JuLT 9, 1900] 



SCIENCE 



39 



dices; factoring, and practise in general 

 algebraic manipulation. 



In mensuration, experimental testing of 

 the rules for lengths of curves, for example, 

 in the case of a circle, by rolling a disl^, or 

 by wrapping a string around a cylinder; 

 verification of propositions in Euclid re- 

 lating to areas by the use of squared paper, 

 by means of a planimeter, by using Simp- 

 son's or other approximate rules, or by cut- 

 ting the area out of cardboard and com- 

 paring its weight with that of a piece of 

 known area;" rules for volumes of solids 

 verified by their displacement of a liquid. 



The experimental work in this subject 

 ought to be taken up in connection with 

 practise in weighing and measuring gen- 

 erally, finding specific gravities, illustrating 

 the principle of Archimedes, determining 

 the displacement of floating bodies, and 

 other elementary scientific work. Good 

 judgment will indicate the relative amount 

 of experimental, didactic and numerical 

 work. 



The iise of squared paper is especially 

 emphasized. Some of its applications which 

 are mentioned, are the plotting of statistics 

 of general or special interest; study of the 

 curves or lines so obtained, such as the 

 determination of their maximum and mini- 

 mum points, their rates of increase or de- 

 crease, etc. ; interpolation, or the finding of 

 intermediate values; probable errors of 

 observation and the correction of same; 

 determination of areas and volumes, as 

 mentioned above ; plotting of functions and 

 the graphical solution of equations; deter- 

 mination of the laws between observed 

 quantities. 



In geometry, the experimental illustra- 

 tion of important propositions in Euclid, 

 frequently supplemented by demonstration ; 

 measurement of angles by means of a pro- 



' This is the way in which Galileo is said to 

 have determined the area of the cycloid. 



tractor; definitions of trigonometric func- 

 tions and the use of trigonometric tables; 

 solution of right-angled triangles graphic- 

 ally and by calculation; construction of 

 triangles and the experimental determina- 

 tion of their areas; method of locating a 

 point in a plane and in space ; the elements 

 of descriptive geometry and vector analysis. 



The advanced course proposed consists 

 chiefly in an extension and elaboration of 

 the elementary course. It includes demon- 

 strative geometry, and rules in arithmetic 

 and mensuration stated as algebraic for- 

 mulas. In trigonometry, the study of spe- 

 cial limits such as sin x/x and the deriva- 

 tion of the fundamental formulas and re- 

 lations of trigonometry. In mensuration, 

 the method of determining the constants 

 in such physical formulas as pv^ = c. The 

 course then proceeds to differential and 

 integral calculus and their practical appli- 

 cations; differential equations illustrated 

 by practical problems from mechanics and 

 physics, descriptive geometry and vector 

 analysis. 



The reforms proposed by Professor Perry 

 were widely discussed, and were, in general, 

 favorably received. It was not to be ex- 

 pected, however, that the traditional teach- 

 ing of Euclid in Great Britain woidd 

 undergo any immediate or radical change, 

 or, in fact, that any innovation of the kind 

 proposed meet at the outset with a cordial 

 reception. 



In America, however, Professor Perry's 

 views found ready acceptance and were 

 carried more or less completely into effect. 

 The result was what is now called the labo- 

 ratory method of instruction which has 

 been developed independently at several 

 places, although along most radical lines 

 at the University High School, Chicago. 

 An outline of the laboratory system, to- 

 gether with a number of typical opinions 



