154 TRANSACTIONS OF SECTION A. 



electrons which sufficed to maintain the hnninosity, and observations were made 

 to ascertain whether the different series of lines in the Helium spectrum required 

 different e'lectron velocities for their production. It was found that luminosity 

 was never produced until the electron velocity was about 25 volts, and that 

 it could not be maintained at velocities lower than 23 volts, and then only in 

 the presence of traces of impurity. No evidence was obtained that any one of 

 the Helium series could be excited without producing the others also. 



3. The Mther and the Perihelion of Mercury. By Dr. E. A. Houstoun.^ 



It is well known that the perihelion of Mercury advances some 42 seconds of arc 

 per century, and that this progression has been explained by Einstein on his theory 

 of generalised relativity. Sir Oliver Lodge attempted to explain it by assuming that 

 the mass of Mercury was given hj m„/(l—v^/c^)i, where v was the velocity of mercury 

 relative to the jether, the asther being at rest in space, the same law of variation as 

 holds for the mass of a cathode particle, but his attempt was unsuccessful. I recently' 

 suggested that the optical difficulties associated with the earth's motion through space 

 were best met by assuming that the sether to the uttermost corners of space had the 

 same velocity of translation as the earth had, by making it, in fact, geocentric. This 

 suggestion leads to a very interesting result as regards the jserihelion of Mercury. 



For if we use Eddington's equation for the orbit, 



de^ h'hi-^ Too' 



and Sir Oliver Lodge's expression for the mass, but regard v as the velocitj^ of Mercury 

 relative to the earth, since according to my view the aether moves with the earth, the 

 problem reduces to Newton's revolving orbit, and we find that the perihelion rotates a 

 fraction of a revolution equal to 



d^T^l -e'^y 



while the planet moves through one revolution. This expression is the same as 

 Einstein's, except that he has the factor 12 instead of 2. Hence, if the mass of Mercury 

 varied six times as fast as the mass of a cathode particle, we would have perfect 

 agreement. 



4. The Interpretation of the Quantum. By Dr. E. A. Houstoun. 



Planck's theory of radiation assumes that a certain quantity of energy hv, the 

 quantum, is associated with radiation of frequency v. This quantum is alleged to 

 be inexplicable on the basis of Newtonian mechanics and has given rise to much 

 theorising of a revolutionary nature : it seems to have altogether escaped notice, 

 that it can be quite tolerably explained by the ordinary model atom which some of 

 us use in our lectures. 



This model atom consists of a sphere of positive electricity of uniform density p, 

 the radius of the sjihere being a. Inside the sphere there is one electron, which oscil- 

 lates about its centre through the positive electricity. Let v be the frequency (recipro- 

 cal of the period) of the oscillations, and suppose that the radius of the sphere is just 

 large enough for the positive electricity to neutralise the electron. Then 



'' V \3n,n) 



and e = ^ ira V- 



3 '^ 



The sphere is supposed to be rigid. 



Now sujjpose that the electron starts from rest on the surface of the sphere and 

 falls towards the centre of the atom. Let v be the velocity accjuired by the time it 

 reaches the centre. Then v = 2irav. On eliminating p and a these three relations 

 give 



1 Phil. Mag., Feb. 1919. 



