A. Hinrichs on the Rotation, Density, and Age of the Planets. 39 
d?r (5) u 
oe, eS 
dt? dr Fh 
1 dt pop yt 
Pi dt bP 
Finally, a third approximation would likewise take the yet 
neglected term Rsiny into account; but this is in the present 
state of science altogether worthless, as observations but imper- 
fectly suffice to test our second approximation 
_ In order to integrate (1’) the function R must be known. It 
is admitted that, » being a function of the velocity v and » a cer- 
tain constant, 
=r9(). (3) 
According to Newton (Principia, Book H, Sect. VIL; Francoeur 
écanique, 5 éd, art. 228), we have for a sphere of radius @, 
density a moving in a medium of density 9, 
gn: (4) 
8 0A 
: The function @ is generally taken as v? ; but the very accurate 
experiments of Giulio’ prove that for small velocities of the 
Py of the beautiful as a means of investigating the laws of nature instead of the 
0 ics 
show the correctness of our expression we simply introduce the mean velocity 
a 
V=2r p for thereby the third (2) becomes 
a? 
p= 4? os a=aV?, 
.. rd the right cone of radius V and altitude a is of constant volume. _ 
__* It is easily understood that neglecting Resin is the same as assumio the ex- 
ty to be constant. As e now is very small, and Laplace (Méc. Oé/. Liv. X, 
chap. VIL. 8 18) ft Sg ee ae an at : plan 
he obtained PP sted 
Willd 
c= constant | ie } 
; density of ether 
Ur second approximation will be more close for future than for past ages. 
Min 1853; as most of my books are yet in Germany, I cannot cite the memoir of 
Vesti oe my abstract at hand only gives t ‘principal results of bis in- 
