AS AFFECTING F R E C E S S I O N A X D NUTATION. 5 



figure (and rotation). Looking (o the internal motion of par'icles required to pro- 

 duce them, it is easily seen that tlie first (diagram I, Fig. 1, where shaded portions 

 are protuberant ; unshaded, depressed ; and where the attracting body is supposed 

 on the ri(jhf, and above the equator) indicates an infiuitesimally (almost) slight 

 squeezing together of the parallels of latitude or planes of rotation ; the other 

 (diagram III), a minute approximation of meridianal planes to that in which lies 

 the attracting body, and an eloignment of these planes from a meridian normal 

 to the first; a slight slackening of rotary moliou in the approximated planes — an 

 acceleration in the others. 



Fiff 1. 



n. p_ 



P' 



Secular Tide. 



E E 



in P 



E El 



P' 



Semi-diunial 



In neither case is the deviation of the particle from its normal plane of rotation 

 more than a quantity of the second order of minuteness ; regarding tlie develop- 

 ments themselves as minute in the first order. These disturbances are symiiietri- 

 cally disposed equatorially, and whether or not " vortex-motion" hinders in any 

 degree their development, is immaterial. Neither of these two disturbances, nor the 

 components of foreign attraction which induce them, have any influence on preces- 

 sion. 



The case is very different for the diurnal tide (diagram II). The disposition of 

 the disturbance is unsymmetrical both as to the equator and the earth's axis, and 

 cannot be effected without some disturbing effect on that axis. To discuss it I 

 must dismiss tlic impossible S2)hcre and pass at once to the actual figure of equilib- 

 rium (Fig. 2) of a homogeneous rotating fluid, implied by Sir Wm. Thomson's 

 § 26 (" Rigidity of the Earth"). Such a figure has an equatorial oblateness of which 



the ellipticity, e, is (n' = angular ^•elocity of rotation ; </ = gravity at the equator). 



The expression for the tidal disturbance in question is, taken on a meridian directly 

 under the sun (t. e., the line on which lie both the maximum elevations and depres- 

 sions). 



(a) 



y 



-1 - sin V cos V sin Q cos 

 2r\j 



V = sun's declination, polar distance of locality, S, sun's mass, r its distance. 

 (The radius of the earth being taken as unity.) 

 It is easily shown that a slight turirng of the normally oblate ellipsoid around an 



