OP ARTS AND SCIENCES. 187 



ruled plate from the precision-screw of Mr. L. M. Rutherfurd. This 

 plate is marked "-gVtf rev." It consists of 11 lines, covering a space 

 as nearly equal to one millimeter as the even notches of the index 

 of the screw will give this value. A transverse line subdivides the 

 vertical lines. The lines are apparently filled with graphite, and 

 they are protected by a coating of transparent varnish. 



I first measured the ten spaces of this plate in May, 1878. The 

 plate was then sent to Professor Morley. After its return, and before 

 comparing the results already obtained, it was again measured. In 

 April and May, 1879, still another series of measures was made. The 

 plate was then placed in the hands of Mr. J. R. Edmands, who is a 

 skilful and careful observer with the microscope. 



The measures made by Professor Morley and myself were of the 

 separate spaces, and the accumulated errors were found by successive 

 additions. Mr. Edmands made some measures in this way, but he 

 also measured the distance of the successive lines from each of the 

 end lines. The differences between the errors of the adjacent lines 

 were then compared with the direct measures of the spaces, while the 

 sums of the errors of the spaces were compared with the errors of the 

 individual lines. The values given by him were obtained by giving 

 to each determination its proper relative weight. 



In accordance with the prearranged plan of observation, each ob- 

 server remained in ignorance of the results obtained by the other 

 observers until the work of measurement was completed. The fol- 

 lowing are the values of the corrections required to reduce each space 

 of this particular millimeter to the mean of all the spaces. They are 

 expressed in millionths of a centimeter. 



