Ay aX4 
Chase.| 602 [April 18, 
448, Phyllotaay in the Asteroidal Belt. 
Kirkwood (Proc. Amer. Phil. Soc., xxi, 266) in discussing the gaps and 
clusters of the Asteroidal belt, says: ‘‘In three portions of the ring the 
clustering tendency is distinctly evident. These are from 2.35 to 2.46, 
from 2.55 to 2.80, and from 8.05 to 3.22; containing forty-three, ninety- 
six and forty asteroids, respectively. We have thus an obvious resem- 
blance to the rings of Saturn; the partial breaks or chasms in the zone 
corresponding to the well known intervals in the system of secondary 
rings.’’ He accounts for the gaps by the periodic harmonic perturbations 
of Jupiter, but he gives no explanation of the clustering tendency. 
If we take ,%, 4, and $ of Jupiter’s mean distance, we have 2.401, 2.601, 
8.252. The numbers 2 x ,';, }, and gare all phyllotactic. The first of 
the clusters, 4;, seems to indicate a harmonic connection with the primi- 
tive rupture of the Uranus-Neptune belt which was pointed out in the 
foregoing note. 
449, Constant of Aberration. 
Magnus Nyrén has published, in the Memoirs of the St. Petersburg 
Academy, a valuable paper on the determination of the constant of aber- 
yation. A summary of his results is given by A. M. W. Downing, in 
The Observatory, vi, 865. The value which has long been accepted by 
astronomers is 20//.445. Struve discussed the possible sources of error, 
some years after the publication of his memoir, and adopted the value 
20/463. Nyrén deduces, from three different sets of observations at 
Pulkowa, 20//.492 4- 0//.006, which Downing thinks ‘‘must be an ex- 
tremely accurate value of this important constant, and will probably have 
to be considered final until it can be corrected by an equally accurate and 
extensive series of determinations made in the southern hemisphere, Such 
a determination is, at the present time, a desideratum in astronomy.’’ 
450. Succession of Harmonic Mass Influences, 
According to the foregoing notes, the first harmonic influence in the 
determination of relative planetary masses seems to have been that of 
simple subsidence, represented by the cubes of masses. Next was the 
simple product of mass by distance, representing the beginning of the 
change from static to rotary equilibrium. Then came the product of mass 
by the square of the distance, representing nebular rotary inertia. This 
was followed by the quotient of mass by the square root of distance, rep- 
resenting simple orbital momentum. These relations seem so natural and 
go important that it may be well to give the calculations in detail, for 
future reference, and also to extend those calculations to the most import- 
ant linkages which have been indicated among the different planetary and 
satellite belts. ‘ 
451. Simple Subsidence. 
There are three planetary illustrations of the determination of mass by 
simple subsidence ; 
1. In the Neptune-Uranus belt (Note 438) the mass of the belt (am, +- 
