XI 



the circle by multiplying half the circumference by the radius, and 

 finding the volume of a pyramid by multiplying the base by a third 

 of the height. There were a great many branches of geometry 

 Which could be illustrated experimentally, though the geometry of 

 angles was what he had chiefly taught by this means. He had set a 

 class of boys, about 20 in number, to draw triangles with a ruler. 

 Naturally the triangles would be of all soits of shapes and sizes, but 

 having taught therrfthe use of the ("protractor," he set them to measure 

 the three angles and tell the number of degrees of them all. One boy 

 Would get it 179deg., and another lSldeg., but all_ would 

 be very near 180deg They soon came to the conclusion that 

 the three angles of all triangles contained ISOdeg., or two right 

 angles, and this was impressed upon their minds before commenc- 

 ing upon Euclid's demonstrations. He also set the boys four sided 

 figures, and told them to measure all the angles, and they always 

 approached 360deg., or four right angles, and their minds were 

 thus led to the conclusion that the angles contained in all quad- 

 rilateral figures amounted to four right angles. He did the same with 

 regard to rive sides figures and polygans. He found that theboys tooKthe 

 greatest possible interest in the study thus afforded them, many boys 

 who had had to confess that they could not see the object of Euclid's 

 demonstrations admitting that they began to see something in it after 

 all. His belief was that if a class of boys were kept at that sort of 

 work for six months they would learn more of Euclid's elements in 

 the ensuino- six months than they would otherwise do in 12 months. 

 He had used this system in teaching elementary trigonometry, and 

 the results of the work he set his boys were surprisingly correct 

 He had got a small class through the elements of this branch of 

 mathematics with the greatest satisfaction both to himsalf and the 

 boys. .There was no royal road to geometry, but the experimental 

 method was an advance on the old one, and the nearest approach that 

 could be found. 



Mr. E C. NowiLL expressed the great gratification he had received 

 from hearing Mr. Mault's paper read, and hoped its effect would 

 extend much further than the walls of the Royal Society's chamber. 

 He hoped some practical steps would be taken by the council of the 

 society to bring the subject under the notice of the State school teachers, 

 and the Director of education, with a request that he would interest 

 himself in introducing this system into the State schools. He was 

 perfectly sure that the proper mode of teaching was to teach the con- 

 crete first and the abstract afterwards. An utterly wrong principle 

 had been adopted in their educational system, as the abstract was 

 first and the student left to find out the concrete himself. A great 

 portion of the time supposed to be spent in education was just thrown 

 away. There were very few people with brains so formed that 

 they could grasp the abstract without the concrete. Although he 

 had forgotten nearly all his geometry, it had taught him the best 

 methods of reasoning, and showed him that one must be very careful 

 of the groundwork. It was well known that things presented to the 

 eye had a greater effect on the mind than those which were only 

 presented to the imagination. He hoped, therefore, that this paper 

 would have some practical effect, and that steps would be taken to bring 

 it before the pointed attention of all those who were engaged in the 

 State schools. , , 



Mr. Bernard Shaw expressed his pleasure at having heard sucn 

 an able paper read and thought Mr. Mault deserved their sincerest 

 thanks. 



On the suggestion of Mr. Morton it was decided that the paper 

 should be published. 



