DR. W. GEOFFREY DUFFIELD ON THE 



have been observed over a wide range of pressure (from 40 to 200 atmospheres 

 inclusive) are plotted against the wave-length, and are joined together by full lines. 

 iMtwl lines join mean values (marked with a x) which have Ijeen made from only 

 t wo or three observations. 



Considering the mean values for/2, 02, pi, ql, q2, and r2, the diagram suggests, 

 in the first place, that the relation between the displacement and the wave-length 

 may be linear, but, if this were the case, it would require that a spectral line with a 

 wave-length of about 2600 A.U. should not suffer displacement under pressure 

 (a value also well in agreement with the graphs for ll, si, t2 (dotted) and for gl, jl)* 

 Measurements have not been made at such small wave-lengths, but we may be 

 guided by our experience in dealing with the copper arc, in which it was found that 

 displacements had been measured for lines whose wave-lengths were smaller than 

 that of the point to which a similar graph for the copper lines tended. 



If we assume that the origin is on the curve, we are led to conclude that the 

 displacement varies with a higher power of the wave-length, and calculation 

 demonstrates that as far as mean values are concerned the relation may be fairly well 

 expressed by 



d = 289 x 10-V or d = 653 x 10- I3 X 3 , 



of which the former is the more satisfactory, because the greatest deviation of any 

 observed point from the mean value given by these formulae is 13 per cent, in the 

 first case and 7 per cent, in the latter. But to choose between them, it is necessary 

 to deal with individual values at different pressures rather than with the mean 

 value. These are given in Tables VI. and VII., in which the quantities d/X 3 and d/\ s 

 are set forth. 



Graphic representation of the above tables is given in Diagrams 3 and 4. 



Comparing these with Diagram 1, we see that in the later diagrams the lines /2 

 and r2 approach more closely to the group of lines between them, and that a criterion 

 for selecting the most probable power of the wave-length lies in choosing that which 

 more exactly makes /2 and r2 coincide with this group. The higher the power of 

 the wave-length, the lower in the diagram do lines with large wave-length fall with 

 respect to lines of lower wave-length ; consequently, r2 tends to fall and /2 to rise. 

 In the diagram for dj\\ it will be seen that r2 has not fallen sufficiently to completely 

 mingle with the group, and that /2 is still too low, but in that drawn for d/X 3 , the 

 ased power of X has been sufficient to cause these two lines to merge completely 



the group. The displacement per atmosphere is thus seen to vary more approxi- 

 the 3rd than the 2nd power of the wave-length. 



This result is quite in keeping with that previously obtained for the copper arc. 

 certain that the displacement varies with a higher power of the 



Had the mean, been taken from 60 to 200 instead of from 40 to 200 atmospheres the line joining 

 9\,}}, would have sloped in the wrong direction. 



