322 Mr. Galbraith on the Figure of the Earth. 



lums on different bases might be reduced to the same. Taking 

 ordinary alluvial formations for the standard density, of which 

 the specific gravity may be about 2-5, — and by experiments 

 made on subsoils of light sand, gravel, or clay, combined with 

 those made on sandstone, basalt, schistus and granite,in the same 

 latitude, and thence finding what effect these have in varying 

 the length of the pendulum, — an approximate value of that ef- 

 fect may be pretty well estimated ; whence a rule may be ob- 

 tained, to reduce them all to the standard density, so far as re- 

 lates to the exterior crust of the earth. These, combined with 

 the form of the substratum and other peculiarities, of which 

 several instances may be seen in Captain Sabine's work on the 

 Figure of the Earth, would give the means of obtaining pretty 

 accurately the medium length of the pendulum in any given 

 latitude. Thus it may be inferred, that a variation of the spe- 

 cific gravity from 2 to 3 at the surface, and continued for 

 some distance towards the centre, would give a variation of 

 the length of the pendulum amounting to about 0*01 of an 

 inch. Consequently, if 2*5 were taken for the standard spe- 

 cific gravity at the surface, and the lengths reduced to this, 

 they may be increased or diminished about 0*005 of an inch, 

 — a quantity sufficient to reconcile the most discordant of the 

 pendulum experiments. These reductions, no doubt, should 

 be applied to those experiments only which are likely to be 

 employed to determine the figure of the earth, in order to ob- 

 viate the discordancies from local irregularities ; while the ac- 

 tual lengths from observation applied to other purposes, — such 

 as our standards of weights and measures obtained at a par- 

 ticular spot, — ought to be allowed to remain as they are. In- 

 deed, in an extensive series of experiments, the several correc- 

 tions for the height, shape, specific gravity, &c. of the station, 

 should be all placed in their respective columns beside the 

 original lengths, to be employed or omitted, as might appear 

 advisable, according to the purposes for which they are wanted. 

 No doubt, with regard to these corrections, a good deal is left 

 to the accuracy and judgement of the observer; and in some 

 of them great precision cannot be attained ; but in most cases 

 a probable approximation only, which, although not perfectly 

 accurate, will at least tend to give the mean ellipticity more 

 truly than when they are neglected. — Having stated these pre- 

 liminaries, our attention may now be directed to the formula; 

 for obtaining the ellipticity. 



It appears from our ordinary treatises on the Figure of the 

 Earth, supposing it to differ little from a sphere, that the cen- 

 trifugal force which acts in opposition to gravity, decreases from 

 the equator to the pole as the square of the cosine of the la- 

 titude ; 



