FALLING BODIES AT GREAT HEIGHTS. 321 



In order to meet this necessity, there was no temptation to 

 take up the Book of Nature, after the manner of expositors 

 and critics, merely to cover it with glosses : 



" Mit eitler Rede wird hier nichts geschaflft." 



It was numbers that were sought, and numbers that were 

 found. The overpowering force of circumstances constrained 

 the spirit of inquiry into the right path, and therein led it at 

 once from success to success. 



Now that after long-continued, accurate, and fortunate 

 observations the needful knowledge of the courses and dis- 

 tances of the nearest heavenly bodies, as well as of the figure 

 and size of the earth, has been acquired, we are in a position 

 to treat the question, What is the numerical influence exerted 

 by increased distance from the earth upon the known laws of 

 falling bodies ? and we thus arrive at the pregnant discovery 

 that, at a height equal to the earth's semidiameter, the dis- 

 tance fallen through and the final velocity, for the first second, 

 is four times less than on the surface of the earth. 



In order to pursue our inquiry, let us now return to the 

 objects which immediately surround us. From the earliest 

 times, the phenomena of combustion must have claimed in an 

 especial degree the attention of mankind. In order to ex- 

 plain them, the ancients, in accordance with the method of 

 their naturalistic philosophy, put forward a peculiar upward- 

 striving element of Fire, which in conjunction with, and in 

 opposition to, Air, Water, and Earth, constituted all that ex- 

 isted. The necessary consequence of this theory, which they 

 discussed with the most acute sagacity, was, that in regard to 

 the phenomena in question and all that related to them, they 

 remained in complete ignorance. 



Here, again, it is quantitative determinations, it is num- 

 bers alone, which put the Ariadne's clue in our hand. If we 

 want to know what goes on during the phenomena of com- 

 bustion, we must weigh the substances before and after they 

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