THE OPERATOR "NABLA" 143 



the powerful operator V. Hamilton introduced this differential operator in 

 its semi-Cartesian trinomial form on page 610 of his Lectures and pointed 

 out its effects on both a scalar and a vector quantity. This, it will be 

 remembered, was one of the points especially brought forward by Tait when 

 he began the correspondence with Hamilton. Neither in the Lectures nor 

 in the Elements, however, is the theory developed. This was done by Tait 

 in the second edition of his book (V is little more than mentioned in the 

 first edition) and much more fully in the third and last edition. 



From the resemblance of this inverted delta to an Assyrian harp Robertson 

 Smith suggested the name Nabla. The name was used in playful intercourse 

 between Tait and Clerk Maxwell, who in a letter of uncertain date 

 finished a brief sketch of a particular problem in orthogonal surfaces by 

 the remark "It is neater and perhaps wiser to compose a nablody on this 

 theme which is well suited for this species of composition." 



In 1870, when engaged in writing his Treatise on Electricity and 

 Magnetism, Maxwell sent Tait the following suggestions as to names for 

 the results of V acting on scalar and vector functions : 



GLENLAIR, DALBEATTIE, 



Nov. 7, 1870. 

 Dear Tait 



n d , - d , i d 



V = z -r + J-r + k-T-. 

 dx J dy dz 



What do you call this? Atled? 



I want to get a name or names for the result of it on scalar or vector functions 

 of the vector of a point. 



Here are some rough hewn names. Will you like a good Divinity shape their 

 ends properly so as to make them stick? 



(1) The result of V applied to a scalar function might be called the slope of 

 the function. Lam< would call it the differential parameter, but the thing itself is a 

 vector, now slope is a vector word, whereas parameter has, to say the least, a scalar 

 sound. 



(2) If the original function is a vector then V applied to it may give two 

 parts. The scalar part I would call the Convergence of the vector function, and 

 the vector part I would call the Twist of the vector function. Here the word twist 

 has nothing to do with a screw or helix. If the word turn or -version would do 

 they would be better than twist, for twist suggests a screw. Twirl is free from 

 the screw notion and is sufficiently racy. Perhaps it is too dynamical for pure 

 mathematicians, so for Cayley's sake I might say Curl (after the fashion of 

 Scroll). Hence the effect of V on a scalar function is to give the slope of that 

 scalar, and its effect on a vector function is to give the convergence and the twirl 



