150 Captain Sabine on the 



use of two others, as checks upon his experiments ; the first was 

 that of an invariable pendulum attached to a clock ; the second 

 arose from the variations in the rate of the astronomical clock in 

 different latitudes : we refer to them only as having fully con- 

 firmed the results of his other experiments, for their principle is 

 too well understood to need any illustration. 



Captain Sabine, after having recounted his several observa- 

 tions of coincidences of the pendulums ; of the rate of the clock 

 -with the invariable pendulums ; of transits and altitudes of the 

 Sun and stars for the rate of the astronomical clock and chrono- 

 meters ; of meridian altitudes of the heavenly bodies for the lati- 

 tudes of the places of observation, — all with a fulness of detail, 

 which will enable those who may desire to do so, to trace every 

 step of the process from the original observations to the ultimate 

 conclusions, — proceeds to combine his determinations, for the 

 purpose of calculating the compression of the earth. The mode 

 he employs, using the thirteen stations visited in his voyages, is 

 that given by Laplace, in the third book of the Mechanique Celeste, 

 founded upon the principle of the least squares. 



His calculation gives the fraction — 1— - for the compression : a 

 very remarkable result, in consequence of its being the same that 

 expresses the ratio of the centrifugal to the gravitating force. Not 

 content with his own measures, he has next combined them with 

 those of Kater, at the stations of the British, and of Biot, Arago, 

 §-c, at those of the French survey ; and in every combination he 

 is led to the same result. With such a confirmation, we are 

 Warranted in saying, that we conceive this value for the compres- 

 sion of the terrestrial spheroid, is more entitled to confidence, 

 than any other that has yet been given ; and when we consider 

 its remarkable agreement with the ratio of the central forces, we 

 cannot help believing that there may be some connexion between 

 the external figure of the earth, and its internal constitution, that 

 still remains to be investigated, and which we consider highly 

 deserving the attention of the few mathematicians in the World 

 who are competent to the investigation. 



This determination of an ellipticity of — ± — differs much from 

 any other, whether derived from former experiments with the 

 pendulum, from the measure of contiguous, or of distant arcs of 

 the meridian. It is, however, entitled to the highest confidence, 

 inasmuch, as it is the first that has been drawn from observations 

 of the pendulum, unconnected with any other operation. It is 

 very remarkable, that, whilst the pendulum has a right to be con< 

 sidered as a mode of determining the relation between the polar 

 and equatorial axis, perhaps more certain than any other, it has 

 never before the present day, formed the principal object of ob- 

 servation, but has always been confided to the same persons, who 



