MATUKMATKAL CLASSIFICATION OF PHYSICAL QUANTITIES. 



The convergence of the slope of a scalar function is its concentration. 



The concentration of a vector function is the slope of its convergence, 

 together with the curl of its curl. 



The quaternion expressions, of which the above statements are a transla 

 won given by Prof. Tait, in his paper in the Proceedings of the Royal & 

 of fhfinburyh, April 28th, 1862; but for the more complete mathematical treat- 

 ment of the operator v, see a very able paper by Prof. Tait, "On Green's 

 and other Allied Theorems" (Transactions of the Royal Society of Edinlmnjh, 

 1870), and another paper in the Proceedings of the Royal Society of E<1 

 for 187071, p. 318. 



