XVI 



cient evidence in itself of a practical mind. The first rale of prac- 

 tice is to do all things at the right time and in their proper places ; 

 to proportion the means to the ends and the ends to the means ; 

 above all to know what is possible, and to confine one's endeavours 

 within the limits of the feasible. The author allows, and has 

 habitually acted on the principle, that for the purpose of illustrating 

 lectures on geometry or any other abstract science, the lecturer 

 should lay his hands on the plough, the loom, the forge, the work- 

 shop, the mine, the sea, the stars, all things on earth or under heaven 

 which may help to arouse the attention or interest the imagination of 

 his auditors. But to profess to make the mere applications of a 

 science such as geometry the staple of the matter to be taught within 

 the walls of the college by the Gresham lecturer, to undertake to 

 comprise within a course of geometrical lectures systematic instruc- 

 tion in mechanics, astronomy and navigation, descriptive geometry, 

 engineering and drawing, the method of interpolation, the theory of 

 toothed wheels, the two kinds of perspective, machinery, mapping, 

 the art of shipbuilding, rules for cutting the best form of screws,, 

 and for enabling the citizens of London to qualify themselves for 

 being their own land surveyors, is a suggestion which, with all due 

 deference to its propounder, the author regards as one of the wildest 

 and most visionary which ever entered into the mind or issued from 

 the lips of a practical man." The address, composed at short notice, 

 is a powerful essay on geometrical science. 



He took up the appointment of Professor of Mathematics and Lec- 

 turer in Natural Philosophy at the Royal Military Academy on the 

 15th September, 1855. In August, 1856, the lectureship was taken 

 over by the Professor of Practical Astronomy. The salary of the 

 appointment was 550 per annum combined with a Government 

 residence, medical attendance, and right of pasturage on the com- 

 mon. He occupied K Quarters, Woolwich Common, being the last of a 

 long list of residential professors. The house was commodious and 

 with a good garden. There he frequently entertained his friends from 

 London and distinguished foreign mathematicians. At the same 

 time he always had chambers in London in the neighbourhood 

 of the Athenaeum Club. These he had taken originally with 

 the intention to practise at the Bar, Scientifically this was a 

 glorious period for Sylvester, for, seated under a walnut tree 

 which grew in the centre of his garden, he made some of the 

 great discoveries with which his name will be for ever associated. 

 He wrote about eighty papers, and naturally it is only possible here 

 to glance at a few of those which are of fundamental importance. 

 During 1857-58 he published remarkable advances in the theory of 

 the Partition of Numbers, and in 1859 delivered seven lectures on 

 the subject at King's College, London. The outlines of these dis- 



