94 Dr. A. M. Mayer on the Experimental Determination 



on the assumption that the intensities of the vibrations diminish 

 as the reciprocals of the squares of their distances from the 

 sounding bodies : — 



A's dist. in A. 



B's dist. in X. 



Ratios of in- 

 tensities. 



Residual effects. 



1 



1-5 



•444 



•556 



2 



2-5 



■640 



•360 



3 



3-5 



•734 



•266 



4 



4-5 



790 



•210 



5 



5-5 



■8^6 



174 



6 



6-5 



•854 



•146 



7 



75 



•871 



129 



8 



8-5 



•885 



•115 



9 



9-5 



•897 



103 



10 



10-5 



•907 



•093 



11 



11-5 



•914 



086 



12 



12 5 



•921 



079 



13 



13 5 



•927 



073 



* * * 



* * # 



* * * 



# ■* * 



24 



24 5 



•959 



• -041 



25 



25*5 



•961 



039 



We have projected these related numbers in the accompanying 

 curve, whose abscissa? represent the distances of A from the 

 source of sound, and whose ordinates give the ratios of intensities 

 between A, taken at the distances on the axis of abscissa?, and 

 B at distances from the sounding body always one half wave- 

 length greater than A's distance from its sounding body. The 

 formula of the curve is 



(*+i) s 



If the curve be placed upside down and referred to the corre- 

 sponding numbers on the abscissa? and ordinates (which num- 

 bers are equal to unity minus the numbers at the corresponding 

 points of the curve when in its first position), we have the gra- 

 phical representation of the variation of the resultant intensities 

 contained in the fourth column of the Table. 



In the case of notes of different pitch, the higher note will 

 necessarily force the air to make its vibrations with a greater 

 velocity ; the intensities will therefore not alone depend on the 

 amplitudes of these vibrations, but also on their velocities; 

 and it has been deduced from established principles of dynamics 

 that the apparent intensities of notes of different pitch wdl vary 

 directly as the squares of the amplitudes, and inversely as the 

 fourth power of the wave-length or periodic time (see Mr. Bo- 

 sanquet " On the Relation between the Energy and Apparent 



