Mr. A. Cayley on the Theory of Elliptic Motion. 425 



Wire before annealing, made from copper which hadl 



been melted and allowed to cool in the crucible >-8"937 



containing charcoal J 



Same wire after annealing 8"930 



Piece of an ingot cast iu coal-gas 8"948 



Another piece of the same ingot 8'958 



From these experiments, it will be seen that tough pitch cop- 

 per is copper containing an amount of oxygen equal to from 3 

 to 3*5 per cent, of suboxide of copper, in addition to small quan- 

 tities of foreign metals, such as lead or antimony, or both, and 

 that the existence of a certain amount of oxygen in it is essential 

 to the perfect malleability of such copper. 



That the brittleness of overpoled copper is not due to carbon, 

 but to the foreign metals occurring in tough pitch copper, the 

 influence of which upon the malleability of the metal is no longer 

 counteracted by the oxygen compounds, owing to their having 

 been reduced by the carbon. 



That the porous structure of overpoled copper arises fi'om a 

 reaction between carbon or sulphur (for the anthracite employed 

 on the large scale contains sulphur) absorbed by the metal in 

 the furnace and oxygen absorbed by it whilst casting, which 

 gives rise to a gas. That it may be cast with a dense structure 

 by taking precautions to exclude the action of the air, such as 

 by filling the mould with coal-gas, and pouring the metal so 

 that it shall pass through coal-gas and not through air; and 

 that this porosity is not the cause of the brittleness of overpoled 

 copper. 



That the specific gravity of copper which has been melted 

 under charcoal and cast with a porous structure is increased by 

 being drawn into wire, so that it is nearly as high as wii'e made 

 from copper which had a dense structure at first. 



That the specific gravity of copper which has been melted 

 under charcoal and cast with a dense structure is not increased 

 by being drawn into wire, and that the specific gravity of the 

 wire is the same before as after annealing. 



LIII. Note on the Theory of Elliptic Motion. 

 By A. Cayley, Esq.^ 



IF, as usual, r, denote the radius vector and longitude, and 

 fj, the central mass, then the Vis Viva and Force function 

 are respectively 'ji__il^,J2_|_,.2^'2\ 



r 

 * Communicated by the Author. 

 Phil. May. S. 4. Vol. 11. No. 74. June 1856. 2 F 



