86 Prof. Tait on the Importance of 



doubtful, assertion — Summum jus, summa injuria. We may, 

 without any hesitation, make a parallel but more easily ad- 

 mitted statement : — The highest art is the absence (not, as 

 Horace would have it, the concealment) of artifice. This com- 

 mends itself to reason as well as to experience ; but nowhere 

 more forcibly than in the application of mathematics to phy- 

 sical science. The difficulties of physics are sufficiently great, 

 in themselves, to tax the highest resources of human intellect ; 

 to mix them up with avoidable mathematical difficulties is 

 unreason little short of crime. [To be obliged to evaluate a 

 definite integral, or to solve a differential equation, is a neces- 

 sity of an unpleasant kind, akin to the enforced extraction of a 

 cube root ; and here artifice is often requisite in our present 

 state of ignorance : but its introduction for such purposes 

 is laudable. It does for us the same kind of service which has 

 been volunteered in the patient labour of the calculators of 

 logarithmic tables. It is not of inevitable, but of gratuitous, 

 complications that we are entitled to complain.] The in- 

 tensely artificial system of Cartesian coordinates, splendidly 

 useful as it was in its day, is one of the wholly avoidable en- 

 cumbrances which now retard the progress of mathematical 

 physics. Let any of you take up a treatise on the higher 

 branches of hydrokinetics, or of stresses and strains, and then 

 let him examine the twofold notation in Maxwell's 'Electricity/ 

 He will see at a glance how much expressiveness as well as 

 simplicity is secured by an adoption of the mere notation, as 

 distinguished from the processes, of quaternions. It is not 

 difficult to explain the cause of this. But let us first take an 

 analogy from ordinary life, which will be found to illustrate 

 fairly enough some at least of the more obvious advantages of 

 quaternions. 



There are occasions (happily rare) on which a man is 

 required to specify his name in full, his age, height, weight, 

 place of birth, family history, character, &c. He may be an ap- 

 plicant for a post of some kind, or for a Life Policy, &c. But it 

 would be absolutely intolerable even to mention him, if we had 

 invariably to describe him by recapitulating all these parti- 

 culars. They will be forthcoming when wanted ; but we must 

 have, for ordinary use, some simple, handy, and unambiguous 

 method of denoting him. When we wish to deal with any of 

 his physical or moral qualities, we can easily do so ; because 

 the short specification which we adopt in speaking of him is 

 sufficient for his identification. It includes all his qualities. 

 We all recognize and practise this in ordinary life ; why 

 should we outrage common-sense by doing something very 

 different when we are dealing with scientific matters, especially 



