OF THE VIBRATIONS ON AN INVARIABLE PENDULUM. 
237 
invariable pendulums on the variation of gravity at different parts of the earth’s 
surface, we may remark, in the first place, that such results, being merely rela- 
tive, are not liable to more than a very small proportion of those considerable 
derangements, in which all determinations hitherto made of the absolute length 
of the pendulum are involved. The error to which the relative results of 
invariable pendulums are liable, is limited, in all cases, to a function of the 
difference in the amount of the buoyancy at different stations, caused by va- 
riations in the atmospheric circumstances. With pendulums of the form and 
materials of those used in the present experiments, we obtain from the results, 
0.65, as the co-efficient of the difference ; or in other words, the error to which 
the results are liable is about two-thirds of the difference in the amount of the 
correction for buoyancy computed for the different stations. The proportion 
of this error, occasioned by barometric variations, cannot be otherwise than 
extremely small, in all cases of comparison between stations little removed from 
the level of the sea. The specific gravity of the pendulum being about 8.6, an 
inch in the height of the barometer will correspond in buoyancy to about .2 1 
of a vibration a day, which multiplied by 0.65 is about 0.14 of a vibration. 
In the comparison of tropical and extra-tropical stations, the barometer in the 
middle and high latitudes is liable to fluctuate an inch, and even in extreme 
cases more than an inch, from the mean height, which is uniform, or nearly 
so within the tropics : but as the observations generally include several days 
at each station, and as in proportion to their continuance the barometer will 
approximate to its mean height, it will be found, on consulting the record of 
pendulum experiments, that a difference of half an inch in the barometric 
height at two stations is a rare occurrence. The correction for half an inch is 
not more than 0.07 of a vibration, to be added to the number of daily vibra- 
tions at the station where the barometer was highest. The liability to error 
from variations of temperature at different stations is, however, far more con- 
siderable than from variations of the barometer : sufficiently so, indeed, to be- 
come, in some cases, influential on the ellipticity deduced. A difference of 
40° of Fahrenheit is by no means of rare occurrence between the tropics and 
the high latitudes ; and as 1 6° of Fahr. are equivalent, in their influence on 
the density of the air, to one inch of the barometer, the error in such case 
may amount to 0.52 x 0.65 = 0.34 of a vibration per diem. Moreover, as the 
