GRANTHAM ADDRESS. 291 



proportion upon the supposition of the mass being homogene- 

 ous. That the proportion is different in consequence of the 

 mass being heterogeneous does not in the least affect the 

 soundness of his conclusion. Accurate measurements of a 

 degree of latitude in the equatorial and polar regions, with 

 experiments on the force of gravitation in those regions, by 

 the different lengths of a pendulum vibrating seconds, have 

 shown that the excess of the equatorial diameter is about 

 eleven miles less than he had deduced it from the theory ; 

 and thus that the globe is not homogeneous: but on the 

 assumption of a fluid mass, the ground of his hydrostatical 

 investigation, his proportion of 229 to 230 remains unshaken, 

 and is precisely the one adopted and reasoned from by 

 Laplace, after all the improvements and all the discoveries of 

 later times. Surely at this we may well stand amazed, if not 

 awe-struck.* A century of study, of improvement, of dis- 

 covery has passed away ; and we find Laplace, master of all 

 the new resources of the calculus, and occupying the heights 

 to which the labours of Euler, Clairaut, D'Alembert, and 

 Lagrange have enabled us to ascend, adopting the Newtonian 

 fraction of one two-hundred-and-thirtieth, as the accurate 

 solution of this speculative problem. New admeasurements 

 have been undertaken upon a vast scale, patronised by the 

 munificence of rival governments ; new experiments have been 

 pei'formed with improved apparatus of exquisite delicacy ; 

 new observations have been accumulated, with glasses far 

 exceeding any powers possessed by the resources of optics in 

 the days of him to whom the science of optics, as well as 

 dynamics, owes its origin ; the theory and the fact have thus 

 been compared and reconciled together in more perfect 



* The wholly erroneous measurement of an arc by the two first Cassinis, 

 (Dominic and James,) was supposed to prove the shortening of the degree 

 towards the poles, in opposition to the Newtonian theory. But all doubt 

 on the subject was set at rest by the admeasurement in Peru in 1735, and 

 in Lapland in 1736; and in France more recently. But the error of 

 Dominic and James Cassini was also corrected by the Cassini de Thury, 

 who found that it had arisen from an imperfect measure employed. 



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