﻿500 Notices respecting New Books. 



struck with the extraordinary simplicity of the quaternion mode of 

 attack. Once the quaternion in its true geometrical significance 

 is understood, we need never refer — except in wondering awe — to 

 a treatise on spherical trigonometry. 



With so much that is worthy of praise in Colonel Hime's book, 

 we gladly refrain from criticism of minor details, which are 

 often a mere question of taste. But it is otherwise with a few 

 really serious faults, which seem eminently fitted to perplex the 

 student. Such a fault is the whole of paragraph 11. Whatever 

 it is, it is not quaternions ; indeed it is inconsistent with nearly 

 all the other paragraphs of the book. As a quaternion equation, 

 equation (8) 



is simply nonsense. Having already taught us that i, j, h are 

 coperpendicnlar unit vectors or right versors (the identification of 

 which is one of the bursts of genius in Hamilton's calculus), what 

 reason has the author for declaring that i ==;=&c.? " Equation (8)," 

 we are told, " asserts that all unit-vectors in the first power are 

 equal, as versors, in respect to angle." In short, versors are to be 

 equated when their angles are equal. [For consistency's sake, 

 Colonel Hime should use the equation Uq= TJr as meaning only 

 /_q= Lr. Eurther on we are told that "the symbol V — 1 

 represents them [i, j, Je] only in their character of indeterminate 

 right versors." But i, j, 7c have already been defined in anything 

 but an indeterminate manner. This arbitrary robbing a symbol 

 of its most characteristic feature, so that it no longer is what it 

 was defined to be ; is contrary to the whole genius of — Common 

 Sense. What would the Cartesian analyst say to the equation 



x=y=z= V+l = — x=-y=— z, 



which is certainly less irrational than equation (8). 



Again, at the foot of page 76 we meet with the equation 



l"vr 



which is asserted to mean that h bisects the angle between (3 and 

 y. Then we read : — " This equation may be written ff=yfi, 

 where <; is called the Mean Proportional between j3 and y." Now 

 we are told in previous sections that ^ 2 , the square of a vector, 

 is a scalar; and that y/3, the product of two different vectors, 

 is a quaternion. The legitimate conclusion is that a scalar is 

 equal to a quaternion! The equation c) 2 = y/3 really means that /3 

 and y axe parallel vectors, to whose tensors the tensor of S is the 

 geometric mean. If it meau ought else it cannot be a quaternion 

 equation. But, anyhow, it has no business here. The true 

 transformation of the equation first given is ^- 1 = yo _1 , a totally 

 different thing. 



We hope that the author will in future editions delete the 

 second form of this equation entirely, recast the whole of para- 

 graph 11, and root out the altogether obnoxious equation (8). 



