Elastic Equilibrium of Semi-Infinite Solid. 45 



altitude 45° and aiiionnts to 0. "017 neaiiy. The total effect of a 

 tide of amplitude one metre (which is possibly two or three times 

 the actual amount) found here is not small enougli to be neglected 

 compared with the direct effect of the moon. As the tilting effect 

 and the attraction effect of the tide wave are directly proportional 

 to the height of the tide, the total effect oscillates in time in 

 accordance with the law which the tide obeys. There is, in 

 general, a difference in phase between the lunar effect and tidal 

 effect, which is worthy of closer investigation. But we must bear 

 in mind that the calculation adopted here is nothing but a rough 

 estimation of order of magnitude, since the north Atlantic is far 

 from circular, the tidal loading in it is never uniform. Neverthe- 

 less the above analysis shows that tlie tidal effect on the w^ater- 

 level measurement, even at a point as far from the coast as 

 Chicago, plays an imY)ortant role and cannot be regarded as a 

 small correction. 



Example IV. 



§35. Let us take another example by assuming the normal 

 pressure of the form 



/(r) = — '^- / a- — }-- for >• <r « ^ ^ 



•^^ ^Tzar V I (97) 



= „ r > a J 



to be given at z = 0, II l)eing its total amount. In this case the 

 function Z{}c) becomes 







_ _ 3// f aml- g — kg cos Jca \ .qo. 



Therefore the components of displacement are given by 



