PROCEEDINGS OP SECTION J. 723 



whicli plot out to a straight line. He learns, also, how to deduce the 

 equation to a given line drawn on the paper. Linear equations are 

 solved graphically and then by calculation. 



Then the parabola is studied by plotting physical data, such as the 

 displacement curve of a freely-falling body, the area of an equilateral 

 triangle as a function of its side, &c. Its focus and disectrix are obtained 

 by construction. Also in this connection the differential of a function 

 is dealt with on the principle of limits, and applied to the construction 

 of tangents and normals at any point of the parabola. It is sufficient 

 for some time that the pupil should be able to differentiate a power of 

 the independent variable. Then, in this connection he studies the 

 solution of quadratic equations. Here, again, we call in mensuration 

 to furnish concrete instances. The area of the total surface of a cylinder, 

 or of a cone, is a quadratic fraction of its radius ; the volume of a 

 conical fiustum is a quadratic fraction of the radius of one end. These 

 problems on the cone and cylinder are worked out by solving quadratics 

 from formula and graphically by parabolic intersections with a straight 

 line. 



The rectangular hyperbola is the next curve studied as representing 

 inverse proportionality. The reciprocals of numbers are plotted against 

 the numbers and physical data are supplied for plotting. The function 

 is differentiated, and tangents and normals drawn therefrom. The so- 

 called simultaneous quadratics are solved where one equation is the 

 hyperbola and the other the straight line, or the parabola and straight 

 line are solved. 



Then the circle is studied on the same plan. The functional 

 equation differentiated, tangents and normals drawn, simultaneous 

 quadratics solved where one equation is that of the circle. 



Similar triangles are dealt with ; the proportionality of corres- 

 ponding sides shown, and this proportionality expressed by the trigono- 

 metrical ratios. Simple theorems connecting these ratios are 

 established. 



The course above outlined has given me much greater satisfaction 

 and led to more useful results than the orthodox treatment of algebra 

 and Euclid, from which I have gladly escaped. 



We come now to a subject, the teaching of which has been the 

 occasion for much discussion, and for many attempts at improved 

 methods — chemistry. The search for new methods in the teaching of 

 this subject has arisen on account of didactic methods into which 

 teachers had drifted in dealing with a subject essentially experimental. 

 ' Two methods in particular have gained prominence of recent years, 

 the heuristic and the historic method. The former is the method 

 strongly advocated by Professor Armstrong, and carried out success- 

 fully, I believe, in Irish secondary schools. According to the latter 

 method the pupil retraces the ground covered by early experimenters, 

 in discovering, for example, the nature of combustion, and the existence 

 and properties of the commoner gases. I can see no special force in this 

 method. It is difficult to put oneself in the particular circumstances 

 surrounding the life and work of investigators living some centuries ago. 



