144 Captain Sabine on the 



Huygens, on the other hand, denied that the particles were mu- 

 tually attractive of each other, and assumed that each particle 

 tended towards the common centre, with a force inversely as the 

 square of its distance from that point ; by means of this hypo- 

 thesis, he concluded that the curve by whose revolution the ter- 

 restrial spheroid was generated, was not a conic section, but a 

 curve of the fourth order, although, when the centrifugal force 

 bore but a small proportion to gravity, it would not differ sensibly 

 from an ellipsis. He found the proportion between the greatest 

 and least diameters of this curve to be as 577 to 578, and a con- 

 sequent ellipticity of - s \-^. Different as are these two hypotheses 

 and their results, there is still one remarkable accordance between 

 them, for by both the sum of the fractions that express the ellipti- 

 city, and the excess of gravity at the pole over that at the Equa- 

 tor, are identical. 



The hypothesis of Huygens is now exploded, inasmuch as the 

 mutual attraction of all gravitating bodies is admitted ; but his 

 investigation is not of the less value, for it gives the flattening 

 that would take place, under the received law of attraction, pro- 

 vided the earth were composed of concentric shells, infinitely rare 

 at the surface, and infinitely dense at the centre : and as New- 

 ton's investigation gives the compression in the case of uniform 

 density, we have thus the extreme limits between which every 

 possible difference in the ellipticity of the earth that can arise 

 from a difference in its internal constitution, must be comprised. 



The inferences of Newton were confirmed by Clairaut, who fur- 

 nished strict demonstrations of two propositions assumed by that 

 great philosopher; these are — 1. That the elliptic figure satisfies 

 the conditions of equilibrium ; and, 2. That the centrifugal force 

 varies with the square of the cosine of the latitude. He also de- 

 monstrated a theorem that has since been of much use in deter- 

 mining the shape of the earth, from observations on the intensity 

 of gravity. This important theorem is as follows, viz., The sum 

 of the two fractions, one of which represents the ellipticity of the 

 earth, and the other the ratio of the force of gravity at the Poles to 

 that at the Equator, is equal to f of the fraction expressing the ratio 

 of the centrifugal force at the Equator to the force of gravity. 



We are only acquainted with the mere crust of the globe we 

 inhabit ; but reasoning from the nature of the substances of which 

 it is composed, we might infer an increase in its density, between 

 the surface and the centre. The same inference may be drawn 

 from the experiments of Cavendish with the Balance of Torsion, 

 and the observations of Maskelyne on the attraction of the moun- 

 tain Schehallion: from these different methods a mean density 

 may be inferred of not less than four and a half times that of 

 water, while the outer shell has a specific gravity considerably 

 below 3. Laplace, too, assuming the density of the surface to be 



