858  Kohlrausch and Loomis—Influence of Temperature 
2. jk small correction is necessary when the moment of iner- 
tia of the vibrating weight changes in consequence of fluctua- 
tions in the temperature. In general it is inconsiderable in the 
same series of observations. The temperature in the box con- 
taining the vibrating weight was observed from time to time, 
and the salute of vibration corrected when changes of tempe- 
rature occu is was accomplished by multiplying’ the 
observed fo of vibration by 1—0,00003.A7, where 0,00008 
denotes the coefficient of the en! dilatation of lead, and At 
the variation of tem oe ure. 
oe 
0:000087% or <5,sa5 Of the whole time for one division of 
the scale eo. to one degree of arc). A series of observations 
on the copper wire were incidentally of a nature to afford the 
means of calculating the increase approximately. It amounted 
to 0°:000015% for one division of the scale. The times of 
vibration were reduced by means of these numbers to an infi- 
nitely small amplitude 
Although it would be of interest to examine this phenome- 
non more minutely, it hardly enters within the scope of the 
object in view in these observations. For in consequence of 
the inconsiderable amplitudes which we employed (at most i 
divisions of the scale, or some 3°) the correction in extrem 
cases amounted only to 0°005°*, and-it is almost com coplacaly 
compensated in its influence on the final result. 
Caleulation of the coefficient of temperature.—We have thus 
far obtained a series of tem temperatures with the eenyeeree 
times of vibration. From each two pairs of correspo 
values eg be readily derived the variation of the slestcity for 
1°. We express it as a function of the total cnr! at 0°. 
Ife, designates the modulus of elasticity at 0°, and «,, &,, t 
moduli corresponding to the temperatures “i a ‘the desired de- 
crease for 1° is foun fom formula (1) tob 
where ¢, and ¢, designate the times of alicia for the tempe- 
ratures t, and 7,, and their squares are inversely proportional 
to the modulus of elasticity. 
