MAXWELL'S INDEBTEDNESS 167 



Tait brought out the real physical significance of the quantities 5V a, FVcr, V#. 

 Maxwell's expressive names, Convergence (or Divergence) and Curl, 

 have sunk into the very heart of electromagnetic theory. His suggested 

 word Slope has been replaced by Gradient or Grad, a word of more 

 general etymological intelligibility. But the point is that Maxwell was 

 led to see the far-reaching importance of these conceptions only after they 

 had been presented by Tait in their simple direct quaternion guise. Lame, 

 Green, Gauss, Stokes, Kelvin, and others had the ideas more or less 

 disconnectedly in their minds and utilised them in analysis ; but it is 

 through Hamilton's calculus alone as developed by Tait that the important 

 space relations, Gradient, Divergence, and Curl, appear as parts of a 

 whole. It was Tait who taught Maxwell this deep-lying truth ; and it 

 was Maxwell who spread the good news by his epoch-making treatise on 

 electricity. Most later workers have been content to take the names and 

 the separate conceptions, and reject the central idea embodied in the 

 quaternion operator V. It should not be forgotten, however, that these 

 conceptions were first concisely symbolised and fully discussed in their 

 physical significance by Tait, and remain as a rich legacy from him through 

 Maxwell to the non-quaternionic world. Maxwell gave them names, " rough 

 hewn" he called them in his letter to Tait, whom he invoked as a "good 

 divinity" to "shape their ends properly so as to make them stick." He 

 was their sponsor, but Tait was their parent. Probably very few now 

 using these terms, or their equivalents, in electromagnetic literature have 

 realised the debt they owe to Tait, who first polished the facets of the V 

 diamond. Rough and uncut it passed to him from Hamilton ; and now all 

 the scientific world more or less unconsciously benefit by its radiance. 

 Here then is one outstanding result of Tail's quaternion labours. 



The many vector quantities which call for consideration in modern 

 electrical theory demand some form of vector notation. This was first 

 realised by Maxwell, who, guided by Tait, adopted Hamilton's vector 

 symbolism. Later writers have in many cases followed Maxwell in the 

 spirit but not in the letter. There have arisen in consequence some six 

 or seven distinct systems of vector notations, which are also called systems 

 of vector analysis. The common elements in these rival systems are, with 

 one exception, also common to the quaternion system, which is demonstrably 

 a real analysis and not simply a notation. So far as mere symbolism is 

 concerned, there is little to choose among these various systems. But what- 



