July 31, 1908] 



SCIENCE 



137 



tation. Thus, it often happens that stu- 

 dents will give results to five or seven 

 significant figures when the data do not 

 justify any such apparent precision. 



To correct these evils we must have a 

 convention of mathematicians, engineers 

 and professional computers who will show 

 authors how to produce elementary text- 

 books giving adequate attention to these 

 matters. 



As regards numerical computation, there 

 is in general need of more practise, since 

 it is through the concrete that we learn of 

 the abstract and the fundamental. No im- 

 portant formula in any text-book or 

 treatise should go without an appropriate 

 illustrative numerical example. 



I would like to take advantage of this 

 occasion to express a hope with regard to 

 the future of our country and to the possi- 

 bility of development which may come 

 through suitable cooperation between 

 mathematicians and engineers. Nothing 

 delights me more than to attend a meeting 

 of this kind where mathematicians and 

 engineers have come together. It is an 

 auspicious sign of the times. It is one of 

 the results I have been looking forward to 

 for the past thirty or forty years. Some 

 of us here are old enough to have lived in 

 two epochs, namely, the pre-scientific and 

 the present epoch. We can remember a 

 time when engineers could not have got a 

 hearing such as they have to-day. The 

 history of their rise and development, at 

 least in this country, is well known to some 

 of us. It dates back to a time only about 

 forty years ago. During this time the 

 engineers have fought their way forward 

 to the position now accorded them in con- 

 temporary society. They have won a place 

 in public esteem without which it would 

 have been impossible to hold such a con- 

 ference as we are holding to-day. This 

 esteem has been won in spite of much op- 

 position, coming especially from the older 



academic institutions; but now having at- 

 tained adequate recognition especially as 

 practising engineers, we have a much 

 higher duty to perform, and this I trust we 

 shall be able to meet adequately through 

 cooperation with our friends the pure 

 mathematicians. I know of no work more 

 important to the general advancement of 

 mathematico-physical science than that 

 which may lead to the development of 

 mathematical physicists, men who possess 

 at once good mathematical knowledge and 

 correspondingly adequate equipment in 

 physical science. Here is a field greatly 

 in need of concentrated effort and of ade- 

 quate appreciation. It is a lamentable 

 fact that while we can easily develop pure 

 mathematicians of a high order and experi- 

 mental physicists of an equally high order, 

 it seems very difficult for us to develop 

 minds possessing both qualities. To a 

 large extent I think the development of 

 pure mathematics in the future wiU de- 

 pend, as in the past, on the stimulus fur- 

 nished by mathematico-physical ideas ; and 

 in like manner success in the development 

 of mathematical physics will depend 

 equally in the future on mathematical 

 ability of the highest order. In this line 

 of work we Americans have not done our 

 full duty, and it behooves us as mathe- 

 maticians and engineers, now that we have 

 got together on the plane of mutual in- 

 terest, to give attention to this important 

 field of work. 



The French engineers led by Navier and 

 followed by Lame, Clapyron, and espe- 

 cially by the "dean of elasticians, " Barre 

 de Saint-Venant, have contributed to sci- 

 ence the most important branch of mathe- 

 matical physics, namely, what is commonly 

 called the theory of elasticity. This is 

 superbly difficult in its purely mathe- 

 matical aspects and exquisitely beautiful in 

 its physical aspects, and it stands as a 

 splendid example of the possibilities which 



