74 PROFESSOR W. THOMSON ON THE 
of the Sun being about 1} times that of water, the matter in a pyramidal por- 
tion from his centre to a square foot of his surface is about 
1 x 441,000 x 5280 x 1} x 64 = 62,100,000,000 Ib. 
and the whole annual addition of meteoric matter to the Sun would there- 
fore be 
1900 1 
62,100,000,000 ~ 32,400,000 
of his own mass. In about six thousand years the Sun would therefore be aug- 
mented by sdoo in mass from extra-planetary space. Since the time occupied by 
each meteor in falling to the Sun from any distance would be much less than 
the periodic time of a planet revolving at that distance, and since the periodic 
times of the most distant of the planets is but a small fraction of 6000 
years, it follows that the chief effect on the motions of the planetary system pro- 
duced during such a period by the attraction of the matter falling in would be 
that depending simply on the augmentation of the central force. To determine 
this, let M be the Sun’s mass at any time 7, measured from an epoch 6000 years 
ago; the Earth’s mean angular velocity, and a its mean distance at the same 
time; and 2 h the constant area described by its radius vector per second. Then 
we have— 
wa= 2 , (centrifugal force) 
w a2 =h; (equable description of areas) 
from which we deduce, 
and a 
Now, if M, denote the mass of the sun at the epoch from which time is reckoned ; 
since the annual augmentation is about s5;¢h999 Of the mass itself, we have 
32400000 
u t 
met ri (2 : sx-aur000) 
Qt 
and 2—M2 eet ia 
ees (1 £ 35,200,000) 
Hence, if o,and , denote the angular velocities at the epoch and at the present 
time, T; the angular velocity, which is uniformly accelerated during the interval, 
will have a mean value, 0, expressed as follows :— 
a=1(s Be =o, {1-3 ==} = 2 > la 
and if © denote the angle described in the time T, we have 
ite 
© = Ay (7 pe 
32,400,000 
