•At>4 Mr. H. W. Chapman on 



^{^i+Asin^+c/^+cos^y} jc^+coseV+Asin^ 



A 2 sin 2 



2X.3(^cos^{^.A.in 2 ^c(Scos^) 2 } 



A 2 sin 2 e 

 A J i 



■ / A ,- , hr , . h A 



,. 2gh n lfl-M - A a / J 



= lv vcos0— , . „ „ ; 



« 2 A 2 sin 2 <9 



.:. A 2 siir6>(9 2 ( /v 2M+l+ ~ + 2-cos0) 

 \arm. of a J 



,-, 2 {c(i + co^y.A 2 sin 2 .} + X 2 {^4-(i + cos^} 



= 2Xn(^ +cos^ A y^_-fAsin 2 6> + C^+cos6>y. (U) 



The positive value o£ the root will be the right one if we 

 take n of the same sign as a> 3 , and therefore as o> 3 . This can 

 be done as the sign of n is still at our disposal. 



If we put cos 0=/jl, the equation becomes 



+ A// 2 - A 2 K + 2u j - (X 2 + C?i 2 ) -f gh^ } 



+ /* 2 (X 2 + Crc 2 -~A>z 2 + A 2 K) -2 <jl ^fi 



a' 



2 

 ,3~ 



The height of the centre of gravity of the egg above the 

 horizontal plane is a + h/x. Hence (15) is the fundamental 

 equation giving the vertical motion of the centre of gravity. 

 This defines the nutation. 



