the Rotatory Motion of Bodies. 
83 
being = — . : the radius (Vr*-k*) of tne 
♦/ d e'"zsp2.cdr¥ r F ' ’ 
s/d 
circle dl will be = 
GO 
rXcd -}- r F 
s/d x e x ^2edr? r 2 F 
L=— ; and the velocity 
. ^ 7 . ' J 
( a i on g th e faid circle dl = c % r f: the 
\V e—u\ +i/V d 
up 
per or lower of the double figns taking place according 
as u (= e q= ~j) is lefs or greater than e; that is, according 
i rf r \ 
as the arc PQ.(whofe line is = —) is lefs or greater than 
90°. 
10. As an inftance of the ufe of the preceding con- 
clufions, I will now apply them in the folution of a very 
interefting problem, which I have not before feen folved. 
Suppofe a given fpheroid , wbilft revolving uniformly 
about its proper axis , with a given angular velocity , to be 
fuddenly urged by fome percujfve force to turn , with fome 
given angular velocity , about a diameter of its equator ; it 
is propofed to explain the rotatory motion of the fpheroid 
confequent to the impulfe fo received. 
Fig. 7, 8. Let DOEQ_be the fpheroid, whofe femi-axis 
co = cc^is = b, and equatorial radius cd = ce = r; and 
fuppoling it before the impulfe to revolve about its pro- 
per axis QQjwith the angular velocity c, meafured at the 
diftance r from the axis, let the poles (o and qJ be fud- 
denly urged by fome percuffive force to turn about a 
O o % diameter 
