Stoney— Of Atmospheres upon Planets and Satellites. 313 
where we use II for the two additional cyphers, and V for the five additional 
cyphers, which are necessary to express vw and # in C.G.S. measure.* 
Introducing this value of y into equation 6, we find 
a=g+y=9781 + 3-4 
= 981-5 em. / sec. / sec. (8) 
Again, a= M/k’, where M, the mass of the Earth, is expressed in gravitation 
units, and A’ (the potential at station H’, which is at the top of the atmosphere) 
=M/(R+h). Taking the ratio of these we get rid of J, so that it is immaterial 
in what units it has been expressed. We thus find 
ee ae _, (6878 V 
oat Raha TaS a) Z657S ve 
= 111-7830, (9) 
where /' means ‘‘the number whose logarithm is.’’ This result is expressed in 
C.G.S. measure. 
Now K’= v”/2 (see equation 4), where v’ is the minimum speed of projection 
which would carry a molecule clear away from the Earth, if the Earth were 
stationary. We thus find 
v’ = 1101500 em./sec., 
which is the same as 
v= 11:015 km./see. (10) 
Now the rotation of the Earth carries station £’ along at the rate of 
0-478 km. /sec. Hence a velocity 
v’ — uw’ = 11:015 — 0:478, 
= 10°537 km./sec., 
will suffice, if the molecule be shot off in the direction in which it is already 
travelling in consequence of rotation. And, finally, if a strong west wind is 
blowing at station 4’, which must sometimes happen, a speed of 
o' — wf — a = 10°5 km. /sec. (11) 
may be enough. This then we may take to be the least velocity which enables 
molecules to escape from the Earth. 
* The author has found it very conyenient, especially in investigations touching on molecular physics, 
to use Roman figures to represent factors consisting of 1 followed by the number of cyphers indicated 
by the Roman figure. In this way VI means a million, XII means a billion; similarly, XXI means a 
uno-twentyone, which is about the number of gaseous molecules in each cubic centimetre of air at the 
bottom of our atmosphere. 
TRANS, ROY. DUBL. SOC., N.S. VOL. VI., PART XIII. 3 C 
