208 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1952 



lar case in which we are interested. Sometimes the contribution of 

 the latter to the features which interest us is simple and the problem 

 is one for exact solution by the theoretical physicist. Sometimes the 

 said contribution is complicated, but important, and the solution be- 

 comes more the problem of him who applies approximate, or even 

 rule-of -thumb, methods. 



THE DEVELOPMENT OF METHODS OF THOUGHT 



It is of interest to inquire whether the fundamentals of thinking 

 are necessarily very different today from what they were in past ages. 

 In this connection, it is perhaps not without interest to transport one- 

 self in imagination to the time of Galileo and inquire as to the nature 

 of the thinking of those days. Galileo wrote a book called Two New 

 Sciences, in which he presents his ideas in the form of a supposed dis- 

 cussion between three interlocutors, Salviati, who represents himself, 

 Sagredo, and Simplicio. 



Again and again in these discourses we see the mind of Galileo 

 doing the same kind of thinking that a good experimental physicist or, 

 for that matter, a good mathematical physicist does in the laboratory 

 today, and we cannot question the fact that if Galileo, with all that 

 he had and no more than he had 300 years ago, were planted in one 

 of our laboratories today, he would be an outstanding physicist in the 

 problems which are of interest to us today. 



In this general epoch, we see the birth of Hooke's law on the pro- 

 portionality between stress and strain, and we see the accumulation 

 of those fundamentals going back even to far earlier days, which 

 constitute the basic principles upon which the present engineering 

 science is based. However, I think it safe to say that, by and large, 

 we must regard the pre-Newtonian era as one in which the laws avail- 

 able, such as they were, were of an empirical kind, and even in the later 

 epochs, extending almost to the present time, the fundamental laws 

 were empirical. The growth of the power of mathematical physics, 

 brought about by the invention of the calculus and by the develop- 

 ments of Newton, Lagrange, and others, enabled mankind to extract 

 in richer form the more complete consequences of the empirical laws 

 of hydrostatics, elasticity, dynamics, and so forth, and, indeed, until 

 the advent of the electrical age scientific attention was devoted largely 

 to the unraveling of the consequences of such laws. It is true that in 

 the field of optics there were primitive attempts at theories devised to 

 give a richer content to such empirical laws as existed in that field. 

 Such attempts, however, were guided largely by the ideas of elasticity 

 and inertia characteristic of the mechanical domain. 



