MATHEMATICAL INSTRUCTION 165 



of public instruction with a view to encouraging the introduction of 

 ' Meray's method ' in the teaching of geometry. During last year this 

 method was employed in at least thirty of the French schools, and 

 very enthusiastic reports of improvement were received. The method 

 is expounded in ' Nouveaux Elements de Geometrie par Meray/ as 

 well as in several of the French journals. One of its important *fea- 

 tures is the introduction of the notions of displacements and the group 

 of displacements into elementry geometry. 



While reform movements in mathematical instruction are not new, 

 yet the present movement is without a parallel both with respect to 

 its extent and with respect to its vigor. The question naturally arises 

 whether the mental inclinations of civilized races are undergoing 

 gradual changes so that concepts which at one time give pleasure and 

 power to the youthful mind, at other times are beyond the capacity 

 of the average mind, or whether we are becoming more sympathetic 

 with the difficulties which have to be overcome in mental development 

 and take greater precautions to make the steps natural. Whatever 

 may be the cause, it seems probable that readjustment will be effected 

 without departing very far from the older methods. The most likely 

 changes in elementary instruction are those which Klein has been so 

 actively advocating; viz., the early introduction and frequent use of 

 the concept of a function and the teaching of the elements of analytic 

 geometry and the differential and integral calculus at a much earlier 

 period, before the student begins to specialize. 



