[MILLER] PHOTOGRAPHS OF FOG SIGNALS 165 



p.m., on September 27, 1917. The body of the table gives the cor- 

 rected actual amplitudes, in millimeters on the photographic film, 

 of the first twenty harmonic components of the curves representing 

 the several sounds, based on a fundamental frequency of 87. These 

 are the observed amplitudes corrected for the resonance and free- 

 period distortions of the recording apparatus. The values of the 

 components from 21 to 30 have been omitted as they are so small as 

 to have little influence on the conclusions. 



The analyses as given in Table I. show that the sound of the 

 diaphone as heard at any station is very variable, due, probably, to 

 the incidental conditions of the generating apparatus and to the 

 momentary atmospheric conditions. The ear fully confirms this 

 conclusion. A comparison of the amplitudes, or even of the wave 

 forms of sounds conveys a very inadequate idea of their efifects, since 

 the intensities, or loudnesses, vary as the squares of the amplitudes 

 and also as the squares of the frequencies of the components. Usually 

 it is most instructive to interpret analyses of sounds in terms of in- 

 tensities. There is no available method for expressing the loudness 

 in absolute measure, but the analyses do give the data for relative 

 measures, and the intensities of all the components of all the records 

 have been computed. For the present purpose an arbitrarily assumed 

 standard is the average value of the loudness of the first three fog- 

 horn sounds shown in the table, reduced to the distance of the middle 

 station, 860 feet from the fog-horn, and this loudness is represented 

 by the number 10,000. The values of the loudness of the components 

 of this average sound are shown in line abc of Table II. Similar 

 reduction and averaging has been made for curves d and e, for / and 

 ,;', and for i and /; the loudnesses for the single curves //, k, /, m, and 

 ;/ have been computed. Table II. gives the final data in terms of the 

 loudness of ten components, based on a fundamental of 174, of all 

 observations taken on the axis of the horn at distances at sea from 

 860 feet to 13,500 feet. The table also gives the total loudness of 

 each sound, the sum of all its partials, and the loudness of a sound 

 intensity 10,000 at the distance 860 which varies simply according 

 to the inverse-square law. 



The diaphone is designed with the purpose of producing a sound 

 having the energy concentrated in a "master-tone" of a frequency 

 of 174. which pitch has been adopted by the British light-house 

 authorities as having the most satisfactory carrying qualities. The. 

 variability of the sound of the diaphone is shown more strikingly by 

 Table II. than by Table I, but it appears that the master- tone carries 

 better than the others, as shown by the observations at distances of 

 10,500 feet and 13,500 feet. However, the second partial of fre- 



