300 FEAGMENTS OF SCIENCE. 



which the ecstasy of Archimedes was but a simple ex- 

 pansion, heard him exclaim, ' I have it, sir.' The con- 

 sciousness of self-power, thus awakened, was of im- 

 mense value; and, animated by it, the progress of the 

 class was astonishing. It was often my 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 habit- 

 ually declined. The boys had tasted the sweets of in- 

 tellectual 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 indi- 

 cated at the commencement of this discourse, and en- 

 deavouring 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 advan- 

 tage of a small boy over a large one when turning 

 short, particularly in slippery weather; all became 

 subjects of investigation. A lady stands before a 



