254 Mr. Barlow on the rules and principles for 
Experimental examination of the limits within which an error 
in spherical aberration and dispersion may have place , without 
producing a sensible defect in the object-glass . 
17. Although I feel convinced that the method we em- 
ployed for measuring a tool, would give us a true result 
within ^^Q-th part of the radius, yet it by no means follows 
that a new tool can be made within the same limits to meet 
any computed radius. In fact, if all the accuracy of radii 
were requisite which the strict theory requires, it would be 
almost impossible to construct an object-glass that would 
bear a practical examination ; fortunately, however, this is 
not the case ; some scope may be allowed, without any very 
sensible change in the performance of the telescope ; and to 
ascertain within what limits it was necessary to confine the 
error, was the object of the following experiments. 
Experiment 1. 
18. According to the preceding computation (art. 14), we 
ought to have for an 80 inch focus the following curves ; the 
index of the flint being r6oo, of the plate 1515, and dis- 
persion ' 66 , viz. 
r = 28* 91 , ] 
, h P^te 
/ ” — * 27* 2 j J 
J y compound focus 80 inches. 
r =— 27-191 
r"' = — 271- 9 j’ flint _ 
Messrs. W. and T. Gilbert had by them two tools, which 
upon accurate measurement were found to be 26*4 and 264, 
