290 INDUCTION. 



its heat, the particles would be in complete contact. This is no move than 

 a guess, and of the most hazardous sort, not a legitimate induction : for 

 since we neither know how much heat there is in any body, nor what is 

 the real distance between any two of its particles, we can not judge whether 

 the contraction of the distance does or does not follow the diminution of 

 the quantity of heat according to such a numerical relation tliat the two 

 quantities would vanish simultaneously. 



In contrast with this, let us consider a case in which the absolute quan- 

 tities are known ; the case contemplated in the first law of motion : viz., 

 that all bodies in motion continue to move in a straight line with uniform 

 velocity until acted upon by some new force. This assertion is in open op- 

 position to first appeai'ances ; all terrestrial objects, when in motion, grad- 

 ually abate their velocity, and at last stop ; which accordingly the ancients, 

 with their inductio per enumeratiojiem s^mj!??^oem, imagined to be the law. 

 Every moving body, however, encounters various obstacles, as friction, the 

 resistance of the atmosphere, etc., Avhich we know by daily experience to 

 be causes capable of destroying motion. It was suggested that the whole 

 of the retardation might be owing to these causes. How was this in- 

 quired into ? If the obstacles could have been entirely removed, the case 

 would have been amenable to the Method of Difference. They could not 

 be removed, they could only be diminished, and the case, therefore, ad- 

 mitted only of the Method of Concomitant Variations. This accordingly 

 being employed, it was found that every diminution of the obstacles di- 

 minished the retardation of the motion : and inasmuch as in this case (un- 

 like the case of heat) the total quantities both of the antecedent and of the 

 consequent were known, it was pi'acticable to estimate, with an approach 

 to accuracy, both the amount of the retardation and the amount of 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 toward 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 experiments to more than 

 thirty hours, by diminishing as much as possible the friction at the point 

 of suspension, and by making the body oscillate in a space exhausted as 

 nearly as possible of its air. There could therefore be no hesitation in as- 

 signing the whole of the retardation of motion to the influence of the ob- 

 stacles ; and since, after subducting this retardation from the total phenom- 

 enon, the remainder was a 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 there- 

 fore of which we have no direct experience, some counteracting cause 

 might develop itself; either a new agent or a new property of the agents 

 concerned, which lies dormant in the circumstances we are able to observe. 

 This is an element of uncertainty which enters largely into all our predic- 

 tions of effects; but it is not peculiarly applicable to the Method of Con- 

 comitant Variations. The uncertainty, however, of which I am about to 

 speak, is characteristic of that method ; especially in the cases in which 

 the extreme limits of our observation are very narrow, in comparison with 

 the possible variations in the quantities of the phenomena. Any one who 



