* 
that originally were situated in the same straight lin 
ee & Ke § ns 
doy * cg act ; ot 
142 G. Hinrichs on Planetology. 
form throughout the nebulous mass. Then the nebula 
rotate like a solid, but the angular velocity of any 
2 
will be oe 
or, by (24), A a 
As # (23) is constant for the whole nebula, we see that 
gular velocity is proportional to the square root of the densily 
“rere to (17), greatest near the center of the nebula. 
If 6 be the angle of position of those particles which 
originally (i.e. when t= 0) in one and the same straight 
have at the time ¢, 
Wee a A wR 8 ae 
or by (29) 
62 = 4.8.17, 
Remembering that the density is a inden of the 
(16) and also of the time on account of the progressing col 
sation, we see that (31) may be written, 
0? = ut?F (a, t 
t any given moment of time (¢ esate all a 
eee a” a ae 
will now form the curve 
62 = g(a), © 
. This contains the Jpmzaage principles of 
chanical theory of the spiral nebul, 
Substituting Laplacc’s law of ihe density (17) in (1) % 
we obtain as the aa of the spiral 
— 62 
wherein «=y.4.¢* depends upon the agit f (3 
A at the center, and the time ¢, whilst C =cut? depends } 
same m and tand the rate of variation of the eh We 
these spires are limited, for 0<d<a; and that the swe? 
the abe increases with the age of the nebula, the density 
Sit dies rent in different meridians, pene thé ens 
stoma in the same shell, i. e. the same in all meridians. | 
if the brightness in the nebula was Sickel! y greatest 12 & 
posite meridians AC and BC, (F ig. 1.) and it rotates 
rection of the arrow around the axis C, the spiral” 
2,) would result. As the age increases, the sweep, OF 
