On the Differential Equation of Electrical Flow, 419 

 / sin g ( n z w 4 • . \ d sin a 



-(4 + 44 +& c.)^ +& c.} a 



As might have been anticipated, the effect of the additional 

 terms is to broaden out the line and convert it into a rather 

 complicated group of lines, as can sometimes be observed 

 with a bad grating. At any given angle the same effect can 

 be produced by variation of the plate from a perfect plane. 

 Likewise the effect of errors in the ruling may be neutralized 

 for a given angle by errors of the ruled surface, as noted in 

 the earlier portions of the paper. 



XL. On the Differential Equation of Electrical Flow. 

 By T. H. Blakesley, M.A* 



THE object of this paper is to point out that the theory 

 of electrical discharge, as exemplified in the mathe- 

 matical expressions employed to represent the physical facts, 

 is incompetent to explain all the phenomena observed in 

 extreme cases ; and to show that the admission of certain 

 properties of matter not usually recognized is the only way of 

 satisfactorily obviating the imperfection of the existing views. 



In some of the investigations I shall not employ exclu- 

 sively algebraical symbolic methods, but, where it may more 

 advantageously be adopted, I shall avail myself of the geome- 

 trical method. Such cases most frequently arise where magni- 

 tudes under consideration are capable of having negative 

 values. All tidal effects, using the word in its most general 

 sense, involve such magnitudes. 



Electrical currents in a given conductor may have all 

 possible values in one direction or in the opposite direction, 

 but are otherwise restricted. 



The projection of the line joining two points in space 

 upon a fixed straight line is a geometrical magnitude of this 

 sort. With respect to the direction in space, sometimes one 

 of the projected points will be on one side of the other 



* Communicated by the Physical Society : read March 24, 1893. 



