number of pupils to the University well skilled in solving deductions and examples; nor have I ever known a really able and zealous teacher to fail. I am happy to supplement my own testimony by an extract from the very interesting lecture on Geometrical Teaching by Dr. Lees, of St. Andrews. 'Whatever may be the cause of failure in England, it is clear as any demonstration can be that the failure cannot be ascribed to Euclid. Because in Scotland we do employ Euclid as the text-book for our students, and in Scotland we have the teaching of Geometry attended with the most complete success; and this not only in the colleges, but in all the higher and more important schools and academies of the country, and in many of the parish schools even, where the attention of the teacher is necessarily so much divided.' See also the remarkable Narrative-Essay on a Liberal Education, by the Rev. S. Hawtrey, A.M., Assistant-Master, Eton.
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During the existence of the East India Company's military college at Addiscombe, it is well known that the cadets were instructed in mathematics by the aid of a course drawn up by the late Professor Cape. The geometry in this course was of the kind which our modern reformers recommend, being founded on Legendre, and adopting the principle of hypothetical constructions which is now so emphatically praised. In certain large schools where youths were trained for the military colleges it was usual to instruct a class of candidates for Woolwich, in Euclid, and a class of candidates for Addiscombe in Cape's adaptation of Legendre. Fairness in the procedure was secured by giving the same number of hours by the same masters to each class; and the honour and rewards which attended success supplied an effectual stimulus both to teachers and pupils. Now consider the result. I was assured by a teacher who was for many years distinguished for the number and the success of his pupils, that the training acquired by the Euclid class was far superior to that acquired by the Legendre class. The Euclid
