Z08 Prof. Powell’s Formula for the Dispersion of Light 
This last elimination is easy, and gives as the relation sought 
the following : 
Ss 1—+t Ss 1-—t 
eee ¥ Be Ry ee gt or (20.) 
be so pute ih ei stead 
This relation may be expanded by substituting the values 
(14.) and (15.) so as to put it under the form, 
( (+p ~Fs) (TH wuin e) (TR —T;) ae 
0 = 2 —(up—Hp) (ta —*5°) (75°73) (FH — 75’) r fet) 
L4(@u—Fs) (tr’—TB°) tp’ — TB’) (te TD) J 
and in this way the relation (20.) may be verified, as it will 
then be found to be satisfied independently of the three me- 
dium-constants a) a, a, by the expression (13.) for the four 
indices. 
Now, to proceed to the actual calculation, we have Fraun- 
hofer’s values of A for the standard rays; these are obtained 
from interference, and are absolutely independent of any me- 
dium. Now if ¢' the time which light takes to traverse a 
given length J' zm vacuo, will obviously have 
t! hal EH 
Pie KE 
If then we take ¢’ as the unit of time, we have for the time 
of a vibration 7m vacuo 
Aa 
T= i ih 
Thus if 7’ = ,5455 inch, since by Fraunhofer’s observa- 
tions we have ~ = ‘00002451 inch, it follows that we have 
axis "BABL aa similarly 
tp = 2175 tp = "1794 ty = 4G. = (22) 
Now, there is a circumstance which may be remarked 
among these numbers, which affords a considerable facility in 
our calculation. The square of +, will be found to be almost 
exactly an harmonic mean between the square of the extreme 
values t, T,,: or we have 
te? = 2 (ty + 73) (23.) 
so that in the notation of 5.) 
yee (24.) 
