REVERSED AND NON-REVERSED SPECTRA. 135 



but quite consistent with each other. The reason for this could not be made 

 out. But for the inevitable tremors the observations would all have been 

 acceptable. 



80. Computation. Since the ends of the air-tube are perpendicular to 

 the beam of light 



(i) 



where AN is the difference of the displacements of the micrometer in the 

 presence and absence of air in the tube, e the effective length of the air column, 

 and n the index of refraction of the air for the given wave-length X. The 

 equation presupposes a knowledge of the dispersion of air O/JL/ dX; but, as this 

 is small, the term may be temporarily omitted. If X is constant, it corre- 

 sponds to a constant correction of AN throughout the experiments. 



Again, if we have an equation of the form of Mascart's, nn referring to 

 o C. and normal barometer, and N to the absence of air in the tube, 



M-i p i + /3(ft-76) = JVp-JV = AJVp 

 jU 7(( -l 76 i + crf Nn-No AN n 



where a and /3 are two constants. If the tube is not quite exhausted (8B 

 remaining), the observations for a plenum (barometric pressure, B) and 

 exhausted air being made at the same temperature, 



or nearly 



B ~ NB-N O ~ AN B 



Thus if one neglects the small correction i fiB of SB 



T) 



(3) AN B =AN B - SB g^g 



the micrometer displacement AN B in case of complete exhaustion at the 

 barometric height, B, and the displacement AN B - 5B corresponding to partial 

 exhaustion B dB, are proportional to those pressures. Since dB was quite 

 small, this equation was assumed, and p 8B is thus nearly the height of the 

 mercury column of the partially exhausted tube. In the table this is briefly 

 called p, and differs from the barometric height. 



Finally, for two partial pressures p and p f and temperatures i and t' of the 

 air 



AAT and AN 7 being the micrometer displacement corresponding to p, t, and 

 p', t', respectively. Hence if care be taken to make p = p', nearly, 



i + at' _ i + at _ a(t'-t) =a8t 



AN '' AN' '~~AN-AN'Nl> 



