OF PHYSICAL QUANTITIES. 265 



conception. We require a vector word, which shall indicate both direction and 

 magnitude, and one not already employed in another mathematical sense. I have 

 taken the liberty of extending the ordinary sense of the word slope from topo- 

 graphy, where only two independent variables are used, to space of three 

 dimensions. 



If <r represents a vector function, Vcr may contain both a scalar and a 

 vector part, which may be written SVa- and Fv<r. 



I propose to call the scalar part the Convergence of cr, because, if a closed 

 surface be described about any point, the surface integral of a; which expresses 

 the effect of the vector cr considered as an inward flux through the surface, is 

 equal to the volume integral of Sv<r throughout the enclosed space. I think, 

 therefore, that the convergence of a vector function is a very good name for the 

 effect of that vector function in carrying its subject inwards towards a point. 



But Vcr has, in general, also a vector portion, and I propose, but with 

 great diffidence, to call this vector the Curl or Version of the original vector 

 function. 



It represents the direction and magnitude of the rotation of the subject 

 matter carried by the vector cr. I have sought for a word which shall neither, 

 like Rotation, Whirl, or Twirl, connote motion, nor, like Twist, indicate a helical 

 or screw structure which is not of the nature of a vector at all. 



/' \ v 



( " J -> V 



CONVERGENCE. CURL. CONVERGENCE AND CURL. 



If we subtract from the general value of the vector function cr its value 

 cr at the point P, then the remaining vector cr o- will, when there is pure 

 convergence, point towards P. When there is pure curl, it will point tan- 

 gentially round P ; and when there is both convergence and curl, it will point 

 in a spiral manner. 



The following statements are true : 



The slope of a scalar function has no curl. 



The curl of a vector function has no convergence. 



VOL. u. 34 



