244 PROCEEDINGS OF THE AMERICAN ACADEMY 



perfection, has rarely if ever been reached in actual practice. All the 

 evidence seems to point to the conclusion that the brilliancy of the 

 spectrum depends as much on the character of the lines, and especially 

 on the character of the edges, as on the equality of the spacing. 



It is obvious, then, that the errors which are to be the most feared, 

 both on account of their magnitude and the likelihood of their escap- 

 ing detection, are those which are periodic in their character. To the 

 investigation of the sources of these errors, in my own machine, sev- 

 eral months of careful study have been given. Without entering into 

 a detailed account of fruitless experiments, I will give only the conclu- 

 sion at which I have arrived ; viz., that the periodicity resides, not in 

 the screiv itself, hut in the mounting of the screw. The evidence on 

 this point seems to be conclusive. In a large number of separate 

 measurements extending over several weeks, substantially the same 

 system of values as those given in column III. were found. These 

 values were also constant for different parts of the screw. Conjectur- 

 ing that the trouble might arise from unequal friction between the 

 screw and the nut at different parts of the revolution, owing to the 

 want of parallelism, between the screw and the fixed way on the bed 

 of the machine, a slight movement was given to the adjusting screws, 

 which clamped the split nut. At once the system of corrections 

 was wholly changed, not only in value but in sign, and the values now 

 found, remained constant under every variety of tests applied. After a 

 few weeks, a slight movement was given to the screws holding the ^\niQ 

 against which the precision screw works as a shoulder. The sign of 

 the errors was again changed, but their magnitude was very much 

 reduced, amounting at the maximum to about ^j^j^tj of an inch. 

 This system of errors also remained, as long as no further changes 

 were made. 



Having definitely found by these and several other similar experi- 

 ments that the periodicity was not due to the precision screw itself, 

 but to the constrained motion caused by unequal friction between the 

 nut, the screw, and the ways on which the gravity slide, which carries 

 the plate to be ruled, is moved, I addressed myself to the task of 

 removing as far as possible this source of error. While I have not 

 succeeded with entire satisfliction, the errors of a periodic character 

 have been so much reduced that those which still remain give no seri- 

 ous trouble. By a device to be presently described, these residuals 

 are overcome by an automatic movement connected with the screw 

 itself. Omitting an account of many fruitless trials, I describe the 

 following permanent changes which were finally made. 



