158 DRS. GUY BARLOW AND H. B. KEENE ON THE ANALYSIS OF SOUND. 
for 3 n are quite abnormal, as no falling off in amplitude was observed for the distances 
21 feet and 43 feet. This is the only occasion on which such an effect has been recorded, 
and may be accounted for by accidental disturbance. 
The table shows that in any one experiment the various harmonics have different 
values of the index p, indicating that the character of the spectrum really changes with 
the distance, but the values of p depend on the experimental conditions. The range 
of p is from 1 to 5, and in general the higher harmonics fall off most rapidly with the 
distance (i.e., have larger values of p) and the harmonic 2 n least rapidly of ail. It is 
not known whether this peculiarity of 2 n is associated with the absolute frequency or 
with the propeller action in which this vibration may have its origin. 
The distances were always measured from the propeller, but it appeared that the 
propeller only acts as an additional source. One can see the sides of the boat vibrating, 
and in calm weather the ripples radiating from the stationary boat are quite evident. 
On several occasions the boat-vibration was examined by placing in the boat a 
frequency-meter of the vibrating reed type. Within the range of this instrument 
(25-50/sec.) responses were obtained corresponding to the harmonics which were simul¬ 
taneously detected in the water. With the rubber diaphragm receiver used in these 
experiments the sound in the telephone was distinct up to 50 feet. Listening directly 
with the Broca tube and rubber tube, the sound was poor even at distances of about 
20 feet. 
Subharmonics. —In the diagrams representing the spectrum of the Evinrude motor 
the subharmonics have, for the sake of clearness, been omitted. As the higher har¬ 
monics are generally small, and not observable beyond the tenth there were very few 
subharmonics to confuse the analysis. Most of the subharmonics were below the funda¬ 
mental, and this region was disregarded in the analysis. The fundamental response 
often showed some irregularity due to the superimposed subharmonic 4(3/^). 
The measurement of the amplitudes of the vibrations up to the tenth harmonic occupies 
about 10 minutes. 
Analysis by Telephone .—It is interesting to note that by putting a telephone (in place 
of the galvanometer) in series with the interrupter the fundamental frequency (10/sec.) 
of the Evinrude motor can be determined with great precision, as the beats are very 
marked when the interrupter is running near that frequency. Also the frequency of 
the harmonics can be determined in a similar way, although with them the effect is 
not so evident. 
PART II.—THE THEORY OF ANALYSIS OF AN ELECTRIC CURRENT BY 
PERIODIC INTERRUPTION. 
The present paper contains an account of the theory of the analysis of an alternating 
current by the method of periodic interruption. The experiments in which this method 
has been applied for the analysis of sounds in air and water are described in Part I. 
