I 28 [May 18, 
Chase,] 
At Earth’s surface, Vgr = 4:9078. Tt varies as V2. Therefore (60) 
x 
Mm, Ms 
18°449? : 4:9073? 68. 
P3 8 
M, > My +: 880482 : 1 69. 
All of the results which have been drawn from (3), (56), and (57) in- 
volve the principle of persistency of vibrations, by which waves tend to 
propagate themselves indefinitely, with the velocity which is due to their 
locus of origination. 
398. Masses of Harth and Venus. 
The influence of Jupiter’s locus of incipient subsidence on the com- 
parative masses of Jupiter and Saturn, finds some analogy in the two 
chief planets of the dense belt, Harth and Venus. 
Molo 5 == Msg 70. 
Substituting Stockwell’s estimate of the secular aphelion of Venus 
(py == “1744234p5) in (69), (70). 
m, == 426750m, ya 
Hill’s estimate is 427240, which differs from (71) by less than $ of one 
per cent. The combined virial estimate of Harth’s relative mass (69) 
differs from the purely oscillatory estimate (Note 23) by less than ? of one 
per cent. 
899. Comparisons of Potential. 
In order to test the numerica) accuracy of the general equation of 
kinetic-velocities (24) we may begin with the consideration of potential 
energy, which has been largely treated in thermodynamics. Gravitating 
potential is usually measured by the height of possible fall, or of virtual 
fall, since the heights which are considered are commonly so small that 
the variation of g is insignificant. The time of fall (ta), or the velocity 
which would be communicated by the fall (2), might be taken with equal 
propriety as the basis of measurement and comparison. The cosmical deter- 
mination of Joule’s equivalent (Proc. Am. Phil. Soc., xix, 20), shows the 
importance and advantage of adopting fundamental units which can be 
readily employed in the greatest possible variety of directions, 
The general equation of fundamental velocity (24) rests on Laplace’s 
principle of periodicity, ‘‘that the state of a system of bodies becomes 
periodic when the effort of primitive conditions of movement has disap- 
peared by the action of resistances.’? Hence (3), (8). 
% =, 72 
Moreover, the natural standards of time, gravitating acceleration, dis- 
tance, oscillation and undulatory velocity which are indicated by the solar 
periodicity of synchronous rotation and evolution at Laplace’s limit, solar 
superficial attraction, Sun’s semi-diameter, and luminous radiation, obvi- 
ously give the following further equality : 
= Ug = Ve = Dy — Vg = VO» fo, 
et aS 
