4G0 Prof. Cayley on a Theorem relating 



Electric quantities maybe compared by the swing of the needle 

 of a galvanometer of any kind. They may be measured by any 

 one in possession of a standard electro-dynamometer, or resist- 

 ance-coil, since the observer will then be in a position directly 

 to determine C 1 in equation (12), or Rj in equation (14). 



Capacities may be compared by the methods described (26) ; 

 and a Leyden jar or condenser (41) of unit capacity, and copies 

 derived from it, may be prepared and distributed. The owner of 

 such a condenser, if he can measure electromotive force, can de- 

 termine the quantity in his condenser. 



The material standard for electromotive force derived from elec- 

 tromagnetic phenomena would naturally be a conductor of known 

 shape and dimensions, moving in a known magnetic field. Such 

 a standard as this would be far too complex to be practically 

 useful : fortunately a very simple and practical standard or gauge 

 of electromotive force can be based on its statical effects, and 

 will be described in treating of those effects (Part IV. 43). 

 A practical standard for approximate measurements might be 

 formed by a voltaic couple, the constituent parts of which were 

 in a standard condition. It is probable that the DanielPs cell 

 may form a practical standard of reference in this way, when its 

 value in electromagnetic measure is known. This value lies 

 between 9 x 10 7 and 1 1 x 10 7 . 



Resistances are compared by comparing currents produced in 

 the several conductors by one and the same electromotive force. 

 The unit resistance, determined as in Appendix D (Brit. Assoc. 

 Reports, p. 163), will be represented by a material conductor ; 

 simple coils of insulated wire compared with this standard, and 

 issued by the Committee, will allow any observer to measure any 

 resistance in electromagnetic measure. 



[To be continued.] 



LXII. On a Theorem relating to Five Points in a Plane. 

 By A. Cayley, F.R.S.* 



TWO triangles, ABC, A'B'C which are such that the lines 

 AA', BB', CC meet in a point, are said to be in perspec- 

 tive ; and a triangle A'B'C, the angles A', B', C of which lie in 

 the sides BC, CA, AB respectively, is said to be inscribed in 

 the triangle ABC ; hence, if A', B', C are the intersections of 

 the sides by the lines AO, BO, CO respectively (where is any 

 point whatever), the triangle A'B'C is said to be perspectively 

 inscribed in the triangle ABC, viz. it is so inscribed by means 

 of the point 0. 



We have the following theorem, relating to any triangle 



* Communicated by the Author. 



