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THE POPULAR SCIENCE MONTHLY.— SUPPLEMENT. 



as to follow the highest of genuine physical rea- 

 soning ; and therefore, when I find apparently 

 profound physical speculation associated with 

 incapacity for the higher mathematics, I feel con- 

 vinced that the profundity cannot be real. One 

 very necessary remark, however, must be made 

 here: not in qualification, but in explanation, of 

 this statement. One of the greatest of physical 

 reasoners, Faraday, professed, as most of you 

 are aware, to know very little of mathematics. 

 But in fact he was merely unacquainted with the 

 technical use of symbols. His modes of regard- 

 ing physical problems were of the highest order 

 of mathematics. Many of the very best things 

 in the recent great works on Electricity by Clerk- 

 Maxwell and Sir William Thomson are (as the 

 authors cheerfully acknowledge) little more than 

 well-executed translations of Faraday's concep- 

 tions into the conventional language of the higher 

 analysis. 



I hope that the time is not far off when no 

 one who is not (at least in the same sense as Far- 

 aday) a genuine mathematician, however he may 

 be otherwise qualified, will be looked upon as 

 even a possible candidate for a chair of Natural 

 Philosophy in any of our universities. Of course 

 such a danger would be out of the question if we 

 were to constantly bear in mind the sense in 

 which Newton understood the term natural phi- 

 losophy. There is nothing so well fitted as mathe- 

 matics " to take the nonsense out of a man," as it 

 is popularly phrased. No doubt a man may be an 

 excellent mathematician, and yet have absolutely 

 no knowledge of physics ; but he cannot possibly 

 know physics as it is unless he be a mathema- 

 tician. Much of the most vaunted laboratory 

 work is not nearly of so high an order of skilled 

 labor as the every-day duty of a good telegraph- 

 clerk, especially if he be in charge of a siphon- 

 recorder. And many an elaborate memoir which 

 fills half a volume of the transactions of some 

 learned society is essentially as unsightly and in- 

 convenient an object as the mounds of valueless 

 dross which encumber the access to a mine, and 

 destroy what otherwise might have been an ex- 

 panse of fruitful soil. 



There are many ways in which these mounds 

 may grow. The miner may be totally ignorant of 

 geology, and may thus have bored and excavated 

 in a locality which he ought to have known would 

 furnish nothing. Or he may have, by chance or 

 by the advice of knowing friends, hit upon a really 

 good locality. Even then there are many modes 

 of failure, two of which are very common. He 

 may fail to recognize the ore when he has got it ; 



and so it goes at once to the refuse-heap, possibly 

 to be worked up again long after by somebody 

 who has a little more mineralogical knowledge — 

 as in the recent case of the mines of Laurium. 

 Here he may be useful — at second-hand. Or, if 

 it be fossils or crystals, for instance, for which he 

 is seeking, his procedure may be so rough as to 

 smash them irreparably in the act of mining. 

 This is dog in the manger with a vengeance. But, 

 anyhow, he generally manages to disgust every 

 other digger with the particular locality which he 

 has turned upside down; and thus exercises a 

 real, though essentially negative, influence on the 

 progress of mining. 



The parallel here hinted at is a very apt one, 

 and can be traced much further. For there are 

 other peculiarities in the modes of working adopt- 

 ed by some miners, which have their exact coun- 

 terparts in many so-called scientific inquiries ; but, 

 for the present, we must leave them unnoticed. 



There is but one way of being scientific : but 

 the number of ways of being unscientific is in- 

 finite, and the temptations alluring us to them are 

 numerous and strong. Indolence is the most in- 

 nocent in appearance, but in fact probably the 

 most insidious and dangerous of all. By this I 

 mean, of course, not mere idleness, but that easily 

 acquired and fatal habit of just stopping short of 

 the final necessary step in each explanation. Far- 

 aday long ago pointed this out in his discourse on 

 " Mental Inertia." Many things which are ex- 

 cessively simple when thoroughly understood are 

 by no means easy to acquire ; and the student too 

 often contents himself with that half learning 

 which, though it costs considerable pains, leaves 

 no permanent impression on the mind, while 

 " one struggle more " would have made the sub- 

 ject his own forever after. 



Science, like all other learning, can be reached 

 only by continued exertion. And, even when we 

 have done our utmost, we always find that the 

 best we have managed to achieve has been merely 

 to avoid straying very far from the one true path. 



For, though science is in itself essentially sim- 

 ple, and is ever best expressed in the simplest 

 terms, it is my duty to warn you in the most for- 

 mal manner that the study of it is beset with dif- 

 ficulties, many of which cannot but constitute real 

 obstacles in the way even of the mere beginner. 

 And this forms another of the fatal objections to 

 the school-teaching of physical science. For there 

 is as yet absolutely no known road to science ex- 

 cept through or over these obstacles, and a cer- 

 tain amount of maturity of mind is required to 

 overcome them. 



