( 89 ) 



IX. — On the Deflection of the Plummet due to Solar and Lunar Attraction. By 



Edward Sang, Esq. (Plate V.) 



(Read 21st April 1862.) 



As the means for making observations on the heavenly bodies become more 

 and more exact, astronomers are compelled to introduce new refinements into their 

 calculations ; new inequalities are discovered, and the computation of those whose 

 sources are already known has to be carried to a greater number of approxi- 

 mative steps. 



Discussions on the amount of solar parallax, of aberration and of nutation, 

 are now carried on to the third and fourth decimal fraction of a second ; with 

 such a refinement of computation, it seems almost impossible to proceed too far 

 in the refinement of theoretical deductions, and on that account, it may not be 

 inopportune to discuss the influence which the sun's and moon's attraction exert 

 upon the direction of the plumb-line. 



The strict and symbolical investigation of this subject presents no difficulty, 

 and offers no point of any interest to the analyst ; it will therefore be sufficient 

 to exhibit the matter in what may be called a popular light ; the more so, that 

 the reasoning will thereby lose none of its strictness. 



The direct attraction of the sun upon a body on the surface of the earth 

 amounts to about the 1600th part of gravitation, and a pressure equal to it, 

 applied horizontally, would deflect the plummet by an angle of 128 seconds. 



The statement, that a body weighing one pound, that is, a body attracted to 

 the centre of the earth by 7000 grains, is also attracted to the sun by 4^ grains, 

 is rather startling. We might expect that direct evidence of so strong an attrac- 

 tion should have been afforded by mechanical phenomena. 



The earth's attraction is at once manifested to us by the pressure which every 

 substance exerts upon that below it, or by the rapidity with which it descends, 

 when left free to move. But there is no solid matter intervening between us and 

 the sun, to resist gravitation towards it, and we are unable to perceive the motion 

 sun-wards, because all surrounding bodies partake of the same motion. 



In one second of time the earth is deflected from its rectilineal course by about 

 one-eighth part of an inch ; now, in that time, its linear motion is about 17 miles ; 

 and we may obtain some remote idea of the curvature of the earth's orbit, by 

 imagining a circle which deviates from its tangent by one-eighth part of an inch at 

 the distance of 17 miles from the point of contact. 



The centre of the earth is carried round the sun in an orbit due to the attrac- 



VOL. XXIII. PAET I. 2 B 



