OP ARTS AND SCIENCES. 



183 



the eye-piece micrometer, the Merz screw, and the filar-micrometer, 

 and in the remaining bands of this plate with the eye-piece microme- 

 ter only, we find the following deviations expressed in millionths of 

 an inch : — 



Number of millionths, 1 2 3 4 5 6 7 8 9 10 11 12 



Number of cases of agreement, 16 30 39 24 15 17 13 8 2 3 4 2 2 



The mean deviation is 34 ten-millionths of an inch. 



(d) Comparing the accumulated errors of the middle point obtained 

 by Professor Morley and by myself, we have : — 



Plate I. 



Plate II. 



Plate III. 



+ 31 



—38 



The numerical value of the average deviation is therefore 17 mil- 

 lionths of an inch. It is to be noted, however, that only the bands of 

 Plate I. are strictly comparable, since these only were obtained in the 

 same way, viz. by successive additions. The values for Plates II. 

 and III., it will be remembered, were obtained in my own case by 

 direct measurement, in which the degree of accuracy may be taken as 

 nearly equal to that of the measure of any individual space, while 

 those of Professor Morley were obtained by direct addition, in which 

 case an error at any point is carried through the whole of the remain- 

 ing series. 



(e) In explanation of the disagreement in the maximum values of 

 the accumulated errors, even in the bands of Plate I., which were 

 ruled at the same time, it is to be said that the graduation was done 

 before I had learned the necessity of dispensing with oil or grease as 



