90 



MR EDWARD SANG ON THE DEFLECTION OF THE PLUMMET. 



tion upon a material point situate at that centre, and all bodies on the earth par- 

 take of that motion ; but the sun's attraction varies inversely as the square of the 

 distance, and is greater for a body on the near side, less for one on the farther side 

 of the earth. Hence a body on the near side would tend to describe an orbit 

 more curved, one on the farther side an orbit less curved, than the earth's actual 

 orbit ; and in either case, there is a tendency to augment the distance between the 

 body and the earth's centre. Thus, as is well known to every one who has studied 

 the theory of the tides, the sun's attraction tends to raise the ocean on the farther 

 as well as on the near side of the earth. 



The perceivable part of the sun's attraction is therefore the difference between 

 the attraction on a body placed at the earth's centre and that on a like body 

 placed at the surface ; or, more strictly, is the resultant of the sun's actual attrac- 

 tion, and of a repulsion equal in intensity, and parallel in direction to the attrac- 

 tion which the sun exerts upon a like body placed at the earth's centre. 



If we put D for the distance of the sun, R for the radius of the earth, and a 

 for the sun's zenith distance, the intensity of the attraction is almost proportional 



to (D -E, cos a)-2 = D-2 + 20-=* R cos a + 3D-^ R^ cos a^ + &c. 



Now, the first term of this series represents the attraction at the earth's centre, 

 wherefore the remaining terms 



D~- -! 2=^COSa + 3=j^2C°S a- + &C. t 



•p 1 



represent the disturbing influence. The value of the fraction jc is about oi Afm*^^' 



and even the first term of the series amounts to a very small quantity ; wherefore, 

 neglecting the succeeding terms, we may hold that, for all practical purposes, the 

 formula 



D""- X 2=pr COS a, 



represents the amount of the disturbing influence exerted in the direction of the 

 attracting body. This influence is zero when the sun is on the horizon, and is 

 greatest when the sun is in the zenith or nadir. 



But when the sun is in the zenith or nadir, ihe disturbing influence is exerted 

 directly upwards, and cannot tend to deflect the plummet ; in fact, the deflecting 

 tendency is proportional to the sine of the zenith distance as well as to the above 

 quantity, so that the tendency to deflect the plummet is finally represented by 



■p T> 



D"~- X 2 pT cos « . sin « = T>~- x p- sin 2a. 



Hence, the plummet is most drawn aside when the attracting body is 45' above 

 or below the horizon. 



For the earth's mean distance D~- may be taken to represent 128" ; and. 



