2 59 
compoiuid lenses and object-glasses, 
course of his practice, and calculating on these, I find 
0*569 1 5 and 0*65617 for the corresponding values of sr, 
so that we may fairly take o*6o for its average value. 
With regard to (x and [/, their limits are much narrower. 
In crown and plate glass, we have 1*504 and 1*544 f° r ^ ie 
extreme indices, while in flint i'5735 and 1*625 are the 
lowest and highest I have met with any account of. Tulley's 
extremes are 1*5735 and 1*599, and it is said to be very 
rare at present to meet with flint higher than r6oo. In 
one specimen only have I observed a greater refraction. We 
may therefore fix on 1*524 and 1*585 for the mean or average 
values of [x and [x'. In order however to embrace a greater 
range of the function, should we be desirous of interpolating, 
as well as to provide for the possible discovery of a mode of 
making flint glass of high dispersive power free from veins, 
(a thing which it seems very reasonable to hope, and which 
the recent liberality of Government in affording facilities to 
experiments on a large scale for this express purpose, gives us 
some ground to expect ) I have computed the coefficients of our 
equations (z) and (A) for values of from 0*50 to 0*75 in- 
clusive, and the results are presented in the following tables. 
Table i. Coefficients of equation ( x ), for correcting the spherical aberration for 
rays parallel to the axis. j 
^7=0-50 2-3123 xr 1 — 15'45°5 x/r + 31-4786 X^ 1 +2-9596 *1/ — 1-1309 X,r n —o 
0 55 
o-6c 
2 * 3 i 2 3 
2-3123 
— 17-1671 
—19-3130 
+ 38-8609 
+ 49-1100 
+ 3* i8i 7 
+ 3 ' 37 ° 2 
— 1-2440 
— 1 * 357 ' 
0-65 
07 c 
2-3123 
2-3123 
— 22.0720 
—257503 
+ 63 9098 
+ 864217 
+ 3-5107 
4 - 3*5793 
— 1-4702 
— i* 5 8 33 
0-75 
2-3123 
— 3 °* 9°°7 
+ 123-1862 
+ 3*5326 
—1-6963 
L 1 
mdcccxxi. 
