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 ares 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 Si» 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 vectors of velocity, as the Anthode is the 
locus of the extremities of the vectors of slowness; so that the 
~ rectangular coordinates of the Hodograph are 2’, y’, 2’, if 
da dy dz 
/— 
Pree no Sy: ints 
May ham eee 
