100 ANNUAL OF SCIENTIFIC DISCOVERT. 



Students in schools were now taught geometry; they were taught the 

 sixteenth, seventeenth, eighteenth, and nineteenth propositions of Euclid; 

 but that description of knowledge was not of the slightest use to his work- 

 men, or to anybody else. They were also taught mechanics and the law of 

 the lever. That was right; but, then, mechanics and the law of the lever 

 were not ordinarily taught in books in such a way as to be of practical use 

 to the British workman. We did not go far enough. But the pupil teach- 

 ers whom he addressed were not to blame. The persons to blame were their 

 teachers. Two years was, perhaps, all the time that could be devoted to 

 education, and six months were often devoted to as many books of Euclid, 

 which were wasted for all practical purposes, unless, indeed, the student 

 intended to become a professor. He would advise them to skip over the 

 beginning, and devote the least possible time to Euclid; in fact, he would 

 advise them to do a very heterodox thing to cut off all the propositions 

 but the useful ones. They might naturally exclaim, " Then how little will 

 be left." Very little, he admitted; but plane trigonometry would be left. 

 Suppose, for instance, a man had but six months in which to learn. Six 

 weeks might, in that case, be given to Euclid, and then trigonometry might 

 be commenced, solid geometry might next follow, and that constituted the 

 whole education of the workman. But that was precisely what he did not 

 get in the present day. He would also teach, in the six months, conic sec- 

 tions, and afterwards the nature of curves, within the first, second, third, 

 and fourth degrees. 



AVhat he had said about geometry was true as to mathematics. Thirteen 

 and a half yards at three and a half cents was not what was wanted. Of 

 far more importance to the working-man was the comprehension of the 

 laws and relations of numbers, so as to enable him to think in figures about 

 the immediate business before him. The first and most important doc- 

 trine to remember in mathematics was, that shape is not size, or size shape. 

 This might appear to be an axiom, and he thought it was as good as any in 

 Euclid. The doctrine of similar triangles was a fundamental principle enti- 

 tled to the dignity of an axiom; and it was that, without regard to shape 

 and size, any number of triangles might be made all of the same shape, and 

 not of the same size. Mr. Russell having illustrated this principle by draw- 

 ings on the board, continued to say that, with respect to solid geometry, the 

 two great duties in a workman's life were conversion of materials and adap- 

 tation to strength. A mason who used up a wrong stone, or a carpenter who 

 selected a wrong plank or piece of timber, showed that he was ignorant of 

 one of the most useful portions of his art or calling. Now, nothing would 

 teach conversion of materials like solid geometry; it was, in fact, the daily 

 business of the workman. It had been said that every block of marble cut 

 from the quarry contained a beautiful statue, but the art was how to get it 

 out of it. This was very true; but what workmen wanted to know was 

 every shape, and how to get out another shape. The workman who took 

 from a heap a block of stone or piece of timber that cost his master fifty 

 shillings, when a piece could be got answering quite as well which cost twen- 

 ty-five shillings, inflicted a loss upon his employer perhaps equal to a week's 

 wages. Hence the necessity of acquiring a knowledge of solid geometry. 

 But if there were beauty in the quantity of numbers, and in regular geomet- 

 rical figures, there was infinitely more beauty in curves. It was the duty of 

 many mechanics, especially of those engaged in ship-building, to make 

 curved lines. To him it had always been an interesting subject to learn how 



