ADDRESS. 31 



should seem little attractive when contrasted with the light companion- 

 ship of the former. The day is yet young, and in the early dawn many 

 things look weird and fantastic which in fuller light prove to be familiar 

 and useful. The outcomings of Science, which at one time have been 

 deemed to be but stumbling-blocks scattered in the way, may ultimately 

 prove stepping stones which have been carefully laid to form a pathway 

 . over difficult places for the children of " sweetness and of light." 



The instances on which we have dwelt are only a few out of many in 

 which Mathematics may be found ruling and governing a variety of sub- 

 jects. It is as the supreme result of all experience, the framework in 

 which all the varied manifestations of nature have been set, that our 

 science has laid claim to be the arbiter of all knowledge. She does not 

 indeed contribute elements of fact, which must be sought elsewhere ; but 

 she sifts and regulates them : she proclaims the laws to which they must 

 conform if those elements are to issue in precise results. From the data 

 of a problem she can infallibly extract all possible consequences, whether 

 they be those first sought, or others not anticipated ; but she can introduce 

 nothing which was not latent in the original statement. Mathematics 

 cannot tell us whether there be or be not limits to time or space ; but to 

 her they are both of indefinite extent, and this in a sense which neither 

 affirms nor denies that they are either infinite or finite. Mathematics 

 cannot tell us whether matter be continuous or discrete in its structure ; 

 but to her it is indifferent whether it be one or the other, and her conclu- 

 sions are independent of either particular hypothesis. Mathematics can 

 tell us nothing of the origin of matter, of its creation or its annihilation ; 

 she deals only with it in a state of existence ; but within that state its 

 modes of existence may vary from our most elementary conception to our 

 most complex experience. Mathematics can tell us nothing beyond the 

 problems which she specifically undertakes ; she will carry them to their 

 limit, but there she stops, and upon the great region beyond she is im- 

 perturbably silent. 



Conterminous with space and coeval with time is the kino-dom of 

 Mathematics ; within this range her dominion is supreme ; otherwise than 

 according to her order nothing can exist ; in contradiction to her laws 

 nothing takes place. On her mysterious scroll is to be found written for 

 those who can read it that which has been, that which is, and that which 

 is to come. Everything material which is the subject of knowledge has 

 number, order, or position ; and these are her first outlines for a sketch of 

 the universe. If our more feeble hands cannot follow out the details, 

 still her part has been drawn with an unerring pen, and her work cannot 

 be gainsaid. So wide is the range of mathematical science, so indefinitely 

 may it extend beyond our actual powers of manipulation, that at some 

 moments we are inclined to fall down with even more than reverence 

 before her majestic presence. But so strictly limited are her promises and 

 powers, about so much that we might wish to know does she offer no 



