THE STORAGE OF FORCE. 71 



of energy as the Falls of Niagara, and to work our 

 cranes, lifts, and machinery of every description by 

 means of sources of power arranged at convenient 

 centres. To these applications the Brothers Siemens 

 have more recently added the propulsion of trains by 

 currents passing through the rails, the fusion in con- 

 siderable quantities of highly refractory substances, and 

 the use of electric centres of light in horticulture as 

 proposed by Werner and William Siemens. By an 

 essential improvement by Faure of the Plante Secondary 

 Battery, the problem of storing electrical energy appears 

 to have received a practical solution, the real importance 

 of which is clearly proved by Sir W. Thomson's recent 

 investigation of the subject. 



It would be difficult to assign the limits to which 

 this development of electrical energy may not be ren- 

 dered serviceable for the purposes of man. 



As regards mathematics I have felt that it would 

 be impossible for me, even with the kindest help, to 

 write anything myself. Mr. Spottiswoode, however, 

 has been so good as to supply me with the following 

 memorandum. 



In a complete survey of the progress of science during the half- 

 century which has intervened between our first and our present 

 meeting, the part played by mathematics would form no insignificant 

 feature. To those indeed who are outside its enchanted circle it is 

 difficult to realise the intense intellectual energy which actuates its 

 devotees, or the wide expanse over which that energy ranges. Some 

 measure, however, of its progress may perhaps be formed by con- 

 sidering, in one or two cases, from what simple principles some of the 

 great recent developments have taken their origin. 



Consider, for instance, what is known as the principle of signs. 

 In geometry we are concerned with quantities such as lines and angles; 



