376 
EXTENSION OF THERMODYNAMIC COMPUTATIONS 
go (2. - *>) = - Cfa (T a - To) = - Pl ^ - è fo» - ?0 >) - 
pl 0 
ffil - <2o) 
must satisfy the dimensions of all these terms, as well as the 
equations P = pRT, and (&- Q 0 ) = (Wi - W 0 ) + (JJ X - U 0 ). 
(Qi ~ Qo) was derived from - (Cp a - Cp w ) (T a - T 0 ) 
+ | (<7i 2 — <7o 2 ) = — (Qi — Qo) so that it has the same dimensions 
D k- i _ , . „ P Pv 
as K = —Cp, and since R = they are the same 
as those for work, (Wi - Wo) = Pw {vi - v 0 ), and for the 
inner energy (JJx — U 0 ) = Cv (T a — T 0 ). In transformations 
from the (M. K. S.) to the (C. G. S.)system the dimension factors 
are, [.M] = 1000 = 10 3 , [.L\ = 100 = 10 2 ; in transformations 
from the (C. G. S.) to the (M. K. S.) system, [M] = 10~ 3 , 
[L] = 10 2 . All are in mechanical units. 
(4) Gravity in meters/sec, [g 0 ] = L) , , 
(Zi - zo) meters, [z, - z 0 ] = L J go {Zl ~ z °> = L = W = * • • 
Pressure, kilog./met. 2 , [Pi~P 0 ] = ML~ 1 ? [~Pi-P 0 ~| _ 
Density, kilog./met. 3 , [Pi 0 ] =ML~ 3 ) L P 10 \ L ~ 
Velocity square, [gi 2 — g 0 2 ] = L 2 = 10 4 = , 
10 4 
Specific heat, [Cp, Cv, R. K.\ = L 2 = 10 4 = 
Heat, [Qi - Qo = (Cp a - Cp 10 ) (T a - To)] = L 2 = 10 4 = 
Work, [{Wx - W 0 ) = P 10 (vi - I*,)] = ML- 1 . M- 1 L 3 — L 2 = 10 4 = 
Inner Energy, [(Z7i - U 0 ) = Cv (T a - P 0 )] = L 2 = 10 4 = 
= 10000 
= 10000 
= 10000 
= 10000 
= 10000 
= 10000 
= 10000 
The common factor for reducing all the terms of the gravity 
and heat equations from (M. K. S.) to (C. G. S.) in mechanical 
units is 10 4 = 10,000. 
From the general equations (Wi — Wo) = Pi o (vi—vo) and 
(Qi — Qo) = (Wi — Wo) + (Ui — U 0 ), we have, 
K 
10 
Ui-Uo 
vi - Vo 
Qi ~ Qq 
vi - Vo 
- P10 
r d 
which is the radiation equation employed in the computations. 
The dimensions of all these terms are the same in reducing from 
the (M. K. S.) to the (C. G. S.), the factor being 
10000 
= 10, as 
1000