‘84 . PROCESS OF POLISHING AND FIGURING 18-IN. GLASS 
Tn this table the first column gives the length from centre of 
semi-diameter (y) in inches; the second and third, the corres- 
ponding magnitude of (w—a') or x, or the amount of abrasion 
required to change the section of a sphere into that of a paraboloid 
of revolution, and the 4th and 5th columns, the longitudinal 
aberration of the latter curve existing at the centre of its main or 
2 
rather least curvature ; calculated from the formula r (approxi- 
mately), and this is known to be four times the amount the same 
speculum would show (if spherical) in the telescope at its focus. 
Although in this case the relative length’ of focus to diameter is 
not by any means an unusually long one, yet, by examining this 
table, some startling truths are revealed. 
In the first place it seems wonderful that the deviation in a ray 
of light should become perceptible by the variation in the reflect- 
ing surface of one-millionth part of an inch, which is actually the 
case. 
At 4 inches from the centre the distance from the two curves 
is only that amount, and yet this produces +5 inch longitudinal 
aberration at ‘the centre of curvature, which, under favourable 
circumstances, can easily be perceived ; but, on the other hand, as 
this small variation might be produced by three strokes of the 
1, 2, and 3. 
foi 
