REVERSED AND NON-REVERSED SPECTRA. 109 



careful preliminary measurement, and they are strong and satisfactory. 

 When this adjustment is given, the presence of liquid in CC, if the two columns 

 are of nearly equal length, does not much modify the adjustment. In fact, 

 the fringes were found much more easily than I anticipated, and in quiet 

 surroundings they are strong and fine. It is necessary, however, that the 

 tube CC should be of sufficient width to avoid all curvature due to capillarity, 

 at least in the axis. Tubes 2 cm. in diameter and 10 cm. long of thin brass 

 were first tried, but proved to be too narrow. No sharp slit images could be 

 obtained with reasonable care as to setting the mirrors. Thereafter tubes 

 4 cm. in diameter were used, but even these are somewhat too narrow. Slit 

 images, however, were sharp and parallel and could be easily brought to 

 coincide. 



With the wide tubes, however, the mobility of the liquid in CC increases 

 enormously, so that only under exceptionally quiet conditions could the 

 fringes be seen, and never quite without quiver. The wind beating on the 

 house, for instance, threw them nearly out of view, so that only a suggestion 

 of their presence remained. In spite of the very promising beginnings, there- 

 fore, it became a serious question whether, with the apparatus as here devised, 

 the purposes of the research could be reached in this laboratory. 



Finally, the flickering of the arc lamp may be a grave inconvenience; for 

 if the columns C, C' as usual are virtually prisms, the coincidence of spectra 

 will for this and other reasons be destroyed by the displacement of the arc. 



58. Equations. Some estimate of the increments to be anticipated may 

 be given here, and expressed in terms of the Dulong-Petit experiment. If a 

 is the mean coefficient of expansion of water at the temperature in question 

 and A// the increment of the head H corresponding to the temperature 

 difference A/ between the columns, 



(i) AH = atfA; 



Again, if AJV corresponding to AH is the displacement of centers of ellipses 

 at the wave-length X, and /* the index of refraction of water, so that n A -\-B/\ 2 , 

 nearly, 



Hence A/ may be computed as 



AN 



(3) At = 



Since the value of A7V is within icr 4 cm. and H=io cm. in the above appa- 

 ratus, we may further write at mean temperatures (25) 



01 = 2.5X10^ A* = 1-333 5 = io- n X3.i 2B/X 2 = o.oi8atthe>line. 



Thus M-i+2#/X 2 = o.35i and AZ= 10^/0.351X2. 5X10^X10 = 0.114. In 

 other words, in case of tubes 10 cm. long, the effect of a difference of tempera- 



