332 On the Velocity of Grooves Cathode Stream. [Dec. 8, 



of surface struck, per second of time, is ^pv* ; of which the equiva- 

 lent in gramme-water-centigrade thermal units is approximately 

 ^ 3 /42,000,000. The initial rate at which this will warm the glass, 

 in degrees centigrade per second, is 



10 6 X 42 . aa 



where <r denotes the specific heat of the glass, and a the thickness of 

 it at the place where the stream strikes it. 



The limiting temperature to which this will raise the glass is 



42,000,000 



,K 



where E denotes the sum of the emissivities of the two surfaces of the 

 glass in the actual circumstances. 



It is probable that p differs considerably from the average density 

 of the residual air in the enclosure. Let us take, however, for a con- 

 ceivably possible example, p = 10~ 8 , which is what the mean density 

 of the enclosed air would be if the vessel were exhausted to 8 x 10~ 8 

 of the ordinary atmospheric density. 



To complete the example, take 



v = 100,000 cm. per sec. 



(being about twice the average velocity of the molecules of ordinary 

 air at ordinary temperature) ; and take 



aa = J era., 

 as it might be for an ordinary glass vacuum bulb ; and take 



which may not be very far from the truth. 



With these assumptions, we find, by (1) and (2) approximately, 1 

 per second for the initial rise, and 375 for the final temperature, 

 which are not very unlike the results found in some of Crookes' 

 experiments. 



The pressure of the cathode stream of the velocity and density 

 which we have assumed by way of example is /at; 2 , or 100 dynes per 

 square centimetre, or about 100 milligrams heaviness per square centi- 

 metre, which is ample for Crookes' wonderful mechanical results. 



The very moderate velocity of 1 kilom. per second which we have 

 assumed is much too small to show itself by the optical colour test. 

 The fact that this test has been applied, and that no indication of 

 velocity of the luminous molecules has been found, has, therefore, no 

 validity as an objection against Crookes' doctrine of the cathode 

 stream. 



