A. Hinrichs on the Density, Rotation, and Age of the Planets, 51 : 
so that according to this law the density at the sun would be 
4+4, or 4 is the decrease in density trom the sun to the planet _ 
(in nebulous state). If we compare this law to that assumed in 
(15) we see that =n or ts constant. 
Always using the upper and lower sign respectively for the 
—— and inferior part of the ring, we find the wis wva dw 
of dm 
dw=wa(1--§)9(A=Fd8)dé dd, (21) 
if we remember that our statement of Kepler's third law gives 
#=av? (see note on (3)). Retaining only the first power of § in 
the differential, but the second in the integral, we obtain 
dw—=ualA+ (34 —9)§]d§ dd, (21’) 
or to 2a) AE = ae Hreonst (22) 
The vis viva w, of the superior part of the ring (from $=0 to 
=§,) will produce direct motion; w, of the inferior part (from 
§=£, to &=0) will produce retrograde motion; hence the whole 
vis viva producing direct rotation in the orbit is W=w,—w, or 
by (22) , 
3A—0 
=2mua(E,—F,)[o4°—“e,48) | (2s) 
As the mutual distance of planets increases from the sun we 
must supppose §,>§,, whereby the first parenthesis of (23) 
always will be positive; hence we have 
W=0,.: for. ctemg 
(24) 
if 
c= gi+5, é. 
2-+-3(5 52) 
Now, 4 is most probably constant, as stated above ; and §,, & 
being ratios, will ikewise be at least nearly constant; hence ¢ 
represents about the same quantity for all planets. Consequently 
(24) reads in words: fy 
The rotary motion in orbit will be direct, zero, or retrograde if the 
Primitive density A at the orbit was greater, equal to, or less than a 
certain quantity, c, depending on the position of the orbit in the 
i (§, and &,) and the variation 0 of the density. 
If d=o, then c=o, and consequently all planets would have a 
direct rotation, as hitherto assumed. But must according to 
all physical knowledge be some positive quantity, however small, 
as the density a in every globe of some extension Increases 
toward the center; i.e, if A is at all greater than c it will be so 
hear the center, and if at all less than c it cannot but be further 
can the center. Hence we may also read (24) in the following 
ner: 
