238 PROCEEDINGS OF THE AMERICAN ACADEMY 



entirely a matter of conjecture. I am well aware of the risk incurred 

 in offering 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 mis- 

 taken." 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. 

 (b) . The operation of pi'oducing on glass, lines of varying degrees of 



fineness. 



If a screw is employed to give the required motion, it woidd seem 

 at first siglit very easy to reach any desired limit of accuracy. In my 

 own machine, the head of the screw, which is 11 inches in diameter, 

 is divided into 100 equal parts. For subdivisions, a microscope is 

 employed, having an eye-piece micrometer, 100 divisions of which 

 exactly cover one division of the screw-head. It is therefore easy to 

 read directly to y^^^^, and by estimation to ^^j^j^^y of a revolution. 

 Since the pitch of the screw is ^^^ of an inch, these numbers corre- 

 spond to a motion of ^4ti'o^^ and y^-^j^jj-^ of an inch. By a device 

 which I shall presently describe, the subdivisions can be carried to 

 rvii^ovxs of ^ 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 in- 

 dividual or accumulated, greater than ^ootjit iiich. I have availed 

 myself of every opportunity to measure the ordinary stage microme- 

 ters furnished by dealers in microscopes, and I find the usual range 

 of error to be between t^q^jj^ and yo^xity ^^ -''^ inch. 



Of course the average error may fall fiir witiiin these limits ; and, 

 especially when the lines are closely ruled, the individual errors may 

 seem by comparison insignificant ; but I have been unable to find any 

 rulings which invariably surpass the limit which I have named. As 

 an illustration of the limit of accuracy attainable, I give in Tables I., 

 II., and III., measurements of an excellent Nobert ditlractiou plate, a 



