272 L.Bell — Absolute Wave-length of Light. 



in the results. It has been the aim of the present research to 

 investigate this fruitful source of errors and as far as possible 

 to avoid the difficulties springing from it. 



In a previous paper,* I briefly discussed the advantages of 

 transmission and reflection gratings. It only remains to add 

 that further experience has convinced me that not only are the 

 speculum metal gratings far superior in brilliancy and sharp- 

 ness of definition, but that it is possible, contrary to what one 

 might suppose from their large coefficient of expansion, to rule 

 them with almost perfect uniformity, over a length as great as 

 a decimeter. This large size too, gives a great advantage in 

 determining the grating space, aside from the fact that speculum 

 metal has a coefficient of expansion not widely different from 

 that of any one of the materials usually employed for standards 

 of length, and that its temperature can be obtained with com- 

 parative ease. 



Methods and Instruments. 



The plane grating can be used for wave-length measurement 

 in a variety of ways according to the preference of the in- 

 vestigator or the arrangement of the spectrometer. Five tol- 

 erably distinct methods may be enumerated. The general re- 

 lation between the wave-length and the angles of incidence and 

 diffraction is 



A = s(sin i + sin (cp — «)) — 



n 



Where X is the wave-length, s the grating space, * and <p the an- 

 gles of incidence and diffraction respectively, and n the order of 

 the spectrum observed. Making i—0° this at once becomes 

 the ordinary formula 



A = _ s sin q> 

 n 



which applies to the two methods of normal incidence, one in 

 which the grating is kept accurately perpendicular to the col- 

 limator ; the other in which it is kept perpendicular to the ob- 

 serving telescope, 



Next is the method used by Angstrom in which 'i is not 

 reduced exactly to 0°, but measured and retained in the for- 

 mula, the grating in this case being kept nearly perpendicular 

 to the collimator. In this method a reading on the slit is nec- 

 essary, and if a and a' are the readings on the circle, and M 

 that on the slit, the working formulae are : 



a + a' , T . -, a — a' 



— I — M = o and = cp 



a 2 



* Am. Jour. Sci., Ill, xxxiii, 167. 



