292 Mr. A. A. Michelson on the Application of 



in fig. 14 b, Plate VI., is a close approximation to the^ truth. 

 Neglecting the effect of a line of feeble intensity at a distance 

 of about '24 from the principal line, the distribution of light 

 in the source is represented in fig. 14 a, which gives for the 

 visibility-curve 



V=J v/3V x 2 + V 8 8 + 6V X V 2 cos 2ttX/28, 



in which y i = 2- X2 / 2002 and V 2 = 2- X2/2602 cos -5/280. 



Fig. 15 b, Plate VI., represents the results of observa- 

 tions on the upper yellow line, omitting some peculiarities 

 due to the presence of one or more lines of feeble intensity. 

 The curve agrees closely with the formula 



V=J V3V! 2 + V 2 2 + 6Y 1 Y 2 cos 2ttX/70, 



in which V 1 =2- X2/1832 and V 2 = 2" X2/126 ' 2 , which represents the 

 visibility-curve produced by two lines of intensities 1 : 3 and 

 separated by 0'019 divisions as shown in fig. 15 a. 



The green mercury-line is one of the most complex yet 

 examined. Tbe constituent lines are nevertheless so fine 

 that the interference-bands are frequently visible when the 

 difference of path is over four tenths of a metre. The full 

 curve in fig. 16 b, Plate VI., gives the results of observa- 

 tions corrected for personal equation, while the dotted curve 

 represents the equation 



V = 2- X2/23 ° 2 V-69V! 2 + -03V 2 2 + -28V!V 2 cos 2ttX/31-4, 

 in which V 1 = -62 + *38cos 2ttX/360 



and V 2 =-77 + -23cos27rX/110. 



This is the visibility-curve corresponding to the distribu- 

 tion represented in fig. 16 a. The components of the line, 

 for simplicity, have been assumed to be symmetrical, as 

 figured ; but the observations are not sufficiently accurate to 

 determine whether, for instance, each component is a double 

 or a triple line. In this case also, as in the preceding ones, 

 it is impossible from the data given to determine whether 

 the smaller component is to the right or left of the principal 

 line. A direct observation with the grating showed, however, 

 that the smaller component is towards the red end of the 

 spectrum. 



The full curve shows that there is at least one other line — 

 probably more than one — whose intensity is roughly one 

 twentieth of the principal line, and whose distance from it is 

 about three times that of the chief components. 



The violet mercury-line is much more difficult to observe 

 than the others. The results obtained by observation, cor- 

 rected for personal equations, are given by the full curve 

 fig. 17 b, Plate VI. The formula for the dotted curve is 



