75 



*' I gave my son directions to show you two other coins 

 of the same set, which you possibly will also reckon Etrus- 

 can. 



" I am, dear Sir William, 



" Your faithful Servant, 



" Thomas L. Cooke." 



The following notice was communicated by Sir William 

 Rowan Hamilton, of a Paper " on the Application of Quater- 

 nions to the Determination of the Distance of any recently 

 discovered Comet or Planet from the Earth." 



This celebrated problem is treated in this paper by means 

 of the formulae which were communicated to the Academy by 

 the author, in July, 1845. The chief step consists in a very 

 easy deduction, from those formulae, of the equation : 



M M\ S.yy'y". 



a(M_M\_ 



.yy a 



where c is the sought distance of the comet (or planet) from 

 the earth ; M is the mass of the sun, and a and b are the 

 distances of earth and comet from that body ; a is the helio- 

 centric vector-unit of the earth, and y is the geocentric vector- 

 unit of the comet ; while y', y" are the first and second diffe- 

 rential coefficients of 7, taken with respect to the time, and 

 determined, along with y itself, from three successive obser- 

 vations : and S is the characteristic of the operation of taking 

 the scalar part of a quaternion. The second member of the 

 equation admits of being geometrically interpreted as a ratio 

 of two pyramids, and can in various ways be transformed by 

 the rules of the calculus of quaternions. 



Mr. Donovan exhibited a table gas lamp of his invention, 

 which generates its own gas, and made the following statement 

 relative to it : 



h2 



