208 jNIr. A. Cayley on the Nomographic Transformation of 



terms lead to auy mistakes regardiug electrical action, or give 

 rise to any false view of the character of electricity or its unity. 

 I cannot find other terms of equally useful significance with 

 these ; or any, which, conveying the same ideas, are not liable to 

 such misuse as these may be subject to. It would be affectation, 

 therefore, in me to search about for other words ; and besides 

 that, the present subject has shown me more than ever their 

 great value and peculiar advantage in electrical language. 



Note. — The fuse referred to in page 199 is of the following 

 nature : — Some copper wire was covered with sulphuretted gutta 

 percha ; after some months it was found that a film of sulphuret 

 of copper was formed between the metal and the envelope ; and 

 further, that when half the gutta percha was cut away in 

 any place, and then the copper wire removed for about a quarter 

 of an inch, so as to remain connected only by the film of sul- 

 phuret adhering to the remaining gutta percha, an intensity bat- 

 teiy could cause this sulphuret to enter into vivid ignition, and 

 fire gunpowder with the utmost ease. The experiment was 

 shown in the lecture-room, of firing gunpowder at the end of 

 eight miles of single wire. Mr. Faraday reported that he had 

 seen it fii-ed through ] 00 miles of covered wire immersed in the 

 canal by the use of this fuse. 



XXX. On the nomographic Ti'ansformation of a Surface of the 

 Second Order into itself'^. By A. Cayley, Esq.-\ 



I PASS to the improper transformation. Sir W. R. Hamilton 

 has given (in the note, p. 723 of his Lectures on Quarter- 

 nions) the following theorem : — If there be a polygon of 2m 

 sides inscribed in a surface of the second order, and (2m — 1) of 

 the sides pass through given points, then will the 2mth side con- 

 stantly touch two cones circumscribed about the surface of the 

 second order. The relation between the extremities of the 2?Mth 

 side is that of two points connected by the general improper 

 transformation ; in other Mords, if there be on a surface of the 

 second order two points such that the line joining them touches 

 two cones circumscribed about the surface of the second order, 

 then the two points are as regards the transformation in question 

 a pair of corresponding points, or simply a pair. But the rela- 

 tion between the two points of a pair may be expressed in a dif- 

 ferent and much more simple form. For greater clearness call 

 the surface of the second order U, and the sections along which 



* See Phil. Mag. vol. vi. p. 326 (Nov. 1853). 

 t Communicated by the Author. 



