52 ADDITIONAL NOTES. 



(1) s/_i A L^ + a) 



^^^ . [r—Ji r' r — xr'l 



The above divitUd liy tlie cooflicicnt of da.stieity E will give tbc elongation per unit of length at 

 any point. Multiply by dx anil integrate from ;t = to ;t = ^, and the total elongatioa is 



E Xr — R 2r' ^ '^ \ r h 



R I R" 1 R' 



lo.r (i _] ^^ ^L 1-"^ &c., the foregoing will reduce, approximately to 



° V r / r 2 /■••' 3 r'' 



Since 



2 STT 



3 E r^' 



If ^1/"= earth's mass, <7 = gravity at its surface, and - the ratio of 71/ to S, and m the ratio of 



length of rod of weight E dicr sipmre inch .section) to R, we shall have : H = ncjE', E=:mgR, and 

 the above expression for total elongation becomes: 



(2) l^R^ 



Take ."^ =_- ^^^^^ - = -A^ ■ i;^4000 X 5280 feet; ?? =310000: m = .4T2 (the latter value 

 r 92000000 23000 



based on E = Z^ niiirns lbs. per square inch, and a steel rod of that section to weigh 3.4 lbs. per foot 



length) and the total elongation (2) becomes 0^'.975. The maximum extension per unit of length is 



S R'' n R' 



at the centre, and is found by putting x = (> in (') fi"d dividing by E. It is = = 



E r' m r^ 



.000000055, indicating a strain of 1".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. 



