476 INDUCTION. 



could not be removed, they could only be diminished, 

 and the case, therefore, admitted only of the Method 

 of Concomitant Variations. This accordingly being 

 employed, it was found that every diminution of the 

 obstacles diminished the retardation of the motion: 

 and inasmuch as in this case (unlike the case of heat) 

 the total quantities both of the antecedent and of the 

 consequent were known ; it was practicable to esti- 

 mate, with an approach to accuracy, both the amount 

 of the retardation and the amount x)f the retarding 

 causes, or resistances, and to judge how near they 

 both were to being exhausted ; and it appeared that 

 the effect dwindled as rapidly, and at each step was 

 as far on the road towards annihilation, as the cause 

 was. The simple oscillation of a weight suspended 

 from a fixed point, and moved a little out of the 

 perpendicular, which in ordinary circumstances lasts 

 but a few minutes, was prolonged in Borda's experi- 

 ments to more than thirty hours, by diminishing as 

 much as possible the friction at the point of suspen- 

 sion, and by making the body oscillate in a space 

 exhausted as nearly as possible of its air. There 

 could therefore be no hesitation in assigning the whole 

 of the retardation of motion to the influence of the 

 obstacles : and since, after subducting this retardation 

 from the total phenomenon, the remainder was an 

 uniform velocity, the result was the proposition 

 known as the first law of motion. 



There is also another characteristic uncertainty 

 affecting the inference that the law of variation 

 which the quantities observe within our limits of 

 observation, will hold beyond those limits. There is 

 of course, in the first instance, the possibility that 

 beyond the limits, and in circumstances therefore of 

 which we have no direct experience, some counter- 



