318 
Mr Barlow on the Practical Construction 
To find the contact surfaces. 
Focal length pL lens. = 3.87. Dec. part of pi. index = .'515, 
3.87 X .515 = 1.993 . . — first product, 
rad. first surface — 6.706, 
1.993 x 6.706 - 13. 365058 = dividend, 
6.706 — 1.993 = 4.713 = divisor, 
4.713)13.365058(2.836 = rad. 2d surf. 
Focal length flint lens = 6.31. Dec. part flint index = .671 
6.31 x .671 = 4.234 . . = 1st product, 
8.082 = rad. fourth surface, 
4.234 x 8.082 = 34.219188 = dividend, 
8.082 -f 4.234 — 12.316 - divisor. 
12.316)34.219188(2.778 = rad. 3d surface. 
Hence for a compound focal length of 10 inches we have the 
following results : 
| 1st surf. rad. 6.706 convex, 
Plate 
Flint 
2d do. 2.836 convex, 
f 3d surf. rad. 2.778 concave, 
1 4th do. 8.082 convex. 
Therefore, lastly, for our 72 inch compound focus we have : 
10 : 72 
10 : 72 
10 : 72 
10 : 72 
6.706 : 48.28 = 1st surf. 
2.836 : 20.42 - 2d 
2.778 : 20.00 = 3d 
8.082 : 58.19 = 4th 
focal length 
72 inches. 
The above examples will, it is presumed, be found amply suf- 
ficient to enable any practical optician to follow out the opera- 
tions given in the preceding pages, not only as it relates to the 
computation of his radii, but also for determining the index of 
refraction, and the dispersive ratio of his two glasses. They 
are in general suited to those who are but little acquainted 
with algebraical formulas, and we therefore offer no apology to 
those who are aigebraists for the length to which some of the 
calculations and illustrations have been carried, because they 
can shorten them at pleasure. It may also be proper to observe, 
that the following table is not extended from that given by Mr 
Herschel on any principle which required more than simple 
