OF ARTS AND SCIENCES. 243 



It is quite evident that in the three cases under consideration, there 

 are numerous accidental errors amounting to ^y^oo ^^ ^^^ i"^^^ *"d 

 more, while in the last case the evidence of periodicit}' is very decided ; 

 its value at the maximum point being ggVo ^^ ^" inch. An exam- 

 ination of the values in Tables I. and II., column IIL, will show how 

 easy it is to be misled by a seeming accuracy when only consecutive 

 spaces are measured. It is only when the errors become magnified by 

 successive increments that they attract attention. 



The following will be found a very convenient and accurate method 

 for measuring directly the magnitude of the periodic errors. 



First, a series of equidistant lines is ruled on thick glass, care being 

 taken to use glass having a plane surface. It is better also to have 

 the spaces correspond to equal parts of a revolution of the screw. On 

 one side a heavy finding line is ruled. This band is then reproduced 

 on microscopic cover glass, having a thickness of about y^^ of an inch. 

 Of course care is taken to use the same part of the screw, and the 

 same divisions of a revolution as before. By cementing the glasses 

 together with balsam, face to face, but with the finding lines coinci- 

 dent and on opposite sides, the periodic errors, if they exist, will 

 appear under the microscope with twice their real magnitude. 



In this way it is easy to measure not only the maximum value, but 

 the values corresponding to every division of the screw-head. If an 

 objective of high power is employed, care is necessary to have the 

 surfaces of both j^ieces of glass as nearly plane as possible. Mucli 

 better results are obtained by using a piece of cover-glass not larger 

 than -jJg^ of a square inch. 



Mr. John M. Blake, of New Haven, did me the kindness to i^hoto- 

 graph on cover-glass, the plate whose measures are given in column 

 III. By reversing the plates, in the way indicated above, he found 

 almost precisely the same value for the maximum periodic error 

 deduced above ; viz., ^xrVo of an inch. 



In passing, it may be interesting to note that though the lines of 

 the Rutherford j^late are more distinct than those of the Nobert plate, 

 and though the errors of spacing are considerably less, yet the former 

 was rejected from the start as an imperfect one, while the latter gives 

 excellent results, yet both plates will show with about equal distinct- 

 ness four lines between the components of the magnesium line b. This 

 is hardly in accordance with the theory that the optical test of paral- 

 lelism of lines, and of equality of spacing, is far more perfect than the 

 test of actual measurement. It is evident that the theoretical limit of 

 accuracy required, in order to produce the solar lines in the greatest 



