"vive 0. i 
give 0, is 
122 [May 18, 
Chase. ] 
by equations (2) and (8), gives the following value for the limiting radius 
(p,) of orbital and ethereal tendencies : 
rN 
» Ir 
P, = Ar =o, 9 10. 
{%] Von 
Laplace’s limit (7) of equal rotary and orbital velocity is given by the 
equation 
8 ) aes 
1=(%)',=()h? i. 
ml ud 
The limit at which the equatorial velocity of stationary motion would 
5 
2 1 
‘ 
18 
t\4 
3 
( t= 
To 
The limit at which the equatorial velocity of stationary motion would 
give v,, as deduced from (10) and (12), is 
Laine i 
+1, =p.+ 7 
(lJ=p,? 775 18, 
The limit of a homogeneous, elastic, ethereal atmosphere which would 
propagate undulations with the velocity of light, is 
M= = 70 [ 1} = 8 alli 14, 
382. Virial Oentres of Oscillation. 
The virials of rotating tendency must influence grosser inert particles or 
masses, 18 well as the sethereal atmosphere. Loci of important oscillatory 
influence may be found at radii of mean sthereal momentum (p,), of 
linear oscillation (pg), of reciprocal linear oscillation, ,), of spherical os- 
: ’ eo , WA ATA nAAg { 106 Wot Tale] ¢ 
cillation (pg ), and of reciprocal spherical oscillation (Pe): laking py as 
the common virial locus of these several oscillating tendencies, we have 
Roe tune 15. 
Pp 1 5a, 16. 
Py = 3p, bit, 
p, = 2.50, 18. 
At emt AN 19. 
All of these forms of action and reaction must be called into play by 
solar and stellar radiation, arid they should all be studied in investiga- 
ting the maintenance of cosmical energy. 
883. Maintained Vibrations. 
Lord Rayleigh (Phil Mag., April, 1888) discusses a vibrating system 
which is subject to dissipative forces, and the necessity, when the vibra- 
tions are maintained, that the vibrating body should be in connection with a 
source of energy. In the usual equation 
VO dé 
j . + nig = 0 20, 
dt’? dt 
—— 
