454 Experiments on the Velocity of Sound in Air. 
11*7 millim. diameter. Very many trials were made; and 
although the best single observation gave 324*78, I have 
reason to think that the mean value 324*56 is too high. I 
hope yet to verify it, and also to continue experiments with a 
tube 902 millim. diameter. 
There is one point connected with the velocity of sound 
which appears to require elucidation, and that is, the modifi- 
cation it may undergo near its point of origin ; for the waves 
which affect us as sound are usually not plane-waves, but 
emanate from an origin which more or less nearly approaches 
a point — this point being the centre of a system of spherical 
waves. 
We may refer to the vibration in conical tubes as bearing 
upon this point. A complete cone, speaking its lowest note, 
with its apex or closed end for the position of the node, is of 
twice the length of a closed cylindrical tube of the same pitch, 
and has the same succession of harmonics as the open cylin- 
drical tube (see Phil. Mag. August 1878). This property is 
independent of the proportion of base to height in the cone; 
and if we assume the base of the cone to be a portion of a 
spherical surface described from the apex, we may continually 
increase the conical angle until the cone becomes a sphere. 
Now, if we consider the effect of this principle and apply it to 
divergent waves, it will be found that such waves cannot have 
exactly the same velocity for all pitches, but that the lower 
the pitch the greater will be the velocity, owing to the differ- 
ence of velocity between the first and succeeding quarter- wave 
lengths. To take a numerical example, we may choose two 
wave-lengths of 32 feet and 8 feet respectively: — 
32-ft. wave . 
8-ft. wave . 
Or, if we assume a velocity in free air (away from origin of 
vibrations) of 1120 feet per second, we shall have: — 
Velocity of sound-wave of any pitch, not including 
first quarter-wave 1120 ft. 
Velocity of 8-ft. wave, or wave of 140 vibrations 
measured from apex of cone, 1120 + 2 . . . 1122 ft. 
Velocity of 32-ft. wave, or wave of 35 vibrations 
measured from apex of cone, 1120 + 8 . . . 1128 ft. 
We thus find that waves near their origin are not of normal 
length. 
Quarter-wave lengths. 
Cylinder. Cone. 
8 ft. 16 ft. 
2 ft. 4 ft. 
Excess in 
Cone. 
8 ft. 
2 ft. 
Difference . . . 
. 6 ft. 
