360 Kohlrausch and Loomis—Influence of Temperature 
By differentiating the above equation we obtain 
de 
oe é, os = a+ 2bt. 
The left hand expression denotes the values contained in the 
second column of Table 2. If therefore we substitute — 
values in ian above equation, the coefficients a and } can 
readily calculat 
By means of least squares there results for the brass wire 
a—90,000368 26=0,00000425 
by means of which the figures in the third column were calcu- 
. In view of the small differences of temperature the 
= cordance must be regarded as satisfactory. It appears still 
more manifest when the time of vibration itself is calculated. 
Since a and 6 are known, the most probable value of the time 
of vibration for 0° may also be rea ily determined by means of 
least squares. The calculation gives ¢, = 205696*° 
The times of vibration calculated from this value of t,, to- 
gether with the times observed, are given in the following Ta- 
b e difference between the observed and calculated 
values of the times of vibration amounts at most to +4, of a 
second, and indicates sufficiently the rupee ped of the sim- 
plified ‘method of reduction, although the regularity in the sign 
of the differences would seem to sndicate that the” rigorous 
method would afford a still greater accordance. 
TABLE 3. 
Times of vibration. 
Temperature. Observed, Calculated. Observ.—Calcul. 
76°°34 20°-9970 205-9986 —0*-0016 
72°25 20°9667 20°9680 —0°0013 
68°97 20°9422 20°9443 —0°0021 
63°79 20°9000 20°9078 —0°0078 
56°52 20°8559 20°8592 —0°0033 
50°66 20°8248 20°8218 +0°0030 
44°92 20°7849 20°7869 —0°0020 
39°74 20°7614 20-7569 +0°0045 
35°04 20°7352 20°7309 +-0°0043 
30°05 20°7065 20°7041 +0°0024 
26°00 20°6861 20°6837 +-0°0024 
24:28 20°6767 20°6751 +0°0016 
4. Temperature and modulus of elasticity of iron, 
copper and 
brass.—The method of observation and reduction, already de- 
ibed fo an example, was fe fk for wie of 
si i as tae 
