1 36 Dr. C. F. Schoenbein on some 



we may obtain a symmetrical equation between any G pairs 

 of coordinates {x^y)^ which shall be independent of the as- 

 sumed constants. The Jixed symmetry of such an equation 

 will express that the six varying points corresponding to the 

 varying pairs of coordinates lie in a conic section. I call it 

 " the conic-sectional synmietry." To return to the question 

 I have suggested as interesting, the following will be its alge- 

 braical statement. Is it possible to find a system of conic- 

 sectionally symmetrical equations, such that no two of the 

 equations shall involve the same 5 pairs of coordinates, and 

 such that, from all of the equations but one, the remaining 

 one shall be a necessary consequence? To solve this and si- 

 milar problems, I want a condensed notation, as free as may 

 be from accidental matter, of the conic-sectional and other 

 fixed symmetries, — the essences, as it were, of genera of form. 

 Rules of elimination between a given number of equations, all 

 of a constant symmetry, may be stated as mere methods of 

 combinatorial arrangement. In the few preceding sentences 

 has been shadowed forth my idea as to a practical mode of 

 establishing a cor\nexion between the solution of geometrical 

 problems of position, and the formation of arrangements of 

 sets so as to possess assigned properties. Some brains may 

 be better adapted for researches of the former kind ; others, 

 for those of the latter. Problems seeking one among finite 

 combinations, when possible, may be worked out by plodding 

 labourers, understanding, remembering, and applying rules, 

 and knowing when to stop, — by machines, in fact, such as 

 Mr. Babbage might construct. In such researches, however, 

 compendious success, when it is due at all to reasoning, is ge- 

 nerally due to reasoning of the inductive or analogical, not 

 the syllogistic type. Such success, indeed, though helped out 

 by reasoning, seems for the most part to spring from the luck 

 of an appropriate inventive faculty akin to imagination. 



XXV. Notice on some peculiar Voltaic Arrangements. By 



Dr. C. F. SCHCENBEIN.* 



I AM not aware that any philosopher has as yet pointed out 

 the possibility of constructing voltaic arrangements which 

 as to their mode of exciting current electricity must be con- 

 sidered in some respects at least as the very reverse of what 

 our ordinary hydro-electric circles are. That such association 

 can be made will appear from what I am going to state. 



• Communicated by the Author. 



