wh? 
¢ 
1888.] 12 1 (Chase. 
quently on the Sun’s rays as ‘‘the ultimate source of almost every motion 
which takes place on the surface of the earth.’’ We may, therefore, rea- 
sonably look to them for evidences of virial efficiency, in various forms, 
which will furnish satisfactory proof of radiodynamic unity. 
379. Haual Virial Action and Reaction. 
Circular orbital velocity which is due to solar action may be represented 
by the equation 
an alabtan tO ah o 1, 
V.=V In? n 
The limiting value of »,, which it cannot exceed, is found at Sun’s sur- 
face (7), where g, isa maximum. It may be represented by 
4 _ 9 
[0 I=V Goro ee 
The third and fourth postulates lead to the equation 
i 2 
V.=Golo o. 
This equation should hold good for all values of in an expanding or con- 
tracting nucleus, inasmuch as gy varies inversely as 7? and the principle of 
conservation of areas requires that the time of rotation should vary direct- 
ly as 7. The product of the two factors should, therefore, be constant. 
880. Numerical Verification. 
Taking Sun’s semi-diameter (7”,) as the unit of length, and the British 
Nautical Almanac estimate of Sun’s apparent semi-diameter (961.//88) as 
the parallactic unit, we find, for Earth’s semi-axis major 
psel4. 457, 4, 
FEarth’s mean orbital velocity (1) may be found by dividing 2 TP by the 
number of seconds in a year (31558149). This gives 
Vy =, 0000001990099 5, 5. 
This value varies slightly with varying orbital eccentricity. The great- 
est secular range of variation, however, is less than 4 of one per cent. 
Circular orbital velocity varying inversely as the square root of the 
radius-vector, we find (2), (4), @) 
[10,] =.00000291562/, =.0006252557, 6. 
Jo==-90000039094457", Ee 
Struve’s constant of aberration gives, by (8) and (7) 
O, == otp==214.457,--497. 827. 4807727, 8. 
{,==1101876 sec.—=12.758 days 9, 
This gives for a double oscillation, or complete rotation of Sun, 25.506 
days. Laplace’s estimate was 25.5 days. The motion of sun-spots near 
the equator is accelerated by centrifugal force, tendencies to orbital velocity, 
” or some other unknown influence. Spérer’s formula gives 
“repulsion, 
24.62 days for the period at the equator, where no spots have ever been 
observed. His third estimate, for 1866, was 25.234 days. 
881. Virials of Rotation. 
The rotating «ethereal tendency of stationary motion, which is limited 
PROC. AMER. PHILOS. 80C. xxI. 114. Pp. PRINTED JULY 10, 1883. 
