23 



Ordinary Meeting, December IGth, 1884, 



Charles Bailey, F.L.S., in the Chair. 



Mr. E. P. QuiNN exhibited several forms of frictional 

 electrical machines. 



"Note on Envelopes and Singular Solutions/' by Sir 

 James Cockle, F.RS., F.R.A.S., &c., Corresponding Member 

 of the Society. 



{Continued from p. 12) 



SO. A differential expression with its complete integral 

 implies a corresponding equation with its complete primi- 

 tive. Solutions and integrating factors remain the same 

 on either assumption. A solution is a substitution which 

 makes the expression vanish or wliich satisfies the differ- 

 ential equation. 



31. Any given solution can always be deduced from the 

 complete primitive. But we may have to replace the 

 arbitrary constant, sometimes by a definite constant, some- 

 times by a variable function, and sometimes by one or the 

 other at pleasure. 



82. If the solution cannot be deduced without aivincf 

 the arbitrary constant a definite constant value the solution 

 is a Particular Primitive. 



33. If it can be deduced in either of two ways indifier- 

 cntly, viz., either in giving to the arbitrary constant a 

 definite constant value or in replacing it by a variable 

 function the solution is an Epicene Primitive. 



34. If it cannot be deduced without replacing the arbitrary 

 constant by a variable function the solution is a Singular 

 Solution. 



Proceedinos-Lit. & Phil. Soc— Vol. XXIV. — No. 4.— Session 1884-5. 



