Interference Methods to Spectroscopic Measurements. 293 



V = V-88V! 2 + •12V 1 V 8 cos 2ttX/23, 

 in which V 1 = 2" X2/742 [ > 62 + '38cos 2ttX/200] 

 and Y 2 = 2- X2/m \ 



the resulting distribution of light shown in fig. 17 a. 



The results of the preceding work are collected for com- 

 parison in fig. 18, Plate VIII., together with the D group in 

 the solar spectrum. From these, as well as from the curves, 

 it will be seen that it is easy by this method to separate lines 

 whose distance apart is only a thousandth of that between 

 D 1 and D 2 , and even to determine the distribution of light in 

 the separate components. The conditions most favourable to 

 high values of the visibility are low density and low tempera- 

 ture, and these conditions were complied with as far as 

 possible. Still, in many cases, the range of visibility due to 

 slight variations of the conditions show that the behaviour of 

 each substance must be carefully studied under all possible 

 circumstances of temperature, pressure, strength of current, 

 size and shape of the electrodes, diameter of the vacuum- 

 tube, &c. 



The effect of temperature and of pressure on the visibility 

 may be readily accounted for on the kinetic theory. In fact, 

 there is but little doubt that these are the chief if not the 

 sole causes of the broadening of the spectral lines and the 

 consequent diminution of visibility ; the latter cause acting 

 by altering ihe period of the source by frequent collisions, 

 and the former, by the change in the wave-length of the light 

 due to the motion of the source in the line of sight. 



If, now, the density of the vapour is very low, the second 

 cause may be ignored, and it will be shown that in the case 

 of hydrogen this is the case when the pressure is one or two 

 millimetres. 



In most of the cases investigated the pressure was so low 

 that the discharge passed with difficulty. Supposing, then, 

 the effect of collisions to be insignificant, let it be proposed 

 to find the effect due to the motion of the molecule in the 

 line of sight. If v be the mean velocity of the molecule and 

 V that of light, then the formula for the resulting visibility- 

 curve, as given by Lord Rayleigh* is h = (l—a n )/(l + a ,r ). 



If the definition of visibility as given above be taken, 

 however, this becomes 



*-*-«>[-- (?v)l 



* " On the Limit to Interference when Light is Radiated from Moving' 

 Molecules," Phil. Mag. April 1889. 



