﻿Notices respecting New Boohs. 153 



has resulted in the filling of our text-books on Hydrostatics with 

 almost interminable mathematical problems on that glaring unreality 

 and source of evil, the whole pressure of a fluid on a curved surface. 

 Of course a flux of electric force through a closed curved surface 

 in an isotropic dielectric acquires physical reality by means of the 

 fact that the " displacement " through the surface at each point is 

 proportional to the value of the force at the point, and thus the flux 

 of force is a measure of the total displacement through the surface. 



This is said, however, without any intention of opposing 

 Mr. Heaviside's proposed definition of a unit mass, or source, but 

 merely for the purpose of showing that something may be said on 

 the other side, and that if the 47r is made to disappear from many 

 expressions, it is at the expense of its appearance in others which, 

 under the B. A. system, were free from it. Quite possibly, 

 Mr. Heaviside's system is, on the whole, the simplest and the 

 best. 



"With regard to his attitude of hostility towards Quaternions — ■ 

 and especially towards Professor Tait's treatise — a little more 

 must be said. 



Maxwell is usually said to have made occasional use of Quatern- 

 ions in his great treatise. It is, however, quite true (so far as my 

 general recollection goes) that he merely avails himself of the 

 employment of vectors, and that the only conception involved in 

 his vectors is that a vector is a mere carrier, translator, or directed 

 line of definite length in space ; that, in fact, there is nothing of 

 the rotation or versor nature involved in his vectors. Maxwell, 

 then, does not use Quaternions at all ; possibly he had no need to 

 do so ; he employs simply Vector Analysis — Orthodox Vector 

 Analysis, I shall call it, to indicate that it is in harmony with the 

 general principles of Quaternions as enunciated by Hamilton. 

 Now, the signification of a vector has been widened by Hamilton, 

 without in any way interfering with its vehicular nature, by endow- 

 ing it with the power of commanding a rotatory operation. Every 

 unit vector is thus also to be looked Upon as optionally standing 

 for the operation of quadrantal rotation in planes perpendicular to 

 the direction of the vector, if we desire so to employ it. Mr. Heavi- 

 side never desires to employ it in this way ; he finds it unnecessary 

 to do so in Electromagnetism. Hence he will have nothing what- 

 ever to do with the versor property in the vector. " Once a 

 vector, always a vector " (p. 301). His vector is like the heir to a 

 title, or to a large property, who repudiates his hereditary advan- 

 tage and insists on adopting poverty. Probably he would say that 

 it is rather to be likened to a man born with an ugly tumour who 

 insists on having it cut off. But " different men have different 

 opinions, &c." according to his own previously quoted maxim. 



Now, in the Hamiltonian system, if i is any unit vector, i 2 = — 1 ; 

 if a is any vector of length a, a 2 =— a 2 ; and if a and (3 are any 

 two vectors of lengths a, 6, including an angle d, Sa/3= — ah cos 0. 

 The minus sign in these results is gall and wormwood to the 

 anti-quaternionists. Of course there is nothing at all strange in 



