AuvausT 20, 1897.] 
this equation is readily translated into a 
curve. Between the limits of 100 and 
4,000 vibrations per second there is closer 
accordance between the results of calcula- 
tion and observation than in the case of 
Fechner’s law, or indeed any other physio- 
logical law for which the attempt has been 
made to express sensation mathematically. 
Between 200 and 2,000 vibrations, includ- 
ing the range most constantly resorted to 
in music, the accordance is satisfactory, 
even when measured by physical rather 
than physiological standards. Due recog- 
nition of these important contributions to 
acoustic theory have been made by Mr. 
Ellis in his translation of Helmholtz’s 
“ Tonempfindungen,’ and by Professor Zahm 
in his recent book (1892) on ‘Sound and 
Music.’ Mr. Ellis gave a special lecture in 
London for the purpose of explaining these 
discoveries and their application to the 
principles of musical harmony. 
It was natural for Professor Mayer to 
apply acoustic methods in work primarily 
undertaken for other purposes. In 1876 he 
devised improvements in what is now gen- 
erally known as the electrographic method 
for the measurement of the velocity of pro- 
jectiles and the determination of pitch. He 
utilized the spark from an induction coil for 
the purpose of marking seconds upon the 
sinuous trace of a tuning fork on smoked 
paper, and attained results of great accu- 
racy. He studied with care the laws of 
vibration of tuning forks, and was the first 
to give accurately the correction to be ap- 
plied in all such determinations on account 
of variation in temperature of the fork. 
Between 1889 and 1894 he conducted an 
elaborate research on the variation of the 
modulus of elasticity of various materials 
with change of temperature, as indicated 
by the transverse vibration of bars. From 
the observed pitch the velocity of propaga- 
tion of sound in the bar is found, and this 
gives the modulus of elasticity. For the 
SCIENCE. 
265 
accurate determination of pitch it was 
necessary to visit Paris, where access was 
had to Dr. Koenig’s grand tonometer, and 
where this accomplished acoustician freely 
gave his time and skill in furtherance of 
the work. The remarkable regularity in 
the results shows that this acoustic method, 
as conducted, is worthy of the greatest re- 
liance. Among the materials thus studied 
was aluminum. Its modulus was found to 
be subject to large variation, and in every 
respect it is far inferior to steel for acoustic 
purposes. 
Among the acoustic discoveries of Pro- 
fessor Mayer may be mentioned his obser- 
vation that the sensation of a sound may be 
obliterated by the simultaneous action on 
the ear of another sound of greater volume 
and lower pitch, but that the converse is 
not true. The higher pitch, even when in- 
tense, cannot obliterate the sensation of 
another sound of lower pitch. This does 
not imply that the higher pitch is thus al- 
ways completely obliterated. Its presence 
modifies the compound perception after the 
possibility of singling it out has vanished. 
The apprehension of this truth caused him 
to suggest certain changes in the method of 
conducting orchestral music, but they were 
not adopted on account of counter-balancing 
inconveniences in practice. 
In 1876 Professor Mayer discovered that 
the air pressure on the inner surface of the 
bottom of a resonator in action exceeds that 
on the corresponding outer surface. This led 
to the construction of the ‘ sound mill,’ com- 
posed of pairs of resonators so balanced 
and pivoted on their supports as to be set” 
into rotation by reaction on sounding near 
them a tuning fork to which they are 
adapted. This phenomenon of acoustic 
repulsion was shortly afterward discovered 
independently by Dvorak in Austria. An- 
other application of resonators by Professor 
Mayer was in the invention of the topo- 
phone, an instrument with which the direc- 
