I^OVEMBEB 13, 1914] 



SCIENCE 



699 



tion, variations calculus of, vector analysis, 

 wave. 



That mathematics is the handmaiden of the 

 sciences is fully confirmed. Only about a 

 fourth of the headings are those of pure 

 mathematics. The wide variation of the sub- 

 jects is evident. They cover the subjects of 

 five sections of the American Association for 

 the Advancement of Science. 



If these facts are pointed out to the stu- 

 dents, it will doubtless give them a greater 

 interest in the subjects of mathematics, for 

 even though they can not understand the 

 references they can at least grasp their signifi- 

 cance and approach their work with a con- 

 viction that it is worth while. It is hoped that 

 this list may prove valuable to teachers in 

 this way. 



The student should appreciate early the 

 importance of his mathematical training in 

 his work, particularly in any subject of exact 

 science. The haste made necessary by the 

 limitations of time and the demand for more 

 and more principles leaves little time for the 

 application of known principles to explain 

 nature in a mathematics class. The utility of 

 the subject may thus not be as obvious to the 

 inexperienced pupil as to the teacher. The 

 subject of mathematics should not be con- 

 sidered by the pupil as mere continued 

 drudgery without ultimate gain. When those 

 uninspiring successions of hooks and crooks 

 are clothed with a garb of meaning provided 

 by nature herself and their real import and 

 significance made manifest, they command a 

 proper reverence because of that which they 

 have accomplished. The beauty of the truth 

 revealed or explained sheds a sense of beauty 

 even over the cold abstract reasoning. 



The student should know that that which 

 he dimly foresees will appear before him as a 

 panorama of extended beauty over which he 

 can roam when once he has mastered that 

 most wonderful and powerful instrument of 

 modem analysis, discovered by Newton and 

 Leibnitz, and so fully developed and applied 

 by that constellation of immortal mathema- 

 ticians the Bernouillis, Clairaut, Euler, La- 

 grange and Laplace, namely the infinitesimal 



calculus. He will then have a deeper insight 

 into, and a partial comprehension of the plan 

 of nature. Beauty concealed by ignorance of 

 the mathematics necessary for interpretation 

 will be revealed to him. He will then see that 

 of which the untutored mind has no concep- 

 tion because lying beyond its comprehension. 



The massive bridge once wonderful because 

 of its enormous size, when its principles of 

 construction are understood becomes a thing 

 of beauty, a wonderful monument to the intel- 

 lect of the designer and constructor. The great 

 tunnels, turbines, subways are changed to ob- 

 jects of wonder to those who are capable of 

 understanding the difficulties overcome in their 

 construction. The stars in the universe above 

 which nightly dissipate some of their light 

 upon the earth bespeak their Creator's glory 

 in voices but faintly heard by those whose 

 training does not enable them to comprehend 

 the reign of law there prevailing. To such an 

 one the heavens declare the glory of God in 

 a more real and exalted sense. The earth is 

 full of His glory. There will be " sermons in 

 stones." 



The extent to which natural laws have been 

 discovered and expressed in mathematical equa- 

 tions must be a source of unending wonder. 

 " Order is heaven's first law." The mathe- 

 matical equation is the apotheosis of order. 

 It will ever be a matter of self -congratulation 

 to mankind that they can thus interpret natu- 

 ral phenomena by expressing the inexorable 

 laws governing them in equations. We should 

 better say that we are thankful to God for 

 revealing to us those laws to which He has 

 subjected His creation. It must compel a 

 higher order of admiration for the Creator 

 that He has made things thus. 



One of nature's demands in which she is 

 inexorable is a study of higher, the highest 

 mathematics. The interpretation of her laws 

 requires it. I close by quoting a scientist of 

 wide fame. Sir John Herschel in the intro- 

 duction to his celebrated " Outlines of Astron- 

 omy " writes : 



The utmost pretension of this work is to place 

 its readers on the threshold of this particular wing 

 of science, or rather on an eminence exterior to it, 



