39-4 Notices respecting New Books. 



the electrostatic system of units, and the second part with the 

 electromagnetic system and the comparison of the two systems ; 

 this is followed by a short chapter on the electromagnetic theory 

 of light, and a supplement is added in which some interesting 

 analogies between electrical and therinodynamical theory are 

 traced. Tbe descriptions of physical instruments, and the accounts 

 given of the things that are measured and the inferences that can 

 be drawn are generally clear and good, bub the more theoretical 

 portions of the work are much less acceptable. Obvious misprints 

 are frequent, and there are not a few mistakes in matters of 

 principle: for example, the argument on p. 17, by which it is 

 sought to be shown that the electric potential is constant within a 

 conductor in electric equilibrium would apply equally to a non- 

 conductor ; again, on p. 90 we read about a point under the action 

 of a couple. The best thing in the book is the application of the 

 methods of thermodynamics to matters (such as the electrification 

 of a crystal by compression) in which there is interaction between 

 the thermal, elastic, and electric properties of bodies. 



Octonions, a Development of Clifford's Bi- Quaternions. By Alex. 



McAulay, M.A., Professor of Mathematics and Physics in the 



Universitt/ of Tasmania. Cambridge : at the University Press, 



1898. 

 This book is a sealed volume to all who are not familiar with 

 quaternions. Probably most students of Hamilton's powerful 

 calculus have dipped into Clifford's brief but suggestive papers ; 

 and to all such the second title of Professor McAulay's book will 

 give some hint as to the character of this generalized system of 

 quaternions, as it might roughly be termed. On the other hand, 

 those acquainted with Sir Robert Ball's System of Screws will have 

 more than a glimmer of the meaning and purpose of Octonions 

 when they are told that it is a mathematical method which sym- 

 bolizes screws and wrenches as self-contained quantities and 

 discusses the laws of their combination. 



The Octonion is, in fact, Clifford's Bi-quaternion, which 

 Professor McAulay is right in regarding as an unfortunate name, 

 since Hamilton had already used the latter term in an altogether 

 different sense. Clifford's terms motor and rotor are, however, 

 adopted ; but Clifford's vector, which is not quite the same thing 

 as Hamilton's vector, is discarded in favour of a new term lator. 

 In the Octonion system, a screw is called a unit-motor, a twist 

 about a screw a velocity-motor, a wrench on a screw & force-motor, 

 and an impulsive wrench a momentum-motor. Dynamically, a 

 motor is a combination of translation and rotation, or of force and 

 couple. In a general sense, the motor plays in octonions the role 

 that the vector plays in quaternions. To transform one vector 

 into another requires the application of a quaternion as an operator ; 

 to transform one motor into another requires the application of 

 an octonion as an operator. 



It will be remembered that Clifford applied his system with 



