FOR DETERMINING THE MEAN DENSITY OF THE EARTH. 
351 
in the insecurity of the indications of the temperature of the pendulums, as inferred 
from the readings of the neighbouring thermometers. After consideration of these 
points, I have thought it best to give equal weights to the results. And for compa- 
rison with the simple mean of these, I have taken the simple mean of the thermo- 
meter-readings. Thus I obtain, — 
j Rate Pendulum 1821 
Loo:, 
Rate Pendulum 8 
Temperature of 
1821. 
Temperature of 
8. 
Fifth Series 
0-00072198 
81-71 
4^80 
Sixth Series 
0-00072827 
53-04 
88-21 
Seventh Series 
0-00072347 
93-41 
50-29 
Eighth Series 
0-00071985 
41-99 
94-29 
The interpretation of these numbers is not without difficulty. From the care taken 
by the observers, it was supposed that the material state of the pendulums would be 
sensibly the same during the whole continuance of the observations, and it was 
expected tiierefore that the results of the Fifth and the Seventh Series would be in 
close accordance, and that the results of tlie Sixth and the Eighth Series would be 
in close accordance. Now the fact is, that the results of the Fifth and Seventh Series 
agree pretty well, when regard is had to the circumstances of forced temperature 
(the discordance 0'00000149 corresponds to 0®'3 per day nearly, or to 0°‘72 of tempe- 
rature) ; but the discordance between the Sixth and Eighth is 0*00000842 (which 
corresponds to 1®’68 per day, or to 4°*09 of temperature). It would therefore seem, 
at first sight, that there is strong reason to suppose that some change took place in 
one of the pendulums after the Seventh Series. 
74 . As there is no reason whatever for supposing a change before the end of the 
Seventh Series, let us take the mean of the Fifth and Seventh Series, and compare it 
(A.) with the Sixth Series alone, (B.) witli the mean of the Sixth and Eighth Series ; 
and from these comparisons let us in each case obtain a relation between the two 
pendulums nearly independent of temperature. Thus we shall have, — 
Comparison A. 
j- Rate Pendulum 1821 
Rate Pendulum 8 
Temperature of 
1821. 
Temperature of 
8. 
Mean of Fifth and Seventh Series 
0-00072273 
89-06 
49-04 
Sixth Series 
0-00072827 
53-04 
88-21 
Mean of the two lines 
0-00072550 
71-05 
68-62 
Comparison B. 
Mean of Fifth and Seventh Series 
0-00072273 
89-06 
49-04 
Mean of Sixth and Eighth Series 
0-00072406 
47-52 
91-25 
Mean of the two lines 
0-00072340 
68-29 
70-15 
When it is considered that corrections for temperature have already been applied, 
founded on the best materials to which at present we have access, it will be per- 
