144 PETER GUTHRIE TAIT 



of that function. The result of V' applied to any function may be called the 

 concentration of that function because it indicates the mode in which the value 

 of the function at a point exceeds (in the Hamiltonian sense) the average value of 

 the function in a little spherical surface drawn round it. 



Now if a- be a vector function of p and F a scalar function of p 



VF is the slope of F 



. VF is the twirl of the slope which is necessarily zero 

 V*F is the convergence of the slope, which is the concentration of F. 

 Also SV <r is the convergence of <r 



Wo- is the twirl of a: 



Now, the convergence being a scalar if we operate on it with V, we find that 

 it has a slope but no twirl. 



The twirl of <r is a vector function which has no convergence but only a twirl. 

 Hence W, the concentration of <r, is the slope of the convergence of <r together 

 with the twirl of the twirl of <7, the sum of two vectors. 



What I want is to ascertain from you if there are any better names for these 

 things, or if these names are inconsistent with anything in Quaternions, for I am 

 unlearned in quaternion idioms and may make solecisms. I want phrases of this 

 kind to make statements in electromagnetism and I do not wish to expose either 

 myself to the contempt of the initiated, or Quaternions to the scorn of the profane. 



Yours truly 



J. CLERK MAXWELL. 



A week later (Nov. 14, 1870) Maxwell, when returning Robertson Smith's 

 letter in which the philology of Nabla was discussed in detail, wrote : 



" I return you Smith's letter. If Cadmus had required to use V and had 

 consulted the Phoenician Professors about a name for it there can be no question 

 that Nabla would have been chosen on the JO 3 principle. It is plain that Hamilton's 

 V derives itself with all its congeners from Leibnitz' d, which has become consecrated 

 along with D d & etc., and a name derived from its shape is hardly the thing. 



" With regard to my dabbling in Hamilton I want to leaven my book with 

 Hamiltonian ideas without casting the operations into Hamiltonian form for which 

 neither I nor I think the public are ripe. Now the value of Hamilton's idea of 

 a vector is unspeakable, and so are those of the addition and multiplication of 

 vectors. I consider the form into which he put these ideas, such as the names 

 Tensor, Versor, Quaternion, etc., important and useful, but subject to the approval 

 of the mathematical world.... 



" The names which I sent you were not for V but for the results of V. I shall 

 send you presently what I have written, which though it is in the form of a 

 chapter of my book is not to be put in but to assist in leavening the rest. I shall 

 take the learned Auctor 1 and the grim Tortor 1 into my serious consideration, 

 though Tortor has a helical smack which is distasteful to me but poison to T." 



' These seem to have been suggestions made by Tail himself, probably more in joke 

 than in serious mood. 



