494 Dr. J. R. Mayer on the Mechanical Equivalent of Heat, 



as such, Lave striven to rise above them, have as yet borne but 

 barren fruit. 



We shall not here discuss the modern naturalistic philosophy 

 (Naturphilosophie) further than to say that its character is already 

 sufficiently apparent from the ephemeral existence of its offspring. 

 But even the greatest and most meritorious of the naturalists of 

 antiquity, in order to explain, for example, the properties of the 

 lever, took refuge in the assertion that a circle is such a marvel- 

 lous thing that no wonder if motions, taking place in a circle, 

 offer also in their turn most unusual phenomena. If Aristotle, 

 instead of straining his extraordinary powers in meditations upon 

 the fixed point and advancing line, as he calls the circle, had 

 investigated the numerical relations subsisting between the 

 length of the arm of the lever and the pressure exerted, he 

 would have laid the foundation of an important part of human 

 knowledge. 



Such mistakes, committed as they were, in accordance with 

 the spirit of those times, even by a man whose many positive 

 services constitute his everlasting memorial, may serve to point 

 us in the opposite road which leads us surely to the goal. But if, 

 even by the most correct method of investigation, nothing can 

 be attained without toil and industry, the cause is to be sought 

 in that divine order of the world according to which man is 

 made to labour. But it is certain that already immeasurably 

 more means and more toil have been sacrificed to error than were 

 needed for the discovery of the truth. 



The rule which must be followed, in order to lay the founda- 

 tions of a knowledge of nature in the shortest conceivable time, 

 may be comprised in a few words. The natural phenomena 

 with which we come into most immediate contact, and which are 

 of most frequent occurrence, must be subjected to a careful 

 examination by means of the organs of sense, and this examination 

 must be continued until it results in quantitative determinations 

 which admit of being expressed by numbers. 



These numbers are the required foundations of an exact inves- 

 tigation of nature. 



Among all natural operations, the free fall of a weight is the 

 most frequent, the simplest, and — witness Newton's apple — at 

 the same time the most important. When this process is ana- 

 lysed in the way that has been mentioned, we immediately see 

 that the weight strikes against the ground the harder the greater 

 the height from which it has fallen ; and the problem now con- 

 sists in the determination of the quantitative relations subsisting 

 between the height from which the weight falls, the time occupied 

 by it in its descent, and its final velocity, and in expressing these 

 relations by definite numbers. 



