100 TRANSACTIONS OF THE 
origin of these two classes of tones is identical in prin- 
ciple. My suggestion of this fact has since been confirmed 
by articles by certain German physicists in Annalen der 
Physik, particularly Clemens Schaefer. 
Several authorities have maintained that the summa- 
tion tone is a difference tone of upper partials according to 
the equation a plus b equal na minus nb or a plus b equal 
na minus mb, where n and m are whole numbers; e. g. 
4 plus 3 equal 7 equal 7 times 4 minus 7 times 3. In 1895 
Rucker and Edser proved the impossibility of this ex- 
planation for objective summation tones. Krueger in 1900 
heard subjective summation tones even when the upper 
partials had been practically eliminated by interference; 
and I proved in 1907, by the beating of auxiliary forks with 
audible summation tones, that the latter are not difference 
tones. My proof rested on the fact that if the pitch of a 
first partial be lowered one vibration per second that of 
the fifth partial, e. g., will be lowered five vibrations. The 
proof was mathematical and has not been questioned. 
Subjective combination tones seem, then, to arise in 
the liquids of the inner ear on the principle of superposition 
of primary vibrations, and like other combination tones, 
are therefore really objective to the sensory end organs of 
hearing. 
