142 THE EEV. S. EAEXSHAW ON THE MATHEMATICAE THEOET OE SOUNH. 
second. The length of the pipe seems to be a matter of perfect indifference, and may 
be nothing more than a hole through a partition of finite thickness. 
27. Since one part of a tube cannot supply ak to, nor conyey ah away from, another 
part. A, faster than at the maximum rate, it is easy to see that if the pipe be supposed 
of finite length, which conveys air into a vacuum, the velocity in every part of the 
pipe will soon be the same throughout, and equal to \/ f/j, and density everywhere equal 
to — • 
S 
From this it would appear that the rate of discharge into a vacuum, which has 
generally been supposed to be that which is due to the height of the homogeneous 
atmosphere, is in reality that which is due to the that is, to httle 
more than the fifteenth part of it; but this requh’es correction for change of tem- 
peratm'e. 
28. If the generating piston move forward and then backward, so as to generate a 
positive wave followed continuously by a negative wave, they will not separate ; for, as 
we have seen, they are each transmitted, as wholes, at the same rate \/ But the main 
body of the positive wave will gradually advance in the type towards its front, and that 
of the negative wave fall back towards its rear ; and consequently for the pm*poses of 
audibility the central part of the compound wave, between the fr-ont of the positive and 
the rear of the negative wave, will become so attenuated that it may be considered of httle 
audible effect, after the waves have been in existence a sufficient length of time to allow 
the formation of bores. The compound wave will therefore have a tendency to produce 
the audible effect of two separate waves, separated by an interval of space nearly equal 
to its whole length. If therefore the length of such a compound wave be sufficiently 
great, it will ultimately produce two distinct sounds separated by a very brief interval of 
time. 
29. If the generating piston move backward and then forward, so as to generate a 
negative wave followed continuously by a positive wave, the positive and negative bores 
will destroy each other as rapidly as they are formed. This, however, supposes the 
positive and negative portions of the original compound wave to be equal. If one 
exceed the other in quantity of motion, the result will be a little modified. A compound 
wave of the kind supposed in this article will therefore be enthely devoid of bores, and 
the sound corresponding to it will be free from that harshness which is probably the 
audible character of a bore. 
30. If there be a continuous succession of positive and negative waves, constituting 
one long compound wave, such a wave will produce a continuous even sormd, called a 
musical note, probably owing its sweetness in some degree to the property just men- 
tioned ; and as every negative portion is succeeded by a positive portion, and every posi- 
tive by a negative, the length of each portion will remain unchangeable, whatever be the 
distance through which the compound wave travels. Hence the pitch of a musical note 
cannot change by distance of transmission. 
