362 THE SCIENTIFIC PAPERS OF 



In substituting 2R for h in formula (1) we obtain A = | R . n-, 

 the expression for the total attraction of the earth, which was 

 determined by Newton ; a verification is thus furnished of the 

 correctness of the above calculation. 



The proportion between the attraction exercised by the upper 

 segment and the whole earth, supposing them to be composed of 

 uniform material, is therefore as ^ : A. = 2nh : |R?r, or as h : |E. 



EATIO OF VARIATION OF ATTRACTION, AS THE DEPTH TO THE 



EARTH'S RADIUS. If sea-water had no weight, the total force of 

 gravitation at the point P would be diminished in the ratio 



- : but. inasmuch as the ratio of the difference of mean 

 f radius 



2-768-1-026 1-737 it 

 rock and sea-water to mean rock is - ~r^7^> -- = a ^o' 



Z'/oo J'/bo 



follows that the real influence of depth, on the supposition of the 

 earth's density being throughout that of mean rock, would be 

 represented by the expression 



2-763 h // 



|R 614 ~ 1-06 R' 

 579 K 



or approximately as the depth to R. 



Thus, for a depth of one thousand fathoms, gravitation 

 diminishes by -^eVr'of itself. 



NECESSITY FOR MODIFYING RESULT, NEITHER COMPRESSION 

 GREAT ENOUGH TO BE SENSIBLE IN ITS EFFECT, BUT THE TWO 

 NOT EQUAL. The rock composing the crust of the earth will be 

 under compression, and therefore denser at the depth correspond- 

 ing to the depth of sea ; but sea-water itself will increase in 

 density with depth in a somewhat similar ratio, so that the com- 

 parison between sea-water and solid rock remains virtually the 

 same for all depths. The greater density of the earth towards its 

 centre will, however, greatly influence the measure of this depen- 

 dence as established by the foregoing calculation ; but in con- 

 structing a measuring instrument it will be safer to rely upon the 

 result of actual measurement, in the absence of reliable informa- 

 tion regarding the increase of density towards the centre, by com- 

 paring its indications with those obtained by means of the sound- 



