Energy and Apparent Intensity of Sounds of different Pitch. 385 



The error of the method of observation may be entirely dis- 

 regarded; the deviations from uniformity are to be taken as 

 resulting from irregularities in the proceedings of the voicer. 

 Collecting the results, we have : — 



W W 



T r 



^0-/0 43-9 + 1-37 J 42-Q + l-OOOfi 



'K^^«'?-!"^i c'it-c'' 47-2 +0-933 



y-c'' 46-4 + 1*57 ~ 



The probable errors of these arithmetic means are appended. 

 From the near equality of these in the results of the two se- 

 parate octaves, we infer that the estimation by the ear of equal 

 intensities of tone has about the same accuracy whatever the 

 pitch may be. 



This discussion establishes almost beyond a doubt the exist- 

 ence of the law of Topfer as a basis ; but the results are affected 

 by irregularities of a more continuous nature than are to be ex- 

 pected in ordinary cases. The upper half of the tenor octave, 

 for instance, furnishes the mean 41*9, which deviates widely 

 from all the rest. If, however, we call to mind the nature of 

 the estimation of intensities (which takes place for the most part 

 by comparison of adjoining notes), we see that an error once 

 committed is liable to perpetuate itself; and therefore precisely 

 this description of continuous irregularity is to be expected. 

 If we admit the existence of an error of this kind in the upper 

 half of the tenor octave, and if we admit that, according to 

 the practice of voicers, some increase in strength is looked for 

 on entering the octave above middle c, we completely account 

 for the discrepancies in the results. 



The b^ (which is omitted in the above discussion) has a wind- 

 consumption quite disproportionate to all the rest ; the tone of 

 the pipe indicates a difference in the voicing : a mouth cut 

 up a good deal higher than usual would account for both 

 effects ; a pipe with a high mouth takes much more wind to 

 reach the upper lip properly. 



On the whole, the law of Topfer is not supported by this 

 discussion as an accurate expression of the properties of the 

 organ-stop examined ; but the very deviations from this law 

 which occur in the above figures support the proposition that 



W . 



— is a measure of the apparent intensity of the tone. 



If I be the apparent intensity of a tone of periodic time t, 



W 



we have seen that it is measured by — ; if, then, w be the 



W 7 

 constant proportion of W (say — ) which reaches a thin plate 



PhU. Mag, S. 4. Vol. 44. No. 294. Nov. 1872. 2 C 



