LYOrSTRIA L MA THEM A TICS 285 



dynamics and statistical mechanics, is rather well understood and usually, by very 

 simple computations, information sufficiently accurate for industrial application, 

 at least, can be found. Frequently, when several equilibria are possible simul- 

 taneously, complicated equations arise, but we rarely solve them directly, but 

 rather set up tables of the dependent variable (the per cent conversion possible) 

 as a function of the independent variables (temperature, pressure concentration). 

 The sources of these data, however, are numerous and at times require complicated 

 mathematics, as in the calculation of thermodynamic properties from spectro- 

 scopic data via quantum statistics. 



The situation is much less favorable in the calculation of the rates of chemical 

 reactions. A semi-empirical method, based on quantum mechanics, has been 

 appKed with a little success to some of the simplest reactions taking place in the 

 gas phase, but virtually no progress has been made in the more important field 

 of heterogeneous reactions (reactions of gases on surfaces, for example). We may 

 say that no satisfactory mathematical theory for such calculation exists at the 

 present time. Some progress is being made, but we are far from being able to 

 predict a suitable catalyst for any desired reaction. For the present we are happy 

 to be able to account for observations made on some simple reactions." 



Future Prospects. It is inconceivable that research in the industry will 

 not continue at at least its present level. Hence more, rather than less 

 mathematical work will probably be undertaken in prospecting and in 

 refining. A demand of moderate proportions should exist for able mathe- 

 maticians with a suitable background of geology and classical physics 

 for the geophysical work, and of physical chemistry and molecular physics in 

 the chemical field. 



Aircraft Manufacture 



The aircraft industry also consists of a number of independent units, 

 and is highly competitive. It is a new industry in which rapid technical 

 development and rapid increase in size has been the rule. It has depended 

 primarily upon government-supported laboratories and, to a lesser extent, 

 upon the universities for its research, and has busied itself with the exploita- 

 tion of that research in the advancement of aircraft design. No unit of the 

 industry has had or, for that matter, now has a research laboratory, in the 

 sense in which the words would be used in older and larger businesses, but 

 the beginnings of research departments have appeared, and individual 

 researchers and research projects are clearly recognizable. 



Numbers of Mathematicians. Some men in the engineering departments 

 of these companies should undoubtedly be classed as mathematicians, but 

 it is impossible to make even an approximate estimate of their number. 

 It is possible, however, to cite pertinent information which bears on the 

 importance of mathematics to the industry. 



