THE HON. J. W. STRUTT ON THE THEORY OF RESONANCE. 
118 
and the expression for the resistance (54) in a simplified form was used. The formula 
for n then runs, 
a 
n= 
2ttL 
vol. of neclc 
vol. of flask x ( 1 + 
7 r R\ 
2 L 
. . . (60) 
When, on the other hand, the necks were short, or simply holes of sensible thickness, 
the following formula was used, 
n=- 
«0'i+?' 2 ) 
V 
• (Cl) 
r„ r» being the radii or halves of the diameters as measured at each end. It is scarcely 
necessary to say that the estimation of pitch was made in ignorance of the theoretical 
result ; otherwise it is almost impossible to avoid a certain bias in dividing the interval 
between the consecutive notes. 
Table I. 
No. of 
observation. 
s, 
in cub. 
centims. 
Y, 
in cub. 
centims. 
L, 
in inches. 
R, 
in inches. 
n, 
by calcu- 
lation. 
n, 
by observa- 
tion. 
Difference, 
in mean 
semitones. 
I 1 
805 
68 
4i 
1 
2 
127-7 
126 
+ •23 
2 
1350 
126-7 
5 f 
5 
8 
107-7 
108-7 
-•16 
O 
O 
1 
7100 
430 
1 3 
4 
2 3 15 
1 til 8 
122-3 
120 
i . o o 
“T OO 
4 
405 
49-9 
°1 O 
1 
2 
179-7 
180 
-•03 
5 
ISO 
21-26 
2 3 
S 
IT 
233-7 
228 
+ •42 
6 
785 
36-84 
9 
4 
17 10 
3 25 10 
174-3 
176 
-•16 
7 
210 
32-5 
H 
1 3 
3 2 
201-9 
204 
-•18 
8 
312 
29-32 
3£ 
3 
8 
186-3 
182 
+ •41 
10 
6300 
270 
°8 
3 8 44 
3 2 5 3 2 
104-2 
102-4 
+ •29 
12 
54-69 
11-6 
9 _JL_ 
•"lti 
not recorded 
391-6 
384* 
+ •34 
In Table I. the first column gives the number of the experiment, the second the 
volume of the reservoirs, including half the necks, the third the volume of the necks 
themselves, the fourth their lengths, and the fifth their radii measured, when necessary, 
at both ends. In the sixth column is given the number of vibrations per second calcu- 
lated from (60), the velocity of sound being taken at 1123 feet per second, corresponding 
to 60° F., about the temperature of the room in which the pitch was determined. 
* 12 was originally estimated an octave too low, so that the number in the Table is the double of what was 
put down as the result of observation. 
