OK THE ADIABATIC RELATIONS OF ETHYL OXIDE. 
183 
what form the function f{t') might be expected to have, so that we are perforce 
driven to employ an empirical formula. With a large amount of time and labour 
it might be possible to find a formula for f{v) simpler in character, and more exact 
in its results, but it did not seem worth while to undertake the amount of trouble 
involved in such a search. The formula can be successfully used for the purposes of 
interpolation within the field of observation, but any use of it for extrapolation would 
be hazardous. 
We may now write the equation for as 
785,300,000 . 317,700,000 . 3,114,000,000 
V-^ ^ 163 L pv - — ---d-^- 
This formula has been obtained as the result of four consecutive approximations, 
and it is possible that each succeeding approximation has led us further from the 
facts. On the other hand, it is conceivable that the errors of the various approxi¬ 
mations have to a large extent neutralised one another. It was thought advisable 
therefore to test the above formula by calculating out the isothermals, and comparing 
them with the observed measurements. The result is shown in fig. 4 ; and it is 
easily seen that the calculated isothermals may be fairly taken as a system of smooth 
lines passing through the observed points. 
From the equation to we obtain 
or, 
17 
E = yp 
785,300,000 
- — V 
1334-2 
, 317,700,000 
0.5 I 
- 1334-2 
,,,, , 3,114,000,000 
' _L -I' 
^ 1334-2 
dp 11 588,000 238,100 2,334,000 
Multiply by — and we get 
11, 27J _ °88,000 238,100 2,334,000 
^. 25/9 
Integrating 
, 9 588,600 , 9 238,100 , 9 2,-334,000 
Hence, 
P - ^11/9 
/,: 1,324,000 , 214,300 1,313,000 
..5/3 
+ 
.7/3 
+ 
The constant k is a-t our disposal, and we may choose it so that the adiabatic shall 
pass through any assigned point. By giving a series of different values to k we obtain a 
system of adiabatic lines. We may get a convenient system by giving to k succes- 
