300 FRAGMENTS OF SCIENCE. 



but a simple expansion, heard him exclaim, * I have it, 

 sir.' The consciousness of self-power, thus awakened, 

 was of immense value ; and, animated by it, the pro- 

 gress of the class was astonishing. It was often iny 

 custom to give the boys the choice of pursuing their 

 propositions in the book, or of trying their strength 

 at others not to be found there. Never in a 

 single instance was the book chosen. I was ever 

 ready to assist when help was needful, but my offers 

 of assistance were habitually declined. The boys 

 had tasted the sweets of intellectual conquest and 

 demanded victories of their own. Their diagrams 

 were scratched on the walls, cut into the beams upon 

 the playground, and numberless other illustrations were 

 afforded of the living interest they took in the subject. 

 For my own part, as far as experience in teaching goes, 

 I was a mere fledgling- -knowing nothing of the rules of 

 pedagogics, as the Germans name it ; but adhering to 

 the spirit indicated at the commencement of this dis- 

 course, and endeavouring to make geometry a means 

 rather than a branch of education. The experiment 

 was successful, and some of the most delightful hours 

 of my existence have been spent in marking the vigorous 

 and cheerful expansion of mental power, when appealed 

 to in the manner here described. 



Our pleasure was enhanced when we applied our 

 mathematical knowledge to the solution of physical 

 problems. Many objects of hourly contact had thus a 

 new interest and significance imparted to them. The 

 swing, the see-saw, the tension of the giant- stride ropes, 

 the fall and rebound of the football, the advantage of a 

 small boy over a large one when turning short, par- 

 ticularly in slippy weather ; all became subjects of 

 investigation. A lady stands before a looking-glass, of 

 her own height ; it was required to know how much of 



