THE THEORY OF GRAVITATION. 155 



ity of the body. Consequently, the resultant retardation is proportional 

 to the excess of the square of the sura over the square of the difference, 

 which (by the eighth proposition of the second book of the Elements of 

 Euclid) is four times the product of the absolute velocities in question. 



XXY. 



To the three difficulties above mentioned may be reduced all those 

 which are plausible, since there can be no other changes in the motions 

 of a heavy body, or in the motions of the gravitational fluid, or in their 

 constitution, except those which proceed from some opposition or inter- 

 position, either on the part of the particles of the heavy body, which 

 hinder the atoms composing the fluid from reaching their destination, or 

 from particles of the fluid itself, the one opposing the other, or, finally, 

 from the effect of the latter on the path of the heavy body. The solu- 

 tions of all these difficulties depend either on the permeability of the 

 heavy body or the subtlety and rapidity of the gravitational atoms — 

 properties to none of which we are obliged to assign two opposing 

 limits. 



This last expression signifies that while several considerations may 

 unite to augment the intensity of such or such property, yet no con- 

 sideration requires a diminution in the intensity of the same property, 

 and that reciprocally no considerations tend to limit the dimiuutive- 

 ness of properties of which certain other considerations limit more and 

 more the magnitude. There are no conditions which give opposing 

 indications, and which therefore obstruct the choice of remedies. This 

 assertion would be tedious to establish, but very few readers will con- 

 test its correctness. 



XXVI. 



While we speak of alterations and remedies it is for me to conform 

 to the irregularity of our ordinary progress in research. Truth never 

 permits us to discover her at first seeking, with all her following train 

 of verities, but we proceed gradually in discovery by tedious gropiugs 

 and corrections. To this procedure a writer ought also in some 

 measure to conform, in the exposition of truths which lie has finally 

 discovered, when the greatness or smalluess of the objects discussed 

 transcends that of the majority of those objects with which we are 

 familiar, and when he believes that his reader will not at first be dis- 

 posed to countenance suppositions so excessive, but only in a measure 

 as he shall have shown him their necessity. For the reader will have 

 had no perspective to apply to this immensity or that diminutiveuess 

 if it has been assumed at the start in sufficient measure to satisfy all 

 phenomena. 



The author might with equal justice assume at the start a magnitude 

 or diminutiveuess sufficient for the purpose, since in explaining the 

 phenomena the physicist takes the place (so far as he may) of the 

 Creator — a being who, having determined precisely in advance all the 



