HVPOTHESES BEARING ON CLIMATIC CHANGES 603 
number of times this velocity a given proportion of molecules 
attain at any instant when they have certain specified tempera- 
tures. For example, the table shows that when the gas is at 
o> ©. A7 Xee, ot 47 per cent. of the molecules have a 
velocity greater than the average velocity at zero centegrade ; 
when the gas is at 1000° C., 47 per cent. of the molecules have 
a velocity 2.2 times the average velocity at 0° C.; when at 1500° 
C., the same per cent. have 2.5 times the average velocity at 
o°C.,etc. To raise the velocity of these molecules to the para- 
bolic velocity of the earth the multiplier must be about 19.8 
(since 1118127 per sec. is the parabolic velocity of the earth 
at the suriacel and miré127 —- 56522 — 19:8, nearly). ‘The table 
shows that the proportion of molecules attaining this velocity or 
over (taking the figure nearest to 19.8) is as follows: 
For 1600" 1.0) << 10,44 HOr 3200088 7-5 6 LOs2° 
Porson,” 4.0605 10735 For 4000° 9.7 X 10-%4 
RorZzoooee 7-22. lOs7 
It now becomes important to ascertain how frequently all 
the molecules, on the average, will acquire the parabolic velocity 
of the earth. Every time a collision occurs the velocities of the 
colliding particles change. The formula for the time required 
for complete change will therefore be y,, where JV is the num- 
ber of collisions per second at o° C. standard pressure, and Pm 
is the proportion of molecules having the parabolic velocity, 
given in terms of 0° C. velocity, standard pressure. 
The number of collisions per second for 0° C. standard pres- 
sure is given by Maxwell as 17,750,000,000 for hydrogen, 7,646,- 
000,000 for oxygen, and 9,720,000,000 for carbon dioxide. For 
the number of collisions for water vapor I find no authentic esti- 
mate, but it probably sustains the same ratio to the collisions of 
hydrogen and oxygen that their velocities do to each other, 
increased by a certain factor representing the effect of the size 
of the molecules. It will here be assumed that the number of 
collisions of the molecules of aqueous vapor is 10,000,000,000 
pet second ato Co standard pressures lhe results can easily 
be modified for any other figure that may be thought nearer the 
