148 Notices respecting New Books. 



complete the proof of the fluid hypothesis, it is necessary to show- 

 that no such arrangement is possible. And this Archdeacon Pratt 

 attempts to do. He says (p. 80), " Suppose some change were 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 on the surface might possibly be unaltered by this change 

 at particular points of the surface, it could not remain the same as 

 before at every point of the surface ;" and then follows some general 

 reasoning too long to quote. Not content with this, he calculates 

 the separate effects of three hypothetical rearrangements, and finds 

 them all inconsistent with the results of pendulum experiments. 

 It must be allowed that the pains bestow 7 ed upon this point show 

 that the Archdeacon is awake to the requirements of strict proof. 

 But we must add that in our opinion he has failed to prove his 

 point. It admits of easy demonstration, that without changing the 

 form of a given mass it is possible to rearrange its particles in an hide- 

 finitely great number of ways consistently with its attraction on all 

 external points continuing the same as before. We are not aware that 

 this fact has ever before been pointed out; and as it may be disputed, 

 we add a demonstration in a postscript. 



It is perhaps worth while to point out one consequence that fol- 

 lows from this theorem. It is stated that the variation of gravity on 

 the earth's surface proves that the matter of the earth must be 

 arranged according to the fluid hypothesis ; so far is this from being 

 true, that it need not be inconsistent with the ascertained variations 

 of gravity if there were distributed irregularly through the earth very 

 dense masses of matter, and likewise cavities filled with very light 

 forms of matter. 



Let us, however, not be mistaken ; we are not advocating any 

 rival theory. If we must have a theory, we incline to accept that 

 according to which the earth was once in a fluid or semifluid state. 

 But we do not see the need of having any theory at all. The 

 fluid hypothesis undoubtedly can be made to comply with all the 

 facts of the case ; but we think it follows from what has been said 

 above, that the evidence derived from the figure of the earth in favour 

 of its actual truth does not rise above a slight probability, and that 

 under any circumstances Archdeacon Pratt has very much over-esti- 

 mated the force of that evidence. 



P.S. — Conceive any mass attracting an external point (P), and 

 conceive the mass to consist of two portions V and V' ; these two 

 portions may be distinct, or may be superimposed wholly or in part 

 in any way whatever. Now the attraction of the whole mass on P 

 must be the resultant of the separate attraction of V and V on P. 

 Conceive (if possible) the matter composing V to undergo any change 

 of arrangement and become v' , such that its attraction on P remains 

 the same; then the attraction of V-f-V on P will be the same as 

 that of V + t/ on P. 



Suppose V to be a spherical shell of uniform density ; then if the 

 matter composing it be rearranged so as still to form a concentric 



