and on Reed Organ-Pipes. 245 



by a stroke below. Suppose in the tirst place that the intervals 

 of the secondary pulses are less than those of the primaries, and 

 take -^B, BC, &c. ( = a) to represent the primary interval, and 

 Aa, aa, &c. ( = s) the secondary. The order of the pulses in this^ 

 case will be evidently that represented in the diagram. 



No. 5. 



A a a B b b C c c D d d E e e T f f 



1 ! 12 IS 12 12 12 



Suppose now that the secondary interval instead of being = s, 

 should = 2a + s, 



No. 6. 

 A B C a D b E q a F d b 



t- 1 12 12 



then taking ^iBC.-.at equal intervals { = a) as before, to represent 

 the primary pulses, we must place a at the interval 2a4s from 

 A, that is, at the distance s from C, a at the distance 2s from 

 E, and so on, and similarly for bb, &c. but in this way we plainly 

 get, after the four first, a series of pulses precisely similar to tho.se 

 we obtained before, both in order of intervals, succession of in- 

 tensity, and alternations of conden.sed and rarefied pulses. If 

 we take the secondary interval = 4a + *, we shall find the same 

 series occurring after the eighth primary, and in like manner 

 when the secondary interval = 2na + s, we always obtain the same 

 succession of pulses after the 4n first which may be neglected, 

 and as we may take the distances AB, Aa, &c. to represent the 

 length of stopped pipes, which give musical notes, the interval 

 of whose pulses are in that ratio respectively; we may say that 

 whatever effect be produced on the ear by applying a pipe, length 

 := s to a vibrating reed who,se note is in unison with a stopped 



