193 
Monficur Pouget gives feveral inftanc- 
es of the coincidence of the deductions 
from the foregoing formulz, with the re- 
fults from a€tual experiment, to about 
three places of figures; and concludes, 
that they may be relied on as fufficiently 
near for practice, where the mixture docs 
not contain lefs than halt its bulk of al- 
cohol. 
For the former of the two kinds of 
brandy propofed in the Queftion, we thall 
have, by the above formula, 






O.1801 iv 
9 mee eee ere? 
% 5 0.2304 X 0.92 
/ 1—0.92 0.1801 7 ae 


—o.5 | 
©.1152X0-92 0.2304 X 0.52 | 
©.5836, the proportion of alcohol or pur 
fpirit in the liquor. And for the latter 
0.1801 i 
0.2304 X%0.9 © 
n/ 19:9 : 
-+- te = Oa5 
O:1152XK0.9 0-2304X0.9 
©.6836, its proportion of alcohol or pure 
f{pirit. 
. ate Queftion was alfo anfwered by Mr, 
e wae 
Question XVII, mifprinted XVI (No. 
V1).—Anfwered by Mr. ©. G. Gregory. 
in the 
figure an- | : 
nexed, let us 
BNGH, be 
fuppofedto 
repreienta ; 
feétion. of .. 
an. hemi-B 


kind, #=0..— 
> 5 


O.1301 
—— 




qv 
r 
fphere, fo fituated that its axis fhall touch 
the tube 
the bafe LLM of the tube LMON, and its 
convex furface pafs through the circum- 
ference of the cther end NO. Then (as 
{pherical fegments are in furface propor- 
tional to their altitudes) we mufi, have 
€D equal to one 2oth of AD, or one 
roth of AC; and the furface of the 
fegment NDOC will be one 2oth of the 
furface of the hemi{phere : under which 
conditions, an eye, looking through an 
aperture at A, would view one zoth of 
the celeftial hemifphere. In the inftance 
before us, where AC is 20 inches, CD 
muft be 1 inch; and then, as may be 
readily found, the difference between 
CD and the axis BE is 414, inches; be- 
tween which and CD, as geometricians 
have proved, CN is a geometrical mean 
proportional: hence 4/4175 X 15;==6.57378 
Mathematical Correfpondence. 
NOY, 
—=CN, and the diameter LM or NO, of 
the tube, is 13.14736 inches. 
N.B. Mr. Emerfon, in his Aftronomy, 
page 36, fays, that a tube whofe length is 
to its diameter, as 100 to 97, takes in one 
tenth of the hemifphere : but his propor- 
tion docs not feem to be very accurate. 


The. fame anfwered by Mr. W. Adazis, 
jun. of Wooturn School., 
The length of the tube being z0 inches, 
and the feld of view one zoth of the he- 
mifphere, therefore 22 is the fegment’s 
height, by Dr. Hutton s Menfuration, p. 
19%, frit editien.; Renee 2o— eee ae 

1 adi ° 
the complete radius; and then 24/414x % 
==13.1473636 is the internal diameter of | 
the tube, by a well-known property of 
the circle. 
The fame anfwered by Mr. Fobn Haycoch, 
of Ware. 
Let LNOM be the tube, A the aper- 
ture, AC the axis, CD the verfed fine or 
height of the vifible fegment, which is to 
be one 20th of the hemifphere.—Sinee 
the furface of any fegmentis as the height, 
we have, as.19:202% 205=AC se AD, 
78 
hence NO=2,2N€=2V — k=... 
FO oie 
24/ 15600 ner : 
> = 137947 96 4nehes, the internal 
19 
diameter required. 

half their arcs, we fhall have, in the pre- 
fent inftance, {=the verfed fine of 16° 
\11’ 39’, haif the arc of the given portion 
of the {phere ; and hence, as radius: tang. 
18° 11' 39”::20:6.6573 inches the femi- 
diameter of the tube, or 13.147. the whole 
diameter required. 
This Qucftion was alle anfwered by Meffis. 
W. Clavey, F. Rusbter, F. Collins. LW. D. 
and F. Hi. 
i coat gE 
New MartrHEeMaTIcAL QUESTION. 
Question XXII.—Sy Mr. ©. G. Gre- 
ee: 
VENUs’s greateft elongation from the 
Sun, as obferved from the Earth, is found 
to be 48°: from this the young aftrono- 
mer is requefted to point out an eafy and 
expeditious method of finding the dif- 
tance of that planet from the Sun,—the 
Earth’s diftance from that luminary being 
95 millions of miles. 
NEW 
