644 Transactions. — Miscellaneous. 



relative dimensions, and the most advantageous location of the 

 plates, as well as those relating to the connecting machinery, 

 and the most economical application of the power employed. 

 These, however, are but questions of constructive detail which 

 do not affect the object of this paper, which is merely to 

 establish the principle involved. 



It is, of course, only by actual trial that the practicability 

 of the idea could be demonstrated. Still, the advantages of 

 such a contrivance, were it capable of being carried into 

 effect, are so obvious that it would be well worth while to 

 make a series of experiments, in the first instance with a vessel 

 of small dimensions, of which the cost would be compara- 

 tively trifling considering the interest at stake. And, though 

 we may never expect that the action of the brake-fins on a 

 ship will equal that of a Westiughouse brake on an express 

 train, or even that of the oars on a skilfully- handled boat, 

 still, if they will shorten by a cable's length the distance at 

 which she will bring up, or reduce to any considerable 

 degree the angle at which she will come round, they may be 

 the means of giving many a " man overboard " a chance for 

 his life, and help to minimise the increasing chances of one 

 of the most appalling of disasters, a collision at sea. 



Aet. LXV. — Mill on Demonstration and Necessary Truili. 



By William Caelile, M.A. 



[Bead before the Wellington Philosophical Society, 8th July, 1891.] 



If any one should endeavour to ascertain what is the received 

 doctrine in England at present with regard to the basis of 

 mathematical demonstration, the true nature of the definitions 

 of Euclid, and the ultimate evidence for the axioms, he would 

 find himself met by a very remarkable diversity of opinion on 

 the part of those who have been recognised as the highest 

 authorities on psychology and metaphysics during the past 

 half-century. To find anything like consistency, indeed, he 

 would have to go back to the philosophers of the pre-Kantian 

 age. 



Hume's opinion was that the truths of pure mathematics 

 were to be put into one class along with identical propositions, 

 and that truths of matters of fact were to be put into another 

 and altogether different class. However certain the latter 

 might be, their certainty, in his view, depended upon an en- 



