OF NATURAL PHILOSOPHY. 25 



he ravings of madmen, than the sober conclusions of 

 people in their waking senses ? 



(19.) They are, nevertheless, conclusions to which 

 any one may most certainly arrive, who will only 

 be at the trouble of examining the chain of reasoning 

 by which they have been deduced ; but, in order to 

 do this, something beyond the mere elements of ab- 

 stract science is required. Waving, however, such 

 instances as these, which, after all, are rather calcu- 

 lated to surprise and astound than for any other pur- 

 pose, it must be observed that it is not possible to 

 satisfy ourselves completely that we have arrived at 

 a true statement of any law of nature, until, setting 

 out from such statement, and making it a foundation 

 of reasoning, we can show, by strict argument, that 

 the facts observed must follow from it as necessary 

 logical consequences, and this, not vaguely and gene- 

 rally, but with all possible precision in time, place, 

 weight, and measure. 



(20.) To do this, however, as we shall presently 

 see, requires in many cases a degree of knowledge of 

 mathematics and geometry altogether unattainable by 

 the generality of mankind, who have not the leisure, 

 even if they all had the capacity, to enter into such 

 enquiries, some of which are indeed of that degree of 

 difficulty that they can be only successfully pro- 

 secuted by persons who devote to them their whole 

 attention, and make them the serious business of 

 their lives. But there is scarcely any person of 

 good ordinary understanding, however little exer- 

 cised in abstract enquiries, who may not be readily 

 made to comprehend at least the general train of 

 reasoning by which any of the great truths of physics 



