1706.7 
locity was 45 miles per hour, was 9,963 lbs. 
avoirdupois : whence, by making ufe of the 
ptinciple before laid down, the velocity cor- 
refponding to the force given in the quefticn,.1s 
readily found to be 45,033 miles per hour. 
For more upon this fubjeét, the reader may 
confult the articles ANENOMETER and WIND, 
in Dr. Hutton’s Distionary above mentioned. 
This Queftion was alfo anfwered by Mr. J. 
H——r. : 
The fame anfwered by . Cygni. 
Suppofe the fluid aéting againft the board to 
be water, and its velocity meafured by the {pace, 
it would move uniformly over in a fecond of 
time==v; then will the force of a ftrcam of 
water, moving with this velocity, be equal tc a 
column of water, whofe baie is the fection of 
the ftream, and height the fpace defcended 
through by a falling body, to acquire this velo- 
city. Wherefore if g=16,1, and /=the height 
of the column, we will have 24/2 g==v, 
b2u? Lapyiiepse 
,o? being 

2 
kU , and the whole column 
; : o 
42 ne 
equal to the furface of the board in f{quare fect. 
Then putting m==the weight of a cubic foot of 
water, and “=the weight of a cubic foot of 
Wi 



b Y . : Bren f2yz 
alt, in avoirdupois ounces, m 1s tO” as_— 
4f 
I 
2d ‘ 
to ee = the force exerted againft the 
4” 
board by the air, exprefied in cubic feet 
I 
mbhruy 2 Gis) 
ef wate: : therefore . Xm=athe force 
478 
‘ I I 
g mh2u2 m  mbrvr 
in ounces, and ie a ea Ee: 
amg" 16 64g 
force in pounds. Hence, by the conditions of 
I 
27,2 
the queftion, “° * — 1o pounds = 4, 
64.2 
which is a general rule for all 
nd 
oe Re Ags 
. b I 
; m 
queftions of this kind, when the air blows di- 
tectly againft the board: in the prefent cafe, 
! I 
a—=10, b=1, and m=}; therefore v = 8 
a/ 128 2==16 4/ 321==90,7492 feet, the ve- 
locity of the wind, or the {pace it moves over 
im one fecond. 
' Cor. Itis difficult to determine accurately 
by experiment the force of the wind. The 
moft proper inftrument for the purpo e feems to 
be that invented by the ingenious Mr Bouguer, 
depending upon the aétion of a fpiral {pring 
he Bb SYeNr. 
QuUEsTION Il.— dnfweredby Mr. 7. EH. 
_ Let the annexed figure © 
teprefent a ftereographic 
Projection of the {phere 
on the plane of the meri- “3 
dian; in which HPRQ \ 
is the meridian, H R 
the horizon: EO the 


T. 
Mathematical Queftions. 

216 
equator; P§ the fix o’clock hour-circle, or 
meridian perpendicular to the plane of projection 5 
B and C the places of fun-rife at equal and con- 
trary declinations, or when AB is equal to CD, 
Then, in the right-angled {pherical triangles 
AOQB, COD, A Bis by confiru&tion equal 
to C D, and the oblique angle AOB=COD ; 
therefore the whole triangles are equal and fimi-. 
lar; and, confequently, A O==O D, or the angle 
APO=OPD; hence then the angle EP A 
==CPR, and the angles EPC-+-EPA=EPC° 
+-C P R==2z right angles; confequently, the 
fum of the lengths of the two days when the 
fun has oppofite equal declinations, are always 
equal to 24 hours, without confide! ing refraction. 
This Queftion was allo aniwered by Mr. 
O. G. Gregory. 
ea 
Question III. dnfwered by Mr20. G. Gregory. 
In this queftion, -as I underftand it, it is re- 
quired to find, from what height a heavy body 
mutt fall, in a non-refifting medium, to acquiie 
a velocity of 1500 feet per fecond. For if we 
withed to determine, how far it muft fail in the 
open‘air to acquire fuch a velocity, we fhould 
find ourfelves at a lofs, as all the theories of the 
air’s refiftance hitherto given, are erroneous 2 
though we are in hopes we fhall fpeedily have 
better affiftance inthis refpet; for the experi- 
ments catried on with fo laudable a motive, 
formerly by Mr. B. Robins, and now by Dr. 
Hutton, have contributed much to the removal 
of the almoft infuperable obftacle which ftood in 
our way. 
Let 2 be put for the diftance between the 
place fallen from and the earth’s centre, r for 
the earth’s radius, g for 16), and'v for 1500, 
the velocity acquired by falling. Then, by Dr. 
Hutton’s Conic Seétions, and Select Exercifes 
(where queftions concerning forces are handled 
in avery fcientific manner) page 182, we have 
Wr/ 4g7 x a—r* 

whence, by redu@tion, 

a 
: ved v2 : 
we obtain a—=" ==. ——. nealy=—Ga 
A ier Ora) 2 AU eh 
this cafe) 34974 feet, or 6.62385 miles, the 
height the ball mutt fall from. Or, a fimilar 
conclufion might be obtained by following a 
different method. 
This queftion was alfo anfwered by Mr. J. 
H-——=1, and Mr. Wm. Vaux. 
EEE 
Question 1V.——4,/wered by Mar. B. F. 
The rule given for this purpofe,. by Mr. Kir- 
wan, is as follows: ‘* Multiply the degrees of 
heat neceffary to reduce any jolid to a fluid flate, 
by the number exprefling the fpecific heat of the 
fluid; divide this product by the difference be- 
tween the numbers exprefiing the fpectfic heat 
of the body i each ftate; the quotient will be 
the number of degrees of temperature, reckoned 
from abfolute privation of heat.” 
So, in the prefent inftance, where itis re- 
quired to determine how many degrees of refri- 

* Note. ihis expredion is maccurately printed 
U=/42)X —r i the book above quoied. 
— aw va 
1 
Yr 

