32 
PROFESSOR G. H. DARWIN ON THE MECHANICAL CONDITIONS OF 
Then, by substitution in (10) and (11), we have 
We will now apply this solution to a case which will put the theory to a severe 
test. Suppose that the limit of the sphere of uniformly distributed energy of 
agitation is nearly as far as the planet Uranus, so that, say a = IQcIq. Then the 
extreme limit of the swarm is at 44^ao j orbit of the planet Neptune is at 
30ao, so that the limit is further beyond Neptune than Saturn is from the Sun. 
Now, if ala^ = 16, I find 
u = 10®'®®^^'^ cm. per sec. 
_ io' 18795(-(^ pg 5 _. annum, 
T = 10'^''^®®°® seconds 
_ ]^q 6-96899-10 ygai’S 
Introducing these values in (39) and putting -^s for I find 
V = iTllrtQ per annum = 5’374 kilom. per sec. ^ 
lO^-roio-io 
Co [wllp] 
T = 107-=^325-10 X f— 
[vjv^] [wllp] 
R = 1 06-4^9 
X/ 
Now we have in Table III. the logarithms of the several factors, which occur last in 
these formulae (41), at various distances from the centre. 
It win suffice for our purpose only to take every other value from Table III. The 
distances from the centre are expressed in terms of the astronomical unit distance, 
viz., the Earth’s mean distance from the Sun. The mean free path is expressed both 
in ihe same unit and in kilometres ; and the mean intervals between collisions in 
days. The criteria DjL and AjC are, of course, pure numbers. Table IV., as it 
stands, is applicable to meteorites weighing 3-| grammes, bat by shifting the decimal 
1 
F.(40) 
J 
Vq = u X 10 ^'®®^^® 
mjs^ 
L = I X 100-33781 
T=t X lOO- 
46863 
wAp 
mjs^ 
[t;/Vo] {wl\p] 
^ = 4 X X Fj X ” 
L la s" 
4 = 4 X 10»'W81 X F, X ? 
6 2a s" 
