230 Mr. R. Phillips on the Magnetism of Pewtei^ Coils. 



not for other than infinite values of certain of the ratios exist- 

 ing between the variables. 



Without for the present further enlarging on the hitherto 

 unexplored and highly interesting theory of Particular Result- 

 ants, I will content myself with stating one beautiful and general 

 theorem relating to them; to wit, "if F = 0, G=0, &c. be a 

 given system of equations with the coefficients left general, and 

 R be the resultant of F, G, &c., and if now the coefficients in 

 F, G be so taken that R comes to contain as a factor or be coin- 

 cident with R'"*, then will R' = indicate that (when the coeffi- 

 cients are so taken as above supposed) F = 0, G = 0, &c. will be 

 capable of being satisfied, not, as in general, by one only, but 

 by {m) distinct systems of values of the variables in F, G, &c., 

 subject of course to the possibility, in special cases, of certain of 

 the systems becoming multiple coincident systems.'^ 



I pass on now to the more recondite and interesting theory of 

 the resultant of Ternary Aggregative Functions, that is to say 

 functions of the form 



which will be seen to admit of some remarkable applications to 

 the theory of reciprocal polars. 



[To be continued.] 



XXXIV. On the Magnetism of Pewter Coils. 

 By Reuben Phillips. 

 [Continued from vol. xxxvii. p. 2^8.] 

 149. TT will be in the recollection of the readers of the former 

 Jl papers, that I thought I had discovered that a jet of 

 steam escaping into the air is magnetic, which I attributed to 

 thermo-electric currents passing between the hotter and colder 

 particles; thence, in endeavouring to discover the equivalent 

 static effect, I found instead, that mode of electrical development 

 consisting of the friction of gaseous matter on water, and which 

 in my opinion completely solves the question of the source of 

 atmospheric electricity. I have found since then I was wrong 

 in ascribing magnetic properties to the jet of steam, the magnetic 

 disturbance being situated in the metallic steam-passages, and 

 it should seem directly related to terrestrial magnetism. 



150. A straight glass tube, about '3 inch diameter and 17 

 inches long, connected the glass coil with the condenser. All 

 effect on the magnetic needle now ceased, even when the coil was 

 kept cool by being partly immersed in water and covered with 

 wet cloth. 



ISd. The brass jet (9.) was united to the end of a glass tube 



