SErTEMBEK 12, 1884.] 



SCIENCE 



231 



was not to learn how to use this the most splendid 

 instrument of intellectual research yet devised by 

 the wit of man. 



There is an underlying consciousness running 

 through the whole scheme of education based upon 

 classical study, that the objects of such study are not 

 in themselves of vital importance to the student, but 

 that their value is chiefly to be found in the reflex 

 influence upon the person submitting to its disci- 

 pline. Pretend to deceive ourselves as we may upon 

 this point, the undergraduate feels this with every 

 breath of his young life. Professor Eddy did not 

 take the position that classical study is in itself a 

 delusion, nor that the ancient languages and philo- 

 logical science are not most worthy and inspiring- 

 objects of study for those who really intend to know 

 something of them, or for those whose tastes and 

 capacities fit them, for their pursuit; but that this 

 demoniacal spirit of study for the sake of discipline, 

 which possesses our colleges, must be cast out before 

 they can rightly train classical scholars, or stand 

 where they should stand in the forefront of higher 

 culture in the liberal arts : and this by the intro- 

 duction of a spirit of study very different from the 

 disciplinary spirit, — a spirit which, for the lack of 

 a better name, we may call the scientific spirit ; a 

 spirit of sincere and earnest inquiry after knowledge. 



There is apparently no reason why the spirit which 

 so largely animates scientific study should be confined 

 to that kind of study, for it is not the nature of the 

 study which determines the spirit in which it shall 

 be pursued. Mathematics is a case very much in 

 point in this regard. The truth is, young men of 

 spirit will not shirk hard work, if they are convinced 

 that by it they can open up any fair field of knowl- 

 edge which appears desirable. And the speaker said, 

 that, under such influences, he had seen students 

 gain, during the first half of their college course, such 

 familiarity with those branches of higher analysis 

 which are the common groundwork of modern inves- 

 tigation in analytical mechanics and mathematical 

 physics, as to have really open to them the literature 

 of these subjects ; and this not in isolated instances 

 merely, but with class after class. It is popularly 

 supposed, as before stated, that the number fitted by 

 nature for mathematical study is small. Such, Pro- 

 fessor Eddy has been convinced against his precon- 

 ceived opinions, is not the fact. It is a study as much 

 sought after, and pursued as eagerly, as any other 

 branch of liberal study ; provided only that the teach- 

 ers thereof are themselves men who have a live in- 

 terest in the subject, are capable, patient, and apt at 

 giving instruction. 



Professor Eddy then discussed somewhat more in 

 detail the scope of mathematical instruction in col- 

 lege. The geometry of Euclid, which should be rele- 

 gated to the schools, has long held a part of honor in 

 the mathematics of the college course. The cause 

 for this is easily seen. It is a subject which lends 

 itself, more readily than any other branch of mathe- 

 matics, to the form of discipline in vogue. It cer- 

 tainly is a matter of vastly more importance as a piece 

 of mathematical training, to have the student of 



Euclid acquire the habit of discovering for himself 

 the demonstration of new propositions, than that the 

 study of Euclid should be made a huge memoriter 

 exercise, as is usually done in college. The clear ap- 

 prehension of geometrical relations, aside from the 

 language describing them, is of the first importance, 

 and may be cultivated by any work which deals with 

 such relations. 



Several other mathematical subjects could well be 

 covered before entering college. These are the ele- 

 mentary parts of algebra, the numerical solution of 

 plane triangles, the practical use of logarithmic ta- 

 bles, and the elementary ideas of analytical geometry. 

 The field would then be cleared, so that the training 

 in all those forms of analysis which are distinctively 

 modern, and which must needs be taught by men in 

 sympathy with its methods, would fall within the 

 years of the college course. 



Objection may be made to the amount of mathe- 

 matical preparation which it is here proposed to put 

 into the schools. 



But what ought the actual scope of mathematical 

 instruction to be during the college course? 



It seems superfluous to say, that, without the mas- 

 tery of the infinitesimal calculus, any mathematical 

 culture of importance is hopeless ; and that a knowl- 

 edge of its methods, accompanied by facility in their 

 employment, is absolutely essential to the understand- 

 ing of the exact sciences. 



Calculus is not omitted from the scheme of study 

 of any classical college in this country; but it is 

 hardly too much to say, that, so far as any real knowl- 

 edge of it is concerned, it might as well be omitted 

 from them all. 



The text-books in use are of such very elementary 

 and defective character, that no sufficient knowledge 

 of the subject can be obtained from them. They are 

 constructed on the plan of omitting almost every thing 

 which may present any special difficulty. It has 

 been in effect assumed by those imbued with the dis- 

 ciplinary spirit, that a knowledge of this subject 

 could be conveyed to the student by daily recitation 

 upon its principles and developments. This is as 

 useless an attempt as to try to prepare an army for 

 the battle-field by a daily lecture instead of a daily 

 drill, or by explaining tactics instead of practising 

 them. The important processes actually employed 

 in calculus are not so very numerous, nor are they 

 especially difficult to acquire. No real use, however, 

 can be made of its methods until these are acquired. 

 It must often happen that the full significance of 

 such processes is not apprehended until long after 

 they are employed with dexterity. Certain it is that 

 such dexterity and familiarity conduce wonderfully 

 to their correct comprehension. 



The daily marking system is perhaps the most 

 characteristic and most pernicious expression of the 

 college disciplinary spirit. How have the evils of that 

 system been intensified in our larger colleges by the 

 wholesale manner in which the work is done! The 

 work of recitation and instruction can, no doubt, 

 often be advantageously combined ; but what is the 

 probability that valuable instruction will be commu- 



