in Buling his Test-Plates. By William A. Rogers. 75 
far as 80,000 to the inch ; the observer having no knowledge of the 
actual number ruled. Two plates in the possession of Frederick 
Habirshaw, Esq., of New York, contain bands proceeding by 
10,000 as far as 120,000 to the inch. The bands of both these 
plates were correctly counted by Samuel Wells, Esq., of Boston, as 
far as 80,000, but beyond that point the number counted was less 
than the number ruled. While the lines of the higher bands seem 
to be nearly as distinct as Nobert's, they are by no means as smooth 
and uniform throughout their whole length. 
The theory which I offer to the Academy is wholly the out- 
growth of my own experience. In the various experiments which I 
have made, I have noted the constant recurrence of certain results 
under certain conditions, and these results form the basis of my 
conclusions. Whether they form a true explanation of Nobert's 
process is, of course, entirely a matter of conjecture. I am well 
aware of the risk incurred in off'ering a theory which can at once be 
refuted by a single stroke of the pen. Nobert has well kept the 
secret of his process. If I have failed to detect it, it is easy for him 
to say, " You are wholly mistaken." Even if this proves to be the 
case, the facts developed in the course of my experiments may 
possess sufficient interest to warrant their publication. 
The problem is naturally divided into two parts : 
(a) The mechanical operation of moving the plate to be ruled 
over given and equal spaces. 
(h) The operation of producing on glass, lines of varying 
degrees of fineness. 
If a screw is employed to give the required motion, it would 
seem at first sight very easy to reach any desired limit of accuracy. 
In my own machine, the head of the screw, which is 1 1 inches in 
diameter, is divided into 100 equal parts. For subdivisions, a 
microscope is employed, having an eye-piece micrometer, 100 divi- 
sions of which exactly cover one division of the screw-bead. It is 
therefore easy to read directly to ttt^tsttj and by estimation to Tuiuiy 
of a revolution. Since the pitch of the screw is of an inch, these 
numbers correspond to a motion of ^Wo-oo- and -^-g-TyVo o of an inch. 
By a device which I shall presently describe, the subdivisions can 
be carried to tttitVotj- of a revolution. 
But nothing can be farther from the truth than to suppose that, 
because this high limit of theoretical accuracy can be reached, there- 
fore the lines ruled are separated by spaces accurate within the 
same limits. It is difficult to name the lowest limit of deviation 
from the truth which it is possible to reach ; but I have long since 
despaired of being able to rule, e. g. 100 lines, covering successive 
revolutions of the screw which shall contain no errors of any kind, 
whether individual or accumulated, greater than ^^t^^tt inch. I 
have availed myself of every opportunity to measure the ordinary 
VOL. XVI. Q 
