TRANSACTIONS OF THE SECTIONS. 39 



pairs of figures of that kind formed an important part of tlie geometry of position, 

 an excellent treatise on wliich had been brought out by M. Theodor Reye. To the 

 physicist he would exhibit the unity of the science, by adopting Hamilton's cha- 

 racteristic function as explained in his papers on systems of rays, and using it in the 

 most elementary form fi-om the very beginning of the subject, leading at once to the 

 undiUatory theory of light. At the same time the practical optician would learn what 

 were the cardinal points of an optical instrument, and would be able to determine 

 them without taking the instrument to pieces. Helmholtz and Listing had pointed 

 out the advantages of the method to the oculist ; and Beck had recently placed some 

 of the elementary points in a clear light. Casorati had also exemplified some of the 

 advantages of the method of homographic figui-es in elementary optics ; but though 

 Gauss, the modern founder of that method, and several others, had made honourable 

 mention of the name of Roger Cotes, and of that theorem with respect to which 

 Newton said that " if Mr. Cotes had lived we should have known something," no 

 one seemed to have suspected that it would form the meeting-point of all the three 

 methods of treating the science of optics. 



On a Natural Limit to the Sharpness of the Spectral Lines. 



By Lord Rayleigh. 



[Published in extenso in ' Nature' for Oct. 2, 1873.] 



On the Injiaence of Temperature and Pressure on the Widening of the Lines 

 in the Spectra of Gases. By Arthur Schtister, Ph.D. 



The question has often been discussed whether it is temperature or pressure which 

 causes the widening of the lines in the spectrum of hydi'ogen. Some spectroscopists 

 are of opinion that this widening of the lines is caused by the clashing together of 

 the gaseous molecules, while others seem to think that the forces which maintain 

 the molecule in vibration are altered by the temperature, and now allow the mole- 

 cule to vibrate in different or less-defined periods. It is difficult to decide the 

 question by experiment. The only means we have to render the gas luminous is to 

 pass an electric current through it. But we know not in what way this current 

 influences the velocity of the molecules, and therefore the number and force of the 

 shocks. We cannot alter the temperature of the spark without altering the pressure 

 within it ; and therefore we cannot decide the question, as has been tried, by merely 

 changing the mode of discharge. The following considerations seem to me to be 

 strongly in favour of the ^^ew that each separate molecule would show at all tem- 

 peratures the narrow lines, but that the shocks of the other molecules cause the 

 widening. Frankland and Lockyer have found that if we increase the pressure of 

 hydrogen while an electric current is passing through it, the lines begin to expand, 

 all the spectrum becomes continuous, and, finally, the resistance becomes so large 

 that the electric current will not pass at all. On the other hand, Gassiot and Pliicker 

 have observed that if we diminish the pressure of hydrogen its electric resistance 

 diminishes, attains a minimum, then increases again ; and if we keep on exhausting 

 the tube, it becomes so great again that the current cannot pass. Pliicker says that 

 a tube exhausted to its utmost limits shows the lines of hydrogen and siUca. He 

 says at one place, "I think that the lines are very fine and distinct." If there 

 had been any widening, he would have been sure to mention it. Now it is not 

 too much to assume that the resistance of the gas at the moment when the 

 discharge just ceases to pass is the same whether the increase of resistance is pro- 

 duced by too great a pressure or too great an exhaustion. At this moment, there- 

 fore, the current is the same, and the same energy must be converted into heat by 

 resistance. But in the case in which the current does not pass on account of the 

 excessive diminution of pressure, there is only a much smaller quantity of gas to be 

 heated than in the other case ; it must consequently be heated up to a much higher 

 temperatm-e ; and yet the spectrum is not continuous ; the lines are not even 

 widened. We are therefore compelled to accept Frankland and Lockyer's original 

 conclusion, that pressure, and not heat, is the cause of the widening of the lints. 



