56 



SCIENCE. 



[N. S. Vol. XXIII. No. 576. 



and not so much open to the objection of 

 violating long established principles. But 

 if I have insisted particularly on the theory 

 of Lorentz, it was just for the purpose of 

 bringing out as clearly and forcibly as pos- 

 sible the differences between the old and 

 the new. 



Besides, there is one minor feature in the 

 form of presentation adopted by Lorentz 

 and Abraham which appeals to me as 

 worthy of attention: it is the consistent 

 use of the vector analysis of Gibbs and 

 Heaviside. And perhaps this is really 

 somewhat more than a mere matter of 

 form. Burkhardt^^ has shown that this 

 vector analysis has a rational mathematical 

 basis. And after the numerous and mani- 

 fold applications that have been made of 

 this method its usefulness can no longer be 

 questioned. The diversity of notations 

 used by different authors can hardly be 

 regarded as a serious objection. Have we 

 not a large variety of notations even in so 

 old and well-established a branch of mathe- 

 matics as the differential calculus? The 

 important thing about vector analysis is 

 that it teaches to think in vectors and 

 fields. E. Picard/^ in a lecture, has re- 

 cently called attention to the importance 

 of the field even in ordinary elementary 

 mechanics. A. Foppl has led the way in 

 using vector symbols in an elementary 

 treatise on technical mechanics. 



Vector addition is now more or less fa- 

 miliar even to the student of the most ele- 

 mentary mechanics, largely owing to the 

 influence of graphical statics. Is it not 

 time to introduce at least the scalar and 

 vector products and the time-differentia- 

 tion of vectors in the mechanics of the 

 particle and the rigid body? The gain in 

 clearness and conciseness in stating the 



^- Mathematische Armalen, Vol. 43 ( 1893 ) , pp. 

 197-215. I 



" ' Quelques reflexions sur la mfieanique, suivies 

 d'uhe premiere legon de dynamique,' Paris, 1902. 



more general propositions is certainly great. 

 In the mechanics of deformable bodies and 

 media (hydrodynamics, elasticity), the 

 general theory of vector fields, with the 

 fundamental notions of divergence and 

 curl, flux and flow, lamellar and solenoidal 

 fields, etc., should surely form the prelim- 

 inary mathematical basis for all further 

 study; and here the simple symbolism of 

 vector analysis is particularly well adapted 

 to the subject. 



But whatever may be the form of pres- 

 entation selected, the study of the fields of 

 scalars, vectors and higher point functions, 

 so intimately connected with the modern 

 views of physical phenomena, might well 

 claim more attention on the part of the 

 pure mathematician than it has so far re- 

 ceived. 



Alexander Ziwet. 



THE SANITARY VALVE OF A WATER 

 ANALYSIS.^ 



TvfENTY years ago, the vice-president of 

 this section, the late Professor William 

 Ripley Nichols, took as the subject of his 

 address, 'Chemistry in the Service of 

 Public Health,' saying: "If any are in- 

 clined to criticize my choice of that branch 

 of applied chemistry with which I am most 

 familiar, I trust they will consider that, 

 after all, few of us have the opportunity, 

 or, let us confess it, the ability to carry 

 research and speculation to the height to 

 which chemistry is capable of rising." 

 Agreeing fully in the sentiment of this last 

 sentence, though not at all as applying to 

 Professor Nichols, whose marked ability as 

 an investigator was recognized by all, I feel 

 that I can best fulfill the clause in our con- 

 stitution which requires the several vice- 

 presidents to give an address before their 



' Address of the vice-president and chairman of 

 Section C, Chemistry, American Association for 

 the Advancement of Science, New Orleans, De- 

 cember, 1905. 



