MAXWELL ON QUATERNIONS 151 



"(Oct. 4, 1872.) How about electromagnetic 4nions as in proof slip 106, 107? 

 I suspect I am not sufficiently free with the use of the Tensor in devectorizing such 

 things as r (distance between two points). The great need of the day is a grammar 

 of 4nions in the form of dry rules as to notation and interpretation not only of 

 S T U V but of . ( ) and the proper position of da, etc. Contents, Notation, Syntax, 

 Prosody, Nablody. 



"(Oct. 9, 1872.) I think I had better consecrate p [in the Treatise] to its pre- 

 scriptive office of denoting indicating or reaching forth unto the point of attention 

 (xyz) Has p a name? It is no ordinary vector carrying a point. It is rather a 

 tentacle or feeler which reaches from the subject to the object. Is he the scrutator? 

 I am glad to hear of the second edition of 4nions. I am going to try, as I have already 

 tried, to sow 4nion seed at Cambridge. I hope and trust nothing I have yet done may 

 produce tares. But the interaction of many is necessary for the full development 

 of a new notation, for every new absurdity discovered by a beginner is a lesson. 

 Algebra is very far from o. k. after now some centuries, and diff. calc. is in a mess 

 and fff is equivocal at Cambridge with respect to sign. We put down everything, 

 payments, debts, receipts, cash credit, in a row or column, and trust to good sense 

 in totting up. 



"(March 5, 1873.) O T'. If, in your surface integrals, ds is an element of surface, 

 is not ds a vector? and does not multiplication by Uv scalarize it? In your next 

 edition tell us if you consider an element of surface otherwise than as Vdadft 

 where a and ft are vectors from the origin to a point in the surface defined by 

 parameters a, b. Here the element of surface is a vector whose tensor is the area 

 and whose versor is Uv. These things I have written that our geometrical notions 

 may in Quaternions run perpetual circle, multiform, and mix and nourish all things. 

 Such ideas are slowly percolating through the strata of Cartesianism, trilinearity, 

 and determinism that overlie what we are pleased to call our minds. 



"(Sep. 7, 1878.) Here is another question. May one plough with an ox and an 

 ass together? The like of you may write everything and prove everything in pure 

 4nions, but in the transition period the bilingual method may help to introduce and 

 explain the more perfect. 



" But even when that which is perfect is come that which builds over three axes 

 will be useful for purposes of calculation by the Cassios 1 of the future. 



" Now in a bilingual treatise it is troublesome, to say the least, to find that the 

 square of AB is always positive in Cartesians and always negative in 4nions, and that 

 when the thing is mentioned incidentally you do not know which language is being 

 spoken. 



" Are the Cartesians to be denied the idea of a vector as a sensible thing in real 

 life till they can recognise in a metre scale one of a peculiar system of square roots 

 of- I? 



" It is also awkward when you are discussing, say, kinetic energy to find that to 



1 " And what was he ? 



Forsooth, a great arithmetician" (Othello, Act i, Scene i). 

 A neat example of Maxwell's ingenuity in literary suggestion. 



