360 Mr. Louis Bell on the Absolute 



series is 2 5, 2, very nearly 0* - 5, or one part in two hundred 

 thousand. 



In the case of IV. the coefficient appeared to be somewhat 

 smaller than that of S a 2 . The range of temperature secured 

 was not large, but as nearly as could be ascertained the coeffi- 

 cient is about lG^l per metre per degree, while that of the 

 standards is 17^9 per metre per degree. However, since 

 the measurements of <f> made with IV. were distributed with 

 a tolerable degree of symmetry on both sides of 20°, any 

 error due to an inexact value of the coefficient of expansion 

 would appear mainly in the probable error of <f>. The varia- 

 tion found would, as a matter of fact, have changed the final 

 value of <f> by less than 0"'2. 



The comparisons of IV. made near 20 c were as follows : — 



6. 



G = DnijS'j + 35-8 



G= „ +35-5 



G = „ +35-6 



G= „ +36-0 



G= „ +34-0 



G= „ +35-8 



G= „ +34-6 



G= „ +36-3 



G= „ +33-3 



G= „ +36-7 

 Combining these and the other observations, 



39,465 spaces = G=L>m ) S a o + 9"-l at 20°. 

 The probable error of the relations found for III. and IV. 

 can hardly exceed one part in a million so far as the distance 

 between the terminal lines selected is concerned. These ter- 

 minal lines were varied at each comparison, so that while each 

 of the above relations represents 39,465 spaces, the lines 

 measured between, though in the same vicinity, are seldom or 

 never identical. 



In gratings I., II., III. the number of spaces was very 

 easily counted, as the dividing-engine automatically rules 

 every hundredth line longer, and every fiftieth line shorter, 

 than the others. In grating IV. the number of spaces was 

 found readily enough by ruling at a known temperature the 

 terminal lines of a test-plate almost exactly a decimetre long, 

 and containing a known number of lines. A comparison of 

 this with the grating gave the quantity required. 



Calibration of the Gratings. 

 In my previous paper the need and method of determining 



