218 SCIENTIFIC METHOD IN PHILOSOPHY 



that where an observed uniformity fails, some wider 

 uniformity can be found, embracing more circumstances, 

 and subsuming both the successes and the failures of the 

 previous uniformity. Unsupported bodies in air fall, 

 unless they are balloons or aeroplanes ; but the principles 

 of mechanics give uniformities which apply to balloons 

 and aeroplanes just as accurately as to bodies that fall. 

 There is much that is hypothetical and more or less 

 artificial in the uniformities affirmed by mechanics, 

 because, when they cannot otherwise be made applicable, 

 unobserved bodies are inferred in order to account for 

 observed peculiarities. Still, it is an empirical fact that 

 it is possible to preserve the laws by assuming such 

 bodies, and that they never have to be assumed in cir- 

 cumstances in which they ought to be observable. Thus 

 the empirical verification of mechanical laws may be 

 admitted, although we must also admit that it is less 

 complete and triumphant than is sometimes supposed. 



Assuming now, what must be admitted to be doubtful, 

 that the whole of the past has proceeded according to 

 invariable laws, what can we say as to the nature of these 

 laws ? They will not be of the simple type which asserts 

 that the same cause always produces the same effect. 

 We may take the law of gravitation as a sample of the 

 kind of law that appears to be verified without exception. 

 In order to state this law in a form which observation 

 can confirm, we will confine it to the solar system. It 

 then states that the motions of planets and their satellites 

 have at every instant an acceleration compounded of 

 accelerations towards all the other bodies in the solar 

 system, proportional to the masses of those bodies and 

 inversely proportional to the squares of their distances. 

 In virtue of this law, given the state of the solar system 

 throughout any finite time, however short, its state at all 



