

52 ADDITIONAL NOTES. 



fl) 



The above divided by the coefficient of elasticity E will give the elongation per unit of length at 

 any point. Multiply by d% and integrate from x = to X = R, and the total elongation is 



S 



E (.r R 2r* \ r 



Since log [1 ) = &c., the foregoing will reduce, approximately to 



V T I r 2 r* o r 3 



2 S R? 



3 #7*" 



If M= earth's mass, or = gravity at its surface, and the ratio of M to S, and m the ratio of 



n 



length of rod of weight E (per square inch section) to R, we shall have : S = ngR>, E = mrjR, and 

 the above expression for total elongation becomes: 



(2) - - R 



3m r 3 



Take = 1- = l # = 4000 X 5280 feet; w = 31GOOO; m = .4T2 (the latter value 

 r 92000000 23000 



based on E = 34 mill'ns Ibs. per square inch, and a steel rod of that section to weigh 3.4 Ibs. per foot 

 length) and the total elongation (2) becomes O ft .975. The maximum extension per 1 unit of length is 



at the centre, and is found by putting x = in (1) and dividing by E. It is = = 



E r 3 m r 3 



.000000055, indicating a strain of l lb .87 per square inch. The ratio of the total elongation (2) to 

 the total length of the rod R is two-thirds of the above, indicating about that ratio for the ellipticities 

 of superficial and central strata of a steel globe distorted by the sun's attraction ; a result thus rudely 

 calculated which differs little from that given in Thomson and Tait, 837. 



