474 
A. L, Millan, giving an interefting ac- 
count of the ifle of France, where he 
now ls. ah 
Helvetius has been commented upon 
by the two greatet men of the prefent 
age, Voltaire and Rouffeau. The for- 
mer publifhed his Obfervations during 
his lite-time; and a copy of the book 
De lEjprit, with Rouffeau’s marginal 
notes, has been lately difcovered. 
The following men of letters and 
artifts, fome time fince, received THREE 
THOUSAND livres apiece, by way of en- 
couragement, fromthe legiflature : 
Brunck, editor and tranflator of fe- 
veral of the Greek poets—Deparcieux, 
natural ft—Dotteville, tranflator of Ta- 
citus and Salluft—Lebas, accoucheur, or 
man-mid ifre—Lemonnier, aftronomer— 
Mioitte, iculptor—Naigeon and Sedaine, 
men of lerters—-Parmentier, phyfictan— 
Vincent and Vien, painters—and Wailly, 
grammarian. : 
N.B. Barthelemy, uncle of the navi- 
gator of the fame name, and author of 
Le Foyage du jeune Anacharfis, alfo re- 
ceived a prefent of 3000 livres in the 
name of the Republic, a little before his 
death, 
he following have received Two 
TUCUSAND livres each : 
Schiveig-Haeufer ; Berenger; Caftillon 
(of Toloufe) ; Deforges ; Fenouillet-Fal - 
baire; Leclerk, men of letters—Gail, 
tranflator of Xenophon; Theocritus, &c. 
—Bridan, fculptor—Giraud-Kéraudon, 
mathematician—-Le Blanc, poet—Mil- 
lin. author of the Antiquities of France— 
Syiveftre-Sacy, on account of his profi- 
ciency in the oriental languages—and, 
Thuillier, geometrician. 
FIFTEEN HUNDRED livres hay 
been prefented to each of the following : 
Beitrai; Defaulnais; Imbert Lapla- 
tiere; Licble; Soules, men of Jetters— 
Devoges; Ferlus, fchoolmafers—Brion 
and Robert Vaugondy, geographers— 
Devoges; Renouv; and Vanloo, painters— 
Duvaure, a farmer—Louis Ribiere, en- 
graver—Stoutt,fculptor—Saverien, natu- 
ralift—Sejan and Miroir, organifts. 
[ Lo be continued. | 

MATHEMATICAL CORRESPONDENCE. 
To toc Editor of ike Monthly Magazine. 
SIR, . : 
O* perufing the laft Number of your 
Mifcellany, I obferve, p. 394, an 
anfiwer ot Mr. Hickman,to queftion VI, 
f.0m which I am inclined to think he has 
Mathematical Correfpondence. 

July] 
rather mifapprehended the problem. The 
defideratum ftated is, to cut a given cone 
through a given point in its fide, by two 
planes, one parallel to the bafe of the 
cone, and the other obliquely cutting 
both fides, fo that the two feétions may 
have equal areas. This problem is ca- 
pable of being folved in every affignable - 
cafe, whatever be the quantity of the 
vertical angle; but Mr. Hickman, by 
fuppofing. in addition to the conditions 
required, another, which is by no means 
fo, viz. ‘bat the tranfuerfe diameter of the 
ellipfe to be formed fall pafs through the 
given pont, has very much narrowed its 
application : it being only poffible to per- 
form this with refpeé to a cone whofé 
vertical angle does not exceed 23° 54/20", 
Our corre{pondent’s deduétion of the equa- 
; y+— 2 — Ab3r2 
tion. #3-+-2hx AR eee ei 
is perfeétly mathematical and correét; but 
had he proceeded farther in his analyfis, 
he would have found, that the only root 
which is always poffible, is ab, giving 
the circular feétion, the two others += 
2(52-Ly2) 
being fo only when 4 is not lefs than 
/11+8,/2.r, and the vertical angle 
confequently not greater than the above 
value. We fhall get a fomewhat fimpler 
expreffion for the folution of this problem 
as puc by Mr. Hickman, by uling the 
fides of the cone infiead of the perpendi- 
cular.—For putting a==LT or LH (vide 
diagram P. 394, col.i) S=TH and 
Xx (P32 tV 227) 
2 
z==LV, we fhall get x3— (24— —)27-- 
a : 
a?z==ab?, whofe roots are ==a,, giving 
I “ 
the circular fe€tion, and 2=T, x (a—é 
+4/a—bael?+44), giving the elliptical 
ones ;—the two latter roots being alfo 
pofhble only when 4 is not greater than 
(4/2—1)a. From hence it is evident; 
that no cone whofe vertical angle is 
greater than 23° 54 20” can be cut as res 
quired, if the given point be to form one of 
the extremities of the tranfverfe; bur that 
every one which is more acute may be 
thus cut by two different cblique planes, 
making with each other an angle at the 
point T, which is evanefcent when the 
angle ef the cone is of the ahove valus, 
and becomes a right angle when the 
latter is =o. : 
Mr. H’s deduction, in his 1f corollary, 
feems 
> 
