246 



PROCEEDINGS OF THE AMERICAN ACADEMY 



objection to this arrangement is a certain amount of lost motion, which 

 seems inevitable. 



It is not to be inferred that all periodic errors have been overcome 

 by the arrangement described above ; but experience has shown that 

 they have been very much diminished. In fact, I have never succeeded 

 in ruling but two precisely similar plates, in which there was an exact 

 coincidence of every line from beginning to end, when examined under 

 tlie microscope. In one plate of 100 lines, ruled with great care, each 

 .interval being tt^\,-^ of an inch, there are, according to three indepen- 

 dent measures made by different persons, 84 cases in which the errors 

 are less than X(j(jVTyTT of an inch, and the greatest individual error is 

 ?T?;(Jo ^^ '^" "^*^'^ ' ^"^ '^® maximum periodic error varies with the 

 different observers between jootjo ^"<JVooTTTT ^^ *" inch. 



Nobert's bands proceed by increments of 5630 lines to the English 

 inch. The following table gives the number of lines to the inch in 

 each band. 



Ubie are these Lines accurately spaced ? 



The ordinary way is to give to the head of the screw, which carries 

 the plate to be ruled, the desired movement over equal intervals by 

 means of a ratchet and pall : but this method is open to the two objec- 

 tions, that one is limited to the number of teeth cut on the disc, or to 

 an even combination of them ; and, also, that all errors of the gear- 

 cutter with which the ratchet was originally cut are transferred 

 directly to the rulings, with the addition of other errors arising from 

 want of centring, &c. 



I have employed for this purpose the following device, which, as far 

 as I am aware, is new in its application : A rigid arm two feet in 



