OF ARTS AND SCIENCES. 179 



III., and IV., the values in column 2 were obtained by measuring the 

 accumulated errors directly with the comparator for short lengths, and 

 the individual errors were found by successive subtractions. 



The first band of Plate I. was measured with great care with a 

 filar-micrometer made by Powell and Leland, with a glass eye-piece 

 micrometer, with a comparator screw by Merz of Munich, and with 

 the Clark screw mentioned above. The results from the Clark screw 

 are somewhat discordant, as they were obtained before the instrument 

 was fairly completed. They are, however, taken into account on the 

 principle adopted of including every measure taken. The values of 

 Plate III. were found by taking the mean of the accumulated errors 

 of each successive group of five spaces, measured directly with the 

 Clark comparator for short lengths. The separate results given 

 under the first and fourth bands of Plate I. are given for the purpose 

 of deducing the probable error of observation. They are not simple 

 repetitions of measures made at one time. Each column refers to a 

 different date. As the different sets of measures were only brought 

 together from the note-books after all the work was done, I had no 

 previous knowledge of the degree of agreement to be expected from 

 separate measures of the same space. In fact, the comparison was 

 made for the first time, soon after receiving the results communicated 

 by Professor Morley. 



