465 



Sir William Betham exhibited two specimens of gold ring 

 money, found at Chiusi and Perugia, in Italy. He also pre- 

 sented to the Academy an ancient brass basin, found in the 

 King's County ; and two antique metallic mirrors, found in 

 Italy. 



Sir William R. Hamilton stated and illustrated a theorem 

 of anthodographic (or anthodic) isochronism, namely, that if 

 two circular anthodes, having a common chord, which passes 

 through or tends towards a common centre of force, be both 

 cut perpendicularly by any third circle, the times of anthodi- 

 cally describing the intercepted arcs will be equal : — the an- 

 thode of a planet being the circular locus of the extremities of 

 its vectors of slowness, or of straight lines representing, in 

 length and in direction, the reciprocals of its velocities, and 

 drawn from a common origin. 



This theorem is intimately connected with the analogous 

 theorem respecting hodographic isochronism (or synchronism), 

 which was communicated to the Academy by SIb William 

 Hamilton, in a note read at the Meeting in last March. He 

 had been led to perceive that former theorem by combining 

 the principles of his first paper on a General Method in Dy- 

 namics, published in the second part of the Philosophical 

 Transactions for 1834, with those of his communication of last 

 December, since published in the Proceedings of the Aca- 

 demy, respecting the Law of the Circular Hodograph. This 

 Hodograph was, for a planet or comet, the circular locus of 

 the extremities of its vector* of velocity, d& the Anthode is the 

 locus of the extremities of the vectors of slowness ; so that the 

 -rectangular coordinates of the Hodograph are x', y', z', if 



, _dx , dy ) _ dz' 

 "" -dt^y ~di'^ "It' 



