246 Mr G. H. Bryan, Note on a Problem [June 1, 



the tube over an Al. cathode, and none was noticed overanH 2 S0 4 

 cathode. There was also no deposit on the walls of the tube. 

 The joint absence of these two phenomena is rather striking, but 

 the exhaustion was not, I think, carried so low as in the previous 

 experiments. 



At the lowest pressure attained, with a Crookes' space of from 

 9 to 10 mm. in length over an Al. cathode, the appearance of the 

 discharge became unsettled. There was nowhere any very bright 

 colour, but throughout the greater part of the tube over an H 2 S0 4 

 cathode the colour along the axis was unmistakeably red. There 

 was a red column somewhat resembling that seen at higher 

 pressures, terminating in a sharp point about 40 mm. over the 

 HoS0 4 surface. Immediately below this the tube appeared blue 

 throughout the entire cross section, but a little lower down there 

 appeared a red column of about half the diameter of the tube. Its 

 base was curved, and its convexity was directed towards the 

 H 2 S0 4 surface, from which it was separated by an interval of only 

 2 to 4 mm. The colour of this interval seemed to vary from black 

 to faint blue. Both these red columns had a blue haze between 

 them and the walls of the tube. This stage seems to answer to 

 that observed with a mercury electrode previous to the discharge 

 assuming a nearly uniform appearance throughout. 



My best thanks are due to Professor Thomson for putting at 

 my disposal the necessary apparatus, and for numerous suggestions 

 during the course of the experiments, which were performed in the 

 Cavendish Laboratory. 



(5) Note on a Problem in the Linear Conduction of Heat. By 

 G. H. Bryan, M.A., St Peter's College. 



The problem of conduction of heat in a bar one end of which 

 is subject to radiation while the other end is at an infinite distance 

 away, has been treated by Mr Hobson in his paper "On a Radiation 

 Problem " published in the Proceedings, Vol. VI., page 184. The 

 author there finds the expressions in the form of definite integrals, 

 representing the temperature due to the given distribution of heat 

 in the medium at the extremity of the bar and to the initial 

 distribution of heat in the bar respectively. 



The expression which Mr Hobson obtains for the second part of 

 the temperature is, however, open to several objections. It appears 

 to fail entirely if the initial temperature is anywhere discontinuous 

 or if any sources, doublets, or other singularities are initially present 

 in the bar. 



Moreover, from the integral obtained, it is shown that the 

 initial distribution is equivalent to a certain distribution of lines 

 of sources and sinks in a rod extending to infinity in both directions, 



