Chase.] 



150 



[March 21, 



Physical charts of the thermal equator give a mean temperature of 

 about 82° F. Taking Ganot's (Dulong's) formula, 



v = 1093 (1 + .003665 *)*, 



and substituting the value t = f (82° — 32°) = 27i°, the mean equa- 

 torial velocity of sound should be 1147.3 ft. per second. The wave-length 



of the lowest do ( c _ d ) is, therefore, 1147.3 X 12 -=- 16 = 860.5 inches. 



The following table gives the number of vibrations and the wave 

 lengths of the fundamental note, for each of the first twenty -six octaves. 



I. Table of Musical Octaves. 



Note. Vibrations per Second. Ware Lengths. 



C- 3 16 860.5 



C . 32 430.25 



C-! 64 215.125 



C 128 107.5625 



(', 256 53.78125 



('; 512 26.890625 



C 4 1024 13.4453125 



C 5 2048 6.72265625 



C 6 4096 3.36132812 



C, 8192 1.68066406 



C 16384 .84033203 



C 9 : 32768 .42016601 



C 10 65536 .21008300 



C„ 131072 .10504150 



C 12 2(12144 .05252075 



C 13 524288 .02626037 



C u 1048576 .01313018 



C 15 2097152 .0065650!) 



C lfi 4194304 .00328254 



C„ 8388608 .00164127 



C 18 16777216 .00082063 



C 19 33554432 .00041031 



C, 67108864 .00020515 



C a 134217728 .00010257 



C 22 268435456 .001)05128 



C 23 536870912 .00002564 



The wave length of C. a corresponds very closely with that of the 

 Fraunhofer C line (.00002586), and the corresponding octave is therefore 

 directly comparable with the prismatic spectrum. Table II. contains a 

 comparative exhibit of the wave-lengths, in hundred-millonths of an 

 inch, o ^he twenty-sixth musical octave, with those of the Fraunhofer 

 lines according to Angstrom's measurements, and the accompanying dia- 

 gram graphically illustrates the comparison. 



