1872.] [Chase. 
2. In consequence of the equality of velocities at 7 and Ao, ¢ (the time 
of revolution) xh. If the mass (G+ ))=81, (82) °<561.043-—571.436. 
In other words, the actual : the experimental value of i : : the virtual time 
of revolution of the Earth’s centre, relatively to the Moon : the virtual 
time of revolution of the centre of gravity of the Earth and Moon. If 
ir ig 
this proportionality is exact, the value of 7 is-— Aor = 91,798,500 
miles. 
3. The greatest distance of the Moon from the Earth is about 637, and 
h 
A-+-r 
4—91,818,400. 
4. The velocity acquired by falling through /, from the distance 7--A, 
is nearly a mean proportional between the velocities of terrestrial 
rotation and revolution. If 4—569.363, 7—91,965,500 and the hourly 
QR~ 
velocity of revolution is 2>3.14185><91,965,500 ~ 8766 .153 = 65,911.77 ; 
: : 1 : : ; i pan oe 
is nearly equivalent to N58 If this equation is exact h=571.25 ; 
1) 
h+r : ae : 
3600 y 2gh—> : 8,280.6, which is a mean proportional between 
65,911.7 and 1,040.8. I can find no indication, in any of the planets or 
satellites, of a greater rotation-velocity than is thus indicated, and as it is 
difficult to conceive the possibility of such a velocity, I am inclined to re- 
gard this as the upper limit of possible value for 7, and to believe, there- 
fore, that the Sun’s mean distance cannot be greater than 91,965,500 
miles. 
ib : ; ipa ; 
5. If we take h/ a third proportional to 7 and h (h’= a ) the vis viva 
7, ? 
of rotation of an elastic particle at the Earth’s surface : the vis viva at 
h! :: the force of gravity at h’ : the force of gravity at the Earth’s 
surface : : the velocity of light : the velocity which would be communicated 
by superficial gravity in one sidereal year. 
r+h! 2 wr Bp 
497.827 gt ( —— fH} 
197. 827g¢--( — )=y NS : 
EERE p+h’)2 
*, ANT. 82Tx xT 2g. = ee : 
Vy 
72 RY yy Ler 2 OYA - F,/—88 1399 - (r op — R22 970 4- 
dati eat RT eA 
f h 
491,595,960. 
We thus obtain five independent determinations, each of which is based 
upon considerations, some of which are necessary resultants of known 
mechanical laws, while others are expressive of actual circumstances of 
equilibrium, the greatest difference between any two of the results being 
less than one-half of one percent. The experimental determination from 
the combustion of hydrogen (1), which differs less than one-hundredth of 
