ISO PETER GUTHRIE TAIT 



a man who has got the Quaternion mind directly from Hamilton. I am unable 

 to predict the whole consequences of this fact, because, besides knowing Quaternions, 

 Tait has a most vigorous mind, and is well able to express himself especially in 

 writing, and no one can tell whether he may not yet be able to cause the Quaternion 

 ideas to overflow all their mathematical symbols and to become embodied in ordinary 

 language so as to give their form to the thoughts of all mankind. 



I look forward to the time when the idea of the relation of two vectors will 

 be as familiar to the popular mind as the rule of three, and when the fact that 

 ij=ji will be introduced into hustings' speeches as a telling illustration. Why 

 not? We have had arithmetical and geometrical series and lots of odd scraps of 

 mathematics used in speeches. 



Nevertheless I do not recommend some of Tail's mathematical papers to be 

 read as an address to the Society, ore rotunda. That on Rotation is very powerful, 

 but the last one on Green's and other allied Theorems is really great. 



The work of mathematicians is of two kinds, one is counting, the other is 

 thinking. Now these two operations help each other very much, but in a great 

 many investigations the counting is such long and such hard work, that the 

 mathematician girds himself to it as if he had contracted for a heavy job, and 

 thinks no more that day. Now Tait is the man to enable him to do it by thinking, 

 a nobler though more expensive occupation, and in a way by which he will not 

 make so many mistakes as if he had pages of equations to work out 



I have said nothing of his book on Heat, because, although it is the clearest 

 thing of the sort, it is not so thoroughly imbued with his personality as his Quaternion 

 works. In this however I am probably entirely mistaken, so I advise you to ask 

 Tait himself who I have no doubt could hit off the thing much better than any 

 one. 



I remain 



yours truly 



J. CLERK MAXWELL. 



It seems appropriate here to reproduce from Maxwell's letters to Tait 

 some extracts bearing upon the quaternion calculus, for which it is clear 

 Maxwell had a profound admiration. The letters of Nov. 2, 1871, and 

 Dec. i, 1873, have been already given in extenso (see above, pp. 101, 

 115); the following are culled from other letters: 



"(Dec. 21, 1871.) Impress on T. that (-^\ + (4rY + (-j-Y = - V 1 and not + V 1 as 



he vainly asserts is now commonly believed among us. Also how much better and 

 easier he would have done his solenoidal and lamellar business if in addition to what 

 we know is in his head he had had say, 20 years ago, Qns. to hunt for Cartesians 

 instead of vice versa. The one is a flaming sword which turns every way ; the 

 other is a ram, pushing westward and northward and (downward ?). What we want 

 a Council to determine is the true doctrine of brackets and dots and the limits of 

 the jurisdiction of operators. 



