330 The Philippine Journal of Science 1921 
cidence than a fundamental principle, 14 we have very good 
evidence that the classical theory is valid for distances much 
smaller than the radius of an atom. It has been experimentally 
verified for positive nuclei (containing both positive units and 
electrons) at distances 15 of about 3 X 10' 12 centimeters. 
It is the purpose of this paper to point out the value of the 
theories of atomic structure which; are based on method 1, 
and to suggest further possible lines of advance along this road. 
The best empirical expression of the mysterious discontinuity 
referred to has been given by Planck, whose quantum theory 
will now be briefly reviewed. 
PLANCK’S QUANTUM THEORY 
Planck’s theory, proposed in 1901, 16 has been recently presented 
by him as follows: 17 Water waves on an inclosed area are re- 
flected from shore, to shore with a constant subdivision into 
shorter waves. If the wind originally causing them ceases, they 
become converted into smaller and smaller waves until finally 
all the energy has gone into the form of molecular motion, that 
is, heat. The classical theory would lead us to expect that simi- 
larly confined and reflected light or heat waves would also be 
converted into very short waves. To continue, in Planck’s own 
words : 
But of such a phenomenon no trace can be discovered in Nature; The 
conversion sooner or later attains a perfectly definite and assignable limit, 
and after that, the radiation-conditions remain stable in every respect. 
In order to reconcile this fact with the Classical Theory the most varied 
experiments have already been made, but the result has always been that 
the contradiction went too deep into the roots of the Theory to leave 
them unhurt. So again nothing remains but to re-examine the foundations 
of the Theory. And again we must admit that the principles of Thermo- 
dynamics have shown themselves to be unshakable. For the only method 
so far found to promise a complete solution of the riddle depends directly 
upon the two laws of Thermodynamics; though it combines with them 
14 Einstein’s law of gravitation is sometimes considered as an instance 
of how a complicated dynamical effect may superficially appear simple. 
The whole tendency of the relativity theory, however, is to show that ob- 
served slightly complicated laws are converted into simple ones by four- 
dimensional mathematical treatment. No suggestion which could explain 
a discontinuous dynamical effect is found in the development of the re- 
lativity theory. 
15 Geiger, H., and Marsden, E., Phil. Mag. 25 (1913) 604. 
36 Planck, Max, Ann. d. Physik. 4 (1901) 553. 
17 New paths of physical knowledge, Phil. Mag. 28 (1914) 66. 
