 
Signy making it Aa ah 3”? alfo, at page 118, line third from the top, read * (=~ IX -> 
nh ssatiog oA | 
V/ ab=) fab.” 

Erratum in Mr. Taylor’s Tranflation from Plato. ood 
The concluding paragraph, page 32, ‘ Plato was prevented by death from finifhing, &c.”* 
fhould be read as a note of the tranflator. It is entirely through the careleffnefs of the printer 
that it has been thus mifplaced. er ee 
In page 557, the gentleman, Mr. Greenwood, who is ftated to have committed fuicide, is, ws 
are told, ftill living. The correétion reached us too late. 
END OF VOL. [¥e 
