278 Mr. G. Boole's Notes on Quaternions. 



the magnet, the plates of soft iron become the seat of suffi- 

 ciently intense sounds for a great number of persons to be 

 able to hear them simultaneously. 



176. Finally, I tried to induce at the same time electricity 

 of tension and magnetism in the steel and iron discs. For 

 this purpose, the bar which supports them was placed in the 

 centre of a glass tube m, 02 in diameter, to which was fixed a 

 horizontal circle of wood, m *18 in diameter by m, 018 in 

 thickness. This circle, entirely covered with tinfoil, commu- 

 nicates with a good electric machine. Parallel to the surface 

 which is made to vibrate, it is thus brought as near as possible 

 to it without the spark being emitted to it. The acoustic 

 properties of the three discs remained indifferent to this new 

 action. The plate of tempered steel had acquired a perma- 

 nent magnetism which did not at all interfere with its musical 

 properties. 



177. It results from these experiments, that electric or 

 magnetic induction has no appreciable action on the elasticity 

 of different sonorous bodies, such as glass, copper, brass, soft 

 iron, and steel tempered or untempered. The number of vibra- 

 tions executed by them in the unity of time remains the same. 

 But this conclusion must probably not be accepted in too abso- 

 lute a manner. It might be that extremely energetic and very 

 durable causes of induction determine an action which, in my 

 experiments, has been too weak to be observed*. 



Geneva, April 15, 1848. 



XLII. Notes on Quaternions. By George Boole, Esq.f 

 Interpretation of Quaternions. 



MR. CAYLEY'S ingenious researches, published in the 

 last Number of the Philosophical Magazine, have re- 

 called to my mind some speculations of my own upon the 

 same subject. To the purely mathematical treatment of it I 

 have indeed little to add. What I shall say will rather have 

 reference to its philosophy. 



It were much to be desired that the general principles which 

 govern the use of signs, as instruments of reasoning, were re- 



* M. G. Wertheim has found that no modification of elasticity is per- 

 ceptible in an iron or steel wire occupying the centre of an electro-magnetic 

 bobbin, when the current has only traversed it for a short time. According 

 to that ingenious experimentalist, the magnetization does not act directly 

 upon the elasticity, but produces a new molecular arrangement. — Annates 

 de Chimie et de Physique, December 1844, vol. xii. p. 623. 



f Communicated by the Author. 



