343 
in this case is of the order 5.10“ 8 . In the case of hydrogen, for 
all the values of v — 1 considered in § 16., we find the ratio (3) 
to be about 5.10 -9 . 
Let us now consider the effect on the value of the other con¬ 
stant, Z), when equation (2), § 15., is made use of instead of (3), 
§ 15. Writing D* for the exact and D for the approximate value: 
D* _ 2 {(V + 2) (V — 1) * 2 2 - (V + (V - 1) V} 
D 
( 4 ) 
— 1)V —(^2 —4^i 2 } 
If we suppose that v 1 and v 2 are but slightly different and that 
both v 1 — 1 and v 2 — 1 are small, we get from (4) approximately 
2 )* 
~D 
i+±(v-mf) 
(5) 
where v is an intermediate value between v 1 and v 2 . As an example, 
let us take again the comparatively unfavourable case of carbon 
dioxide; let us consider a definite pair of numerical data e. g. 
A, = 4,677 ... v t == 1,0004550 
4 = 6,438 ... v 2 = 1,0004487 
If we calculate D*/D from equation (4) we find 
D* 
D 
= 1.0000737 ; 
taking v = 1,000452 and substituting in (5) we obtain 
D* 
1 ) 
= 1,000075. 
Thus the value D = 3394,3 found in § 21. would now become 
D* = 3394,6. 
In other cases the correction is even smaller. These results may 
be sufficient to show that the corrections with which we have been 
dealing here may be legitimately omitted. 
§ 23 . In estimating the significance of the results we have 
hitherto considered it must be remembered that they depend on 
the justice of an assumption which, judged a 'priori , may appear 
precarious (§ 15.) Nevertheless these , results seemed to be inter¬ 
esting in connection with a general rule presently to be considered 
(see § 24.); it was thought accordingly that something might be 
