60 



Now, ah is the arc of a circle which the plane of rota- 

 tion of the disc would appear to describe if placed 

 at the pole, and cd is the arc which it would appear to 

 desci'ibe in the same time in the latitude AB ; and since 

 the arcs are to each other inversely as the times of de- 

 scription of the whole circumference, it follows that 

 the time of describing the whole circumference in 

 latitude A : time of describing the whole circumference at P 



=1 ah : c d. 



— 1 : sin lat. A. 



Time at P 24 hours 



Time in lat A = 



sin lat. sin lat. 



and Time at Equator = — = Infinity. 



As I am by no means certain of the correctness of 

 some of the conclusions at Avhich I have arrived, I submit 

 them to the Society with considerable diffidence and dis- 

 trust, as subjects for discussion' rather than as demon- 

 strated truths. They seem to me, at present, to follow 

 legitimately from the doctrine of compound rotatory 

 motion. If there is any error in my reasoning, I am not 

 able to discover it ; and I shall feel greatly obliged to 

 any one who will indicate where it is, as I shall thus be 

 enabled to approach nearer the truth than the point 

 at which I have arrived by my own independent inves- 

 tigations. 



Professor Elliot thanked Professor Hamilton for the 

 more than ample justice he had dealt out to him in 

 noticing his instruments. He begged leave to make some 

 additional statements regarding his own researches 

 on the subject, as well as those of others. Professor 

 Hamilton had correctly described his (Professor Elliot's) 

 instruments for illustrating, both in regard to fact and 

 principle, the precession of the equinoxes, the nutation of 



