OP THE VIBRATIONS ON AN INVARIABLE PENDULUM, 237 



invariable pendulums on the variation of gravity at diiferent 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 .21 

 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 diffei'ence 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 16° 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 



