October 22, 1909] 



SCIENCE 



553 



Illinois and have made two assumptions 

 which no doubt hold elsewhere. 



First. Text-book work predominates 

 throughout, and hence the texts used fur- 

 nish a rational basis from which to judge 

 both the kinds of principles used and their 

 frequency of application. 



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were investigated. These are architectural, 

 civil, mechanical and electrical engineer- 

 ing. Similar courses offered, such as mu- 

 nicipal and sanitary, railway, civil and 

 others, furnish results in every way analo- 

 gous to those above mentioned. The archi- 

 tectural engineering course is included 



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To fab -Serrate Courses 



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Second. The principles, as applied in 

 these texts, are used as often in the lectures 

 and problems given for solution as in the 

 texts themselves. 



The list of authors of the texts studied 

 includes the names of men connected with 

 at least a dozen technical schools of recog- 

 nized merit besides those of men at Illinois. 

 The emphasis placed on the principles of 

 the calculus will, necessarily, vary with 

 the instructors in charge of the different 

 courses; yet, as giving an average, the 

 above assumptions seem reasonably ac- 

 curate. 



Any investigation of this nature will un- 

 doubtedly show that algebra and trigo- 

 nometry are used much oftener than the 

 calculus ; in fact, in the comparison of num- 

 bers it would seem that the calculus plays 

 but a minor role. In enumerating the prin- 

 ciples of the calculus four complete courses 



because in it, as offered at Illinois, are in- 

 cluded those courses which form the back- 

 bone of all the subjects which make use of 

 the calculus. These courses vary all the 

 way from that in architecture, where me- 

 chanics is taught without a course in the 

 calculus, to those in which the mathematics 

 used furnishes the most serious difficulties 

 met. If then a summary is made of the 

 principles used in the four courses men- 

 tioned we have the results, as sho'WTi in 

 Plate 1. This shows the minimum number 

 of times a student in any of the courses, 

 listed might reasonably expect to encounter 

 the various principles of the differential 

 and integral calculus. Plate 1 gives us 

 quantitative results; a qualitative analysis 

 is given in Plates 2 and 3. 



Concerning the notions of the differential 

 calculus used it can be said that the differ- 

 entiation.s, both algebraic and trigonomet- 



