ON SPECTEOSCOriC MEASUREMENTS. 181 



current, size and shape of the electrodes, diameter of the vacunna 

 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 the period of the source by frequent collisions, 

 and the former by the alteration 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 dis- 

 charge 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 mole- 

 cule and V that of light, then the formula for the resulting visibility 

 curve as given by Lord Rayleigh^ is h^{l — a") /Q + a"). 



If the definition of visibility as given above be taken, however, this 

 becomes 



If A be the difference of path at which the visibility is reduced to 

 half its value at X=0, then 



A=-A/ ~ • ^' 



or approximately, 



A V 



If we take for hydrogen 17=2000 metres per second, then , =22500. 



Again, if we ignore the difference in the temperature (about which 

 there is considerable uncertainty), at which the other substances were 

 examined, the velocities v would vary inversely as the square root of the 

 atomic weight, and the number of waves in the difference of path at 

 which the visibility is 0'5 is therefore 22500 n/to. 



Considering the difficulties and uncertainties of the problem, the 

 following table shows a very remarkable agreement between the values 

 actually found and the calculated results.^ 



' ' On the Limit to Interference when Light is Kadiated from Moving Molecules, ' 

 PMl. Mag., April 1889. 



- It should be stated that the value of A for the yellow sodium line, if taken 

 from the curve, would be much larger than that given. This was the mean of a 

 number of observatioDs taken within the past month. As has been stated before, 

 this particular curve has not been obtained since last year. A few other substances, 

 very difficult to examine, either because the lines are too feeble, or because the 

 spectrum is so unstable, have given results not quite so consistent as the above, 

 though all are of the same order of magnitude as that required by theory. 



