Archdeacon Pratt on the Fluid Theory of the Earth. 431 



on this subject about three months before the appearance of 

 your notice of my book in February last ; but the latter remains 

 uncompleted, as I have not been able to satisfy myself on an in- 

 vestigation upon which I entered to determine whether there 

 were any other exceptions than that presented by the sphere. 



2. Having said thus much, I will now discuss the proposition. 

 The object I had in introducing it I state in the previous article 

 of my book. It was to refute a wrong notion which has of late 

 years appeared in print, that the law of gravity at the surface of 

 the earth can be obtained theoretically without any reference to 

 the arrangement of the mass. The original investigation from 

 which this result was supposed to flow is referred to at p. 190 of 

 Mr. Airy's ' Mathematical Tracts,' fourth edition ; and the fol- 

 lowing is an extract from the investigation itself: — 



"■ Without assuming the earth's original fluidity, but merely sup- 

 posing it consists of nearly spherical strata of equal density, and 

 observing that its surface may be regarded as covered by a fluid, in- 

 asmuch as all observations relating to the earth's figure are reduced 

 to the level of the sea, Laplace has established a connexion between 

 the form of the surface and the variation of gravity, which in the 

 particular case of an oblate spheroid agrees with the connexion which 

 is found on the hypothesis of original fluidity. The object of the 

 first portion of this paper is to establish this general connexion with- 

 out making any hypothesis whatever respecting the distribution of 

 matter in the interior of the earth, but merely assuming the theory 

 of universal gravitation." 



In a note at p. 83 of my book I point out a false step in the 

 reasoning of this investigation, and in art. 86 show that when 

 this is corrected the investigation is in no respect more general, 

 nor assumes less, than Laplace's. .But I was anxious, besides 

 showing where that particular investigation broke down, to prove 

 a priori that the notion which it was attempted to establish is 

 not true. For this purpose my proposition under consideration 

 was produced, which, for this single object, would better have 

 been worded as follows : — 



Prop. To prove that if the form of the earth's surface is a sphe- 

 roid of equilibrium, the arrangement of the earth's mass cannot be 

 independent of that form. 



For " suppose some [arbitrary] change were to be made in 

 the arrangement of the earth's mass without altering its external 

 form. It is evident that, although the resultant attraction of the 

 whole mass might possibly be unaltered by this change at par- 

 ticular points of the surface, it could not remain the same as 

 before at every point of the surface/' unless the arbitrary change 

 happen to satisfy the precise equations of condition for the ex- 

 ternal attraction of the mass to remain the same. In the first 



