284 



Archdeacon Pratt on the Thickness of 



nics, equal to one moment 



8 , . ,z. . 27 . 5 C d.a b e 



— ■= TTfJb sm / sin co v 1 — sin' 5 / sir ft) 1 p — -y— #« 



about a diameter in the plane yz, making an angle yjr with the 

 axis of y such that 



tan , \fr= — cot co -f- cos /. 



7. In the accompanying 

 diagram let Q, P be the poles 

 of the ecliptic and earth on 

 the mean spherical surface of 

 the earth, the earth's centre, 

 Q P q the solstitial colure, V 

 the vernal equinox, V G the 

 equator cutting the plane y z 

 in G. Then P Q G equals /, 

 the sun's longitude, Q Y = co, 

 the obliquity. Then, by sphe- 

 rical trigonometry, as PG = 



90°, we have 



cos /= cos PQG= — cot QG . cot QP, 



.'. tan QG = — cot co -4- cos /= tan yjr. 



Hence QG = ->|r, and OG, the line in which the plane of the 

 equator intersects the plane yz, is the diameter about which the 

 disturbing force of the sun tends to make the earth revolve. 

 And the angular accelerating force round that diameter 



= — ~7ru, sin /sin co */ 1 — sin 2 / sm 

 5 



the divisor being the moment of inertia of the earth, 



C d.a b e 7 8 r d.a 5 , 



^«y^ da ^' ir yi^ da , 



where 



= — 3/A/sin I sin co s/ 1 — sin 2 1 2 co, 

 „ C d . a b e 7 C d .a 5 7 



This will generate an angular velocity about OG in the time dt 



= 3/jfsin I sin co v\ — sin 2 / sin 2 co . dt. 



But the earth revolves round its axis OP. The combined 

 effect of these two angular velocities is, that it will revolve round 



