16 Rev. 0. Fisher on the Surface Elevations and other 



inequality shows that — is zero when the ratio vanishes. 



A fortiori then is the ratio of -, which is always less than 



that of — , a quantity of the order of — , and therefore its square 



may be neglected. This will reduce the equation of the 

 temperature-curve to 



v = const. H — j== x : 



which signifies that, to the depths with which we are con- 

 cerned, we have a family of straight lines only to deal with, 

 all starting from the same point on the surface, and becoming 

 more nearly vertical as the time increases. This consideration 

 will facilitate the calculation. 



. . mt 3 4/c£ 3 a 2 , , . , , ,.. 



Again, — , or ^ — j-= ^-j, may be neglected when multi- 

 plying -J-, for it will be found that 



J' 



r dt 2 r 2 



It is also evident that j 6 dx, when divided by r 2 , may be 



neglected. Therefore, dividing by r 2 , integrating for t, and 

 neglecting the small quantities referred to, the equation is 

 reduced to 



- d £ = 2ej>-2eB + f{x 



where f(x) is to be determined by the limits of t, the same for 



$ and 0. These are, (1) the time when the level of no strain 



was at x, and (2) the present time, when it is at the depth 



3 a 2 . 



3 — . It is obvious that <f> and 6 were identically equal at the 



former epoch ; their difference was then 0. 



At the second epoch, since we are permitted to regard the 

 temperature-curve as a straight line, 



b 3 a 2 . 



0= const. -r — ? 



T a 2 r 



and a b 



u= const. as: 



