316 
Mr Barlow on the Practical Construction 
And then, 
10 : : 46 : 10-898 : 5013 inches. 
This arrangement would therefore give, for the four surfaces, 
1st surface = 31.510 
2d 
3d 
4th 
= 10-212 
= 10-212 * 
= 5013 
compound focus 46 inches. 
It should be observed, however, that these changes ought to 
be made as little as possible, because the tendency of them is to 
produce inaccuracy or defect of compensation ; although they 
may be introduced without a very sensible error in common 
cases. It is obvious that we might have taken a mean between 
the two contact radii, and have adjusted both the first and fourth 
surface accordingly. 
There is also another practical convenience which may some- 
times be consulted, and which, within certain limits, leads to no 
error, — this is, when the workman may have a pair of contact 
tools, which are nearly such as the calculations require. In 
this case, instead of altering his tools, he may change all the 
radii in the proportion which the radii required bears to the 
tools in question. This will make an inch or two difference in 
the focal length of the object-glass, which will be of no material 
consequence. 
Suppose, for example, that, in the last case, the workman has 
a pair of contact tools, which measure exactly ten inches, he has 
only to say, 10.212 : 10 : : 31.51 : 30.85 — 1st sur. 
10.212 : 10 : : 50.13 : 49.09 = 4th sur. 
10.212 : 10 : : 46.00 : 45.09 = foe. len. 
We have thus the following results: 
1st surface 30.85 inches. 
2d 10.00 
3d 10.00 
4th 49.09 
focal length 45.09 inch. 
Such is the nature of the calculation required for determining 
the radii of curvature in the construction of achromatic object 
glasses, and of which we may give one other example. 
4 
