6 INTERNAL STRUCTURE OF THE EARTH 



equatorial axis, 0, perpendicular to the solstitial line (t. e., a tilting of the equator 

 towards the sun) through an angle measured by 



(6) 1^-, sin V cos V* 



r w 



will, relativehj to ihe normal 2'>osition of surface, produce exactly the disturbance 

 denoted by above expression {(i). Tn the case of Sir Wm. Thomson's hypotlietical 

 body acted on by mere centrifugal (i.e., repeUiwi-line^ force unthout the "vortex- 

 moiion" which produces that force, the above computed turning of the entire hoihj 

 (or what is equivalent to it since motion, as such, is disregarded) would actually 

 ensue. Or, to state the matter a little differently, the tidal developments of the 

 equilibrium theory express not merely "deformations" (such as are the "secular" 

 and " semi-diurnal" tides), but, in the " diurnal" tide, an actual tilting under the 

 precession-producing "couple" of the foreign attraction ; a tilting which is checked 

 very intelligibly on the fixed repelling line hypothesis, by its repulsion, which, un- 

 changeably normal to the unchanged direction of the line, finds in the changed 

 position of the body the conditions requisite to the production of a neutralizing 

 couple. We find here a reason why tlie earth should be but minutely drawn from 

 its angle of obliquity, couj-)led with a reason why there should be no precession. 



Is the above the true mechanical exhibition of the matter"? Is the centrifugal 

 force, like that of the hypothetical repelling line, thus uncliaugeably constant in 

 origin and in the planes of its direction % Or, if its axis of origin and its planes of 

 direction shift at all, do they sliift with the totality of the figure % The latter sur- 



* The angle tliroiigh wliicli tlie fiarnre must he turnefl so that the displnrcd suvface will have an 

 elevation above the original surface represented by the expression (a) will result from dividing («) hy 



^ for an ellipse of ellipticity e ; or by 2e sin e cos 9. Performing the division ami substituting |"' 



for fife, we get the above expression (&). 



