1921-22.] Prof. Whittaker’s Quantum Mechanism in the Atom. 221 
XIV. — Note on Professor Whittaker’s Quantum Mechanism in 
the Atom. By Dr R. A. Houstoun. 
(Read May 8, 1922. MS. received May 29, 1922.) 
It seems desirable to check Professor Whittaker’s model numerically ; 
algebraical expressions when evaluated sometimes have the wrong order 
of magnitude. 
Let us suppose that initially the magnet system is at rest, and that 
the electron starts from the origin with velocity u. Then, referring to 
Professor Whittaker’s paper, p. 133, we have, instead of (5), 
Mex 
Aij/ 
This gives by substitution in (6) 
(a^ + x^y- 
= 0. 
1 
2A {a^ + x^) ' ^ ' ’ ’ " 
The electron consequently oscillates about the origin. The maximum 
energy of oscillation possible is obtained by putting x = 0 at x=oc , and 
must be identified with the quantum. Thus 
M2g2 
hv z= 
2A 
( 2 ) 
This is one quarter of the energy lost by the electron passing through the 
system from infinity. The oscillations are not isochronous, unless x^ can 
be neglected in comparison with in the denominator in (1). Let us 
suppose this is so. Then 
M2g2^^2 
2Aa^ 
+ = ^mu^. 
This is the energy equation corresponding to vibrations of frequency 
Me 
V = . . . - . 
27ra J{mA) 
Squaring (3) and dividing into (2), 
(3) 
or 
- = 27T^ahn 
V 
o h 
(A 
* Containing the substance of remarks made in the discussion on Professor Whittaker’s 
paper, pp. 129-142. 
