FOR DETERMINING THE MEAN DENSITY OF THE EARTH. 
317 
TTient, and was filled up by interpolation as far as was required, and no further. It is 
unnecessary to give it here, as all the essentials are contained in the table which has 
just been exhibited. 
The application of this number to the logarithm of the mean Rate of the Detached 
Pendulum upon the Clock Pendulum, under the actual circumstances, gave the loga- 
rithm of mean Rate of the Detached Pendulum upon the Clock Pendulum, supposing 
the arc of vibration of the Detached Pendulum to have been indefinitely small. 
The Commencing and Concluding Arcs which were used as Arguments for the 
table were those corresponding to the means of the Coincidences retained at the 
beginning and at the end of the Swing, 
33. The next correction is that depending on the temperature of the Pendulum. 
On considering the slight discordance in the coefficients of expansion found by dif- 
ferent experimenters, as well as the difficulty of exactly identifying the quality of the 
metal on which they experimented, it appeared to me best to adopt the result of 
Colonel Sabine (Experiments*, page 202 — 207), both because the method of experi- 
menting was precisely the same as the method of using the pendulum in these opera- 
tions, and because there can scarcely be a doubt that the metal was similar, as nearly 
as is possible in different bars. A small correction is required to Colonel Sabine’s 
results, because at the time of his drawing the conclusion as to the effect of tempera- 
ture, the ancient erroneous computation for the effect of buoyancy was still in use. 
Adopting his multiplier 1*655 of the correction computed for mere statical buoyancy, 
as applicable to pendulums of the same form as those used in these experiments -f-, 
the corrections to the numbers in the “Experiments” are as follows: — 
Page 202, for 6*25 read 10*34 ; which gives for Pendulum 3, 86166*49. 
Page 203, for 6*2 read 10 26 ; which gives for Pendulum 4, 86174*99. 
Page 205, for 5*65 read 9*35 ; which gives for Pendulum 3, 86149*61. 
Page 206, for 5*7 read 9*43 ; which gives for Pendulum 4, 86159*35. 
Page 207, the results for 1° Fahrenheit will be respectively 0*4318 and 0*4300. The 
mean 0*4309 corresponds to 86166 vibrations in one day. 
Hence, to reduce the vibrations observed at the temperature f of Fahrenheit to the 
vibrations which would have been observed in air of the same density at temperature 
50°, the number of observed vibrations must be multiplied by 4309 
or by l-l-(^— 50) X 0*00000501. I do not at present form the logarithm of this quan- 
tity, as there will be another term depending on temperature, introduced by the con- 
sideration of the buoyancy-correction, which will be combined with this. 
* “ All Account of Experiments to determine the Figure of the Earth by means of the Pendulum vibrating 
seconds in different Latitudes, as well as on various other subjects of Philosophical Inquiry. By Edwakd 
Sabine, &c. London, 1825.” 
t Philosophical Transactions, 1829. 
