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SCIENCE 



[N. S. Vol. XXVI. No. 663 



can not be considered as conditioning the 

 evolution of spirit, but rather as reflecting 

 its trend. 



To illustrate the meaning of a pause such 

 as mentioned, the hiatus of sixteen cen- 

 turies which intervened between the statics 

 of Archimedes and the dynamics of Ste- 

 vinus and Galileo may be cited. The diffi- 

 culty experienced by students in passing 

 from statics to kinetics has frequently been 

 remarked by teachers, and has led to a re- 

 vision of instruction in mechanics by begin- 

 ning the subject with kinematics and treat- 

 ing statics as a special case of dynamics. 

 This order of development might, however, 

 have been inferred from the historic rela- 

 tion of the subjects, for the history of 

 mechanics shows that the statics of Archi- 

 medes consisted in little more than the law 

 of the lever, and that no advance was made 

 until the subject was approached from the 

 standpoint of motion. In fact such an 

 elementary principle of statics as the paral- 

 lelogram of forces was not proved or even 

 commonly accepted until after the enun- 

 ciation of Newton's laws of motion. In 

 this case, then, the pause emphasizes the 

 degree of attainment essential to a proper 

 understanding of the laws of motion, and 

 also the necessity of approaching the sub- 

 ject from the proper direction, both of 

 which are of the greatest pedagogical im- 

 portance. 



The long interval of time, approximating 

 4,000 years, which was spent by the an- 

 cients in acquiring the fundamental ideas 

 of number is another instance in point, and 

 indicates the necessity of thoroughness in 

 the first stages of instruction. Here again 

 theory has been anticipated by experience 

 in the method proposed by Grube, which 

 consists in spending the entire two first 

 years of mathematical instruction in ex- 

 haustive number analysis. There is no 

 doubt but that under the present forcing 



system too little time is devoted to this 

 basic work, the result being that ability to 

 make numerical calculations with ease and 

 facility is the exception rather than the 

 rule. This also explains the reason for the 

 unfavorable comparison sometimes drawn 

 between our modern schools with their mul- 

 tiplicity of subjects and too often super- 

 ficial treatment, and the old red school- 

 house of the last generation, where instruc- 

 tion was limited to the three R 's, but where 

 each was taught with such thoroughness as 

 to leave a permanent impress on the char- 

 acter of the scholar. 



The movement recently inaugurated in 

 Germany and England with a view to re- 

 vising the present instruction in mathemat- 

 ics indicates the lack of harmony between 

 ancient and modern civilization. A char- 

 acteristic expression of this dissatisfaction 

 with existing methods of instruction is 

 found in the so-called "Perry movement" 

 and its rapid spread throughout England 

 and America. The chief feature of the 

 modification proposed by Professor Perry 

 is the laboratory method of instruction, 

 which may be characterized as an attempt 

 to visualize mathematics, at the same time 

 making it utilitarian as well as concrete. 

 It is, therefore, a reversion to the basic 

 needs of humanity and the means which 

 were used for supplying them. Thus arith- 

 metic originated with the Phoenicians and 

 Chaldeans to supply their commercial 

 needs, while even with the Greeks the be- 

 ginnings of geometry may be traced to the 

 attempt to solve certain practical problems 

 in mensuration. It is, in fact, a general 

 truth that the chief stimulus to the develop- 

 ment of mathematics has always been found 

 in the attempt to explain natural phenom- 

 ena, and make them subservient to the 

 physical needs of humanity. The labora- 

 tory method, then, may be used as a basis 

 for the inductive development of mathe- 



