Theory of the Dispersion of Light. 309 
1 in 6 
~= (Ss ); 
1 sin( bie 
conegn are) 
Then developing the sine and dividing by the arc 
] 7 NS 
1 — at i] cw +,&c. 
—--_— 
De cans, iy, 23ce 
And for a first approximation, neglecting the terms above two 
dimensions, this will be easily reduced to 
re 6? Gi78 
soe sida akg 
By 6 6 A; 
whence we obtain 
iz. 
yin (1— 7) 
Ar.2 
‘San 
Hence the practical method referred to will be as follows: 
Let there be assumed a subsidiary arc $ such that 
be 
6 
log 6 = } log faya] + log sin 9. 
a, 
And since i. = sec® ¢, we have also 
log. sec. = 3} (log pw, — log p). 
These logarithmic formulas enable us to perform the ap- 
proximate calculation with the greatest ease. 
