170 PETER GUTHRIE TAIT 



study, and the method has not as yet furnished new results of a kind to attract 

 attention." 



These words were spoken of the first edition, which was strictly, in 

 accordance with its title, an Elementary Treatise. But it is in the later 

 editions that Tait displays his strength. The two chapters on Kinematics 

 and Physical Applications abound in numerous illustrations of the power 

 and flexibility of the calculus. The last chapter, which extends to 101 

 pages in the third edition, passes over nearly the whole range of mathematical 

 physics, from statics and kinetics of bodies through optics and electrodynamics 

 to the series of remarkable sections dealing with the operator Nabla, V. 

 Here we find treated gravitational and magnetic potential, hydrodynamics, 

 elasticity, varying action, brachistochrones, catenaries, etc. These later 

 sections are not easy reading. They suffer from what Maxwell playfully 

 called " the remarkable condensation, not to say coagulation, of his style," 

 and cannot be fully appreciated by a student who has not already made 

 some acquaintance with the subjects taken up. It should be remembered, 

 however, that this was exactly what Tait had in mind. His aim was not 

 to write a quaternion treatise on mathematical physics, but to show forth 

 the power and conciseness of the quaternion method when applied to 

 important physical problems. With descriptive letter-press interpolated 

 after the manner of scientific treatises and the details of the symbolism 

 worked out, the last chapter of Tail's Elementary Treatise on Quaternions 

 would form a most admirable text book for advanced students in applied 

 mathematics. The greater generality of the quaternion attack as compared 

 with the usual methods introduces some striking novelties, which the ardent 

 student would do well to follow up. 



