6L4 Notices respecting New Books. 



Skinner (Phil. Mag. Dec. 1901) has also given a formula 



for the variation of K with C. It is K = K»H — (G—a) where 



P 



b and a are constants. This gives C = a when K = Kn and is 



therefore evidently incorrect, for a should certainly depend 

 on p. 



That Skinner's formula will not do has been pointed out by 

 Stark (Physikalische Zeitschrift, 3 Jahrgang, No. 13). The 

 results described in this paper therefore confirm Stark's 

 formula in so far as it applies to the current-density when the 

 cathode is only partially covered by the glow. 



The fact that the glow only covers a definite area on the 

 cathode is evidently a consequence of the existence of a 

 minimum value for the cathode drop. As the current- 

 density falls the drop falls until it reaches the minimum 

 value. Any further diminution of: the current-density would 

 then involve an increase in the drop, so instead of the current- 

 density diminishing, the area of the glow diminishes. 



In conclusion I wish to say that my best thanks are due 

 to Prof. J. J. Thomson for his kindly interest and advice 

 during the carrying out of these experiments in the Cavendish 

 laboratory. 



T 



LXIX. Notices respecting New Boohs. 



Vector Analysis, a Text-hook for the use of Students of Mathematics 

 and Physics, founded upon the Lectures of Professor J. "Willaud 

 Gibbs. By Dr. Edwin Bidwell Wilson. (New York, 

 Scribner's ; London, Arnold, 1901.) 



HIS is one of the Yale Bicentennial Publications, and is in some 

 respects a very remarkable treatise. It is essentially an ex- 

 pansion of a short pamphlet circulated privately by Professor Gibbs 

 some twenty years ago, and forms a goodly volume of fully 400 

 pages. As in that pamphlet, so in this book, the feature which distin- 

 guishes the vector methods elaborated by Professor Gibbs from the 

 vector methods associated with the names of Hamilton, O'Brien, 

 and Grassmann (to name only the originators of distinct methods) 

 is the treatment of the linear vector function in terms of the so- 

 called " dyad." It is this which gives significance to the notation 

 adopted for the scalar and vector parts of vector products. So far as 

 these important quantities are concerned, the substitution of a . /3 

 for — Sa/3 and of a x /3 for Yuj3 is a trifle, for which there could be 

 absolutely no excuse unless the dot-cross notation is based upon some 

 fundamental principle more important than anything which occurs 

 in quaternion vector analysis. If then we leave the "dyad" out 

 of account, there seems to be no sufficient reason why the pictorial 

 notation of Hamilton should be discarded in favour of a purely 



