36 § 
Mr Herschel on Achromatic Ohject-GlasseSo 
Looking out now opposite to 0.55 in the, first column for the 
variations in the two radii corresponding to a change of -f 0.010 
in each of the two refractions, we find as follows : 
]st Surface. 4th Surface. 
For a change = + 0.010 in the Crown, 4- 0.0740 + 1,0080 
For a change r:: + 0.010 in the Flint, — 0.0011 — 0.5033 
But, the actual variation in the crown, instead of 0.010, be- 
ing -—0.005, and in the flint, instead of -j- 0.010, being -}- 0.004, 
we must take the proportional parts of these, changing the sign 
in thci case of the crown; Thus, we find the variations of the 
first and last radii to be, 
For — 0.003 variation in the Crown, 
For + 0.004 variation in the Flint, 
1st Surface. 
— 0.0370 
— 0.0004 
4th Surface. 
— 0.5040 
— 0.2013 
Total variation from both causes. 
But the radii given in Table are. 
— 0.0374 
+ 6.7184 
— 0.7053 
+ 14.5353 
Hence radii interpolated. 
6.6810 
13.8300 
If we interpolate (by a process exactly similar) the same two 
radii for a dispersive ratio 0.60, we shall find respectively, 
1st Surface. 
4th Surface. 
For — 0.005 variation m Crown, 
— 0.0338 
— 0.5524 
* For + 0.004 variation in Flint, 
+ 0.0015 
— 0.2264 
Total Variation, 
— 0.0323 
— 0.7788- 
Radii in Table, - - - 
6.7069 
14.2937 
Interpolated radii, - - - 
6.6746 
13.5149 
Having thus got the radii corresponding to the actual refrac- 
tions, for the two dispersive ratios 0.55 and 0.60, it only remains 
to determine their values for the intermediate ratio 0.567, by 
proportional parts. Thus, 
1st Radius* 
4th Radius. 
For 
0.600 
6.6746 
13.3149 
For 
0.530 
6.6810 
13.8300 
Differences, 
+ 0.030 
— 0.0064 
— 0.3151 
We then say 0.050 : 0.567 — 
0.550 = 0.017 : : 
— 0.0064 : — 0.0022 
and 
30: 
17:: 
— 0.3151 : — 0.1071 
So that 6.6810 — 0.0022 and 13.8800 — 0.1071 ; or 6.6788 and 
13.7229, are the true radii corresponding to the given data. 
