﻿Notices respecting New Books. 151 



first to give a distinct title to the vector 



(dw dv\ .fdu dw\ ,fdv du\ 

 dy ~faj+\fa~fa) +k \d^~dj/)' 



which is derived from any given vector, ui+yj+wk. In the first 

 edition of the ' Electricity and Magnetism ' he proposed to call the 

 first of these the version or curl of the second, and subsequently 

 the rotation. Mr. Heaviside fixed on the term curl* and by this 

 name it is now fairly well known. These two related vectors are 

 of perpetual occurrence in all branches of mathematical physics, 

 and it is well that their relationship should be directly indicated 

 and recognized. 



Thus, for example, the condition that a liquid should be capable 

 of being in equilibrium under the action of any assigned force- 

 system (" forcive," as Mr. Heaviside would say) is that at each 

 point in the space occupied by the liquid, the resultant force and 

 its curl should be at right angles to each other. Hence, if we call 

 the primary vector p, Mr. Heaviside always denotes the first- 

 mentioned as " curl p." The intention is sound and good, but the 

 notation is rather troublesome in the ordinary work of writing, 

 and somewhat tedious in the midst of equations. At the same 

 time, the quaternion notation for the carl p, viz. Vvp, seems to 

 interpose in the mind an operation, y, between p and its curl, and 

 the strength and closeness of the relationship are consequently 

 somewhat impaired. We may, I think, agree with Mr. Heaviside 

 in adopting some simple symbol of direct relationship ; and I 

 would suggest that, for ordinary working purposes, the notation 



P, 



or something closely resembling it, is an improvement on " curl p." 

 Again, the divergence of a vector at any point in space — the 

 amount of the vector, considered as a flux, which, per unit volume, 

 leaves space at the point, as Mr. Heaviside well puts it (Vol. II. of 

 1 Papers,' p. 531) — is simply 



du dv dw 

 dec dy dz ' 



or — S Vp in quaternions; and this Mr. Heaviside always writes 

 "divp." For the same reason as before (inconvenience in work) 

 this notation should be improved. Perhaps we may with ad- 

 vantage denote the divergence of p by the notation 



Mr. Heaviside devotes a large portion of the present work to 

 two fierce attacks — one on the British Association An and the 

 other on the Quaternionists. 



To begin with the first — it is, of course, well known that if the 

 magnitude of the force exerted between two element-sources 

 (whether small quantities of electricity, or magnetic poles, or 



