. iv.J DISSERTATION SECOND. . 97 



ed the intensity of the earth's gravitation to the sun, 

 with the moon's gravitation to the earth, each being 

 measured by the contemporaneous and momentary deflex- 

 ion from a tangent to the small arch of its orbit. A 

 more detailed investigation showed, that the intensity of 

 the central force in different orbits, is as the mean dis- 

 tance divided by the square of the periodic time 5 and 

 the same intensity being also as the quantities of matter 

 divided by the squares of the distances, it follows, that 

 these two quotients are equal to one another, and that, 

 therefore, the quantities of matter are as the mean dis- 

 tances divided by the squares of the periodic times. 

 Supposing, therefore, in the instance, just mentioned, that 

 the ratio of the mean distance of the sun from the earth 

 to the mean distance of the moon from the earth is 

 given (which it is from astronomical observation) ; as the 

 ratio of their periodic lines is also known, the ratio of 

 the quantity of matter in the sun to the quantity of mat- 

 ter in the earth, of consequence is found, and the same 

 holds good for all the planets which have satellites moving 

 round them. Nothing certainly can be more unexpected, 

 than that the quantities of matter in bodies so remote, 

 should admit of being compared with one another, and 

 with the earth. Hence also their mean densities, or 

 mean specific gravities, became known. For from their 

 distances and the angles they subtended, both known 

 from observation, their magnitudes or cubical contents 

 were easily inferred, and the densities of all bodies are, 

 as their quantities of matter, divided by their magnitude. 

 The Principia Phiiosophice Naturalis, which contained all 

 these discoveries, and established the principle of univer- 

 sal gravitation, was given to the world in 1687, an asra, 

 on that account, for ever memorable in the history of 

 human knowledge. 



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