228 



SCIENCE 



[N. S. Vol. XXXIV. No. 



line we find, quoting from tlie four jour- 

 nals chosen, such expressions as "formid- 

 able mathematics," "mathematical rub- 

 bish"; one writer apologizes for his 

 "mathematical fireworks"; another says 

 of a writer that he ' ' enveloped elementary- 

 principles of engineering theory in such a 

 haze as to render pursuit hopeless to any 

 but a confirmed mathematician." Again, 

 speaking of the work of young college 

 graduates, one writer said: "All of them 

 did calculating without checking as they 

 proceeded," and "Accuracy is one of the 

 keys to success." 



From another paper we quote: "It is 

 the pride of mathematicians to compress a 

 great deal into a single formula. But a 

 diet of tabloids, however full of nourish- 

 ment, is not adapted to all digestions; and 

 the present paper goes to the other ex- 

 treme — ^namely, spoon-feeding." Again 

 we quote: "... great respect for mathe- 

 matical proofs — if experimental results 

 don't support the theory so much the 

 worse for experimental results." 



In a third journal we find a writer 

 openly stating that he is writing his article 

 so that the engineer knowing very little 

 calculus, especially the integral, may yet 

 read his article. Many other opinions ex- 

 pressed could be cited, and much discus- 

 sion back and forth concerning proper 

 methods of instruction in engineering 

 mathematics abstracted with profit; yet it 

 seems to me that, after all is said and the 

 smoke of battle has cleared away, the engi- 

 neers would, or should, rather be judged 

 by what they do, and hence I present in 

 the following table, I., a summary of the 

 number of times which it seemed to me the 

 calculus was used in each of the papers 

 mentioned above during the period 1905- 

 1909. The figure will explain itself when 

 it is suggested that as far as a quantitative 

 result is concerned I listed each principle 



of the differential and integral calculus as 

 it was used in an article. It might easily 

 be that, with a viewpoint different from 

 the one used, that the table as made out by 

 another might look entirely different from 

 a quantitative standpoint, yet relatively 

 the results could not differ materially. 

 Different principles, as applied, might be 

 listed numerically differently by two men 

 working out the same problem. In listing 

 these principles I counted a single one only 

 once during a discussion, even though the 

 same expression may have been used many 

 times. However, when the same principle 

 was used in a new form, or a new applica- 

 tion made, it was again counted. 



Regardless of opinions expressed in the 

 journals and on the basis of the use made 

 of the principles of the calculus in the 

 years 1905-1909 we present Figs. 2 to 9 as 

 giving the relative importance placed on 

 these separate principles by the journals 

 named. It may be said that each was 

 used with the idea in mind that the reader 

 was acquainted with all of them, and even 



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