so Mr R. B. HAYWARD, ON A DIRECT METHOD, &c. 



whence as before, 



^ (- jBQ sin c sin 0) = G + Aw i~y + cose) + SI -^ + Q coscj . Q sin c cos (p, 



d ( dd) \ . . . . . 



— I S — i- + cos c 1 = BQ. sm c sin (^ . Q sin c cos + Joj . Q sin c sin (p, 



and therefore w is constant, and 



d?<t) A . . . , . 



-TT = t; wQ sin c sm + Q^ sin- c . sin cos 0, 



dfi B ^ ^ ' 



or approximately 



-^ = - «Q sm c . sin ; 



whence, the rotation about OA being in the same direction seen from A as that of the earth 



seen from the north pole, it will be in a position of stable equilibrium when directed to the 



north, and of unstable equilibrium in the opposite position : also if originally directed in any 



other direction, it will oscillate about its position of stable equilibrium like a circular pendulum 



Bg 



about the vertical whose length is ; , 



AwQ sin c 



Durham, Feb. 19, 1856. H. B. H. 



