178 Mr. R. Threlfall on the 



Suppose gun-cotton could be heated red-hot without de- 

 composition, then its molecular period would be of this order. 

 We are quite unable to say how the period varies with the 

 temperature in solid bodies at low temperatures. But the 

 spectroscope shows that it does not change much at high 

 temperatures. 



The only possible way of obtaining an idea would be to 

 extend the spectroscopic investigation even further than it 

 has been done by Abney ; either photographically, or by 

 means of a thermopile. We will assume, however, that as the 

 bodies cool, their molecular vibrations, if altering at all as to 

 period, tend to become slower, as well as of smaller amplitude. 

 Let us consider the limiting condition of propagation of 

 waves of longitudinal displacement. There seems no reason 

 for supposing that the velocity of propagation would fall off 

 till we come to waves of wave-length comparable with mole- 

 cular distances ; for instance, with the mean free path. Now 

 by experiments on diffusion it seems that the mean free path 

 in oxygen is of the order of 5*6 x 10~ 6 centimetres ; in sugar 

 solution it is 10~ 5 of this, or 5*6 x 10 -11 centimetres ; while in 

 solids it is probably much less. The size of a molecule, how- 

 ever, seems to be of the order 5*8 x 10~ 8 centim., so this will 

 give our superior limit in liquids and solids. 



Suppose that the smallest possible wave-length is the 

 diameter of a molecule, and that the velocity of propagation 

 is the same as that of sound, down to this limit. Then if V 

 be the velocity of propagation, or the number of vibrations 

 per second, and \ the wave-length in water, we have 



Y 1-4 xlO 5 ftJ <M _ 

 -=X = 5^10-- 2 - 4 x 1()l2 - 



But it is unlikely that we could get a wave-length anything 

 like so small as this ; so let us take as our limiting value the 

 wave-length equal to a thousand molecular diameters. This 

 gives us for the limiting frequency 



rc = 2'4xl0 9 . 



Comparing this with the n for the A line, which is 4 x 10 14 , 

 we see that it is about a million times too slow to produce any 

 effect on molecules vibrating so as to emit red light. But 

 bodies at the ordinary temperature might possibly vibrate 

 slowly enough to be influenced directly, though this is 

 unlikely. I must confess to being rather surprised that 

 the numbers are as comparable as they seem to be. If we 

 perform the same operation for gases, putting \ = 1000 mean 



