382 Mr. R. H. M, Bosanquet on the Relation between the 



effect sought is really a predominance of the upper notes, appears 

 as well from the statement of the voicers as from some of the 

 means employed to produce the desired effect. Thus one organ- 

 builder uses two pipes instead of one throughout his trebles ; 

 others employ a heavier wind in the treble ; so that we must 

 allow that in organ-stops the intensity of the treble is required 

 slightly to exceed that of the bass. But, allowing for a variation 

 of this nature (namely, a slight excess in the intensity of the 

 treble over that of the bass), it seems reasonable to assume that 

 the apparent intensity of the different notes of a well-voiced 

 organ-stop is the same. 



The work consumed in an organ-pipe in a given time is mea- 

 sured by the amount of wind it draws from the bellows in that 

 time. 



There is a statement in Topfer^s work on the organ (1842, 

 reprinted 1862, Korner, Erfurt and Leipzig), that when a stop 

 is scaled according to his measures, and properly voiced, the 

 wind-consumption of the pipes is proportional to their lengths, 

 or to the wave-lengths : this law is stated without reasons or 

 measures ; so that some verification was essential ; but before 

 passing to the verification I will notice the immediate conse- 

 quences of the law, if true. 



The quantities of wind consumed by the pipes in a given time 

 are measures of the work done by the weights on the bellows. 

 We have to assume that in similar pipes the work converted 

 into sound is a constant proportion of the whole work supplied ; 

 for undoubtedly loss takes place in the pipes. Subject to this, 

 we derive from Topfer's law the statement that the work con- 

 verted into sound by the pipes of an organ-stop in a given time 

 is proportional to the wave-length of the tone, or the periodic 

 time. 



Admitting, then, that the notes of an organ-stop are fair repre- 

 sentatives of a series of tones of different pitch and equal appa- 

 rent intensity, we have more generally : — Tones of different pitch 

 have equal apparent intensity when the work consumed by them 

 in a given time is proportional to the wave-length or periodic 

 time ; or if W is the work consumed in a unit of time, the in- 



W 



tensity is measured by the fraction — , where t is the periodic 



time — assuming that the intensity in notes of the same pitch is 

 proportional to W, which will not be denied. 



For the purpose of obtaining some verification of Topfer's law, 

 I employed the new open diapason on the great organ of 

 the instrument in St. John's Chapel, Oxford; it draws wind 

 enough to observe conveniently as far up as about the top of the 

 treble staff, and is tolerably uniform in tone. Some difficulty 



