RECENT ADVANCES IN SCIENCE u 



science is universal and that it forms one of the most potent 

 links in international relations. One would, therefore, expect 

 to find a truly international scientific language, i.e. in mathe- 

 matics a notation should exist intelligible to all scientists of all 

 countries and trained at all centres of scientific activity. Un- 

 fortunately, this is far from being the case. It sometimes hap- 

 pens that persons deriving their mathematical knowledge from 

 one source have considerable difficulty in following the argu- 

 ments and results of investigations inspired by a different 

 source, and this is often the cause of discomfort and annoy- 

 ance in the reading of mathematical literature. 



Variation in notation can be of two forms. The more 

 obvious consists in the adoption by different workers, or dif- 

 ferent schools of workers, of different sets of symbols to repre- 

 sent the same physical concepts. A common example is 

 afforded in the discussion of uniform acceleration in dynamics. 

 Whereas we are all agreed in denoting the acceleration due to 

 gravity by the symbol " g," yet some of us denote a uniform 

 acceleration in general by the symbol " a," whilst others use 

 " f." If we compare various books and papers on fluid re- 

 sistance we find that the statement : Resistance varies as the 

 square of the velocity, is symbolised variously as R °c V 2 , R <* U 1 , 

 R <x u 2 , etc., and that sometimes there is no consistency 

 even in the same book. In hydrodynamics many mathema- 

 ticians agree to make the velocity components negative space 

 differential coefficients of the velocity potential ; but not all do 

 so, and in a recent work on aeronautics the authors adopt the 

 negative sign in general but drop it in at least one place. 



Whilst it is a pity that such artificial obstacles should exist 

 in the way of the intelligent and comfortable reading of mathe- 

 matical analysis when applied to physical problems, there is 

 another respect in which notational differences arise, causing 

 considerable confusion in the mind of the mathematical stu- 

 dent. This is in the choice of algebraical signs for geo- 

 metrical concepts. An important case is the choice of a set of 

 axes in three dimensions for problems in astronomy, rigid 

 dynamics, electromagnetism, etc. We are all accustomed to 

 consider the anti-clockwise direction as the positive sense of 

 rotation in dealing with angles in trigonometry, or areas in the 

 integral calculus ; yet, when we come to three-dimensional 

 analysis, there is confusion. Thus, in mechanics it is usual in 



