THE FOUR EXPERIMENTAL METHODS. 



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a. If we do not know the total quan- 

 tities, we cannot, of course, determine 

 the real numerical relation according 

 to which those quantities vary. It 

 is therefore an error to conclude, as 

 some have concluded, that because 

 increase of heat expands bodies, that 

 is, increases the distance between 

 their particles, therefore the distance 

 is wholly the effect of heat, and that 

 if we could entirely exhaust the body 

 of its heat, the particles would be in 

 complete contact. This is no more 

 than a guess, and of the most hazard- 

 ous 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 cannot judge 

 whether the contraction of the dis- 

 tance does or does not follow the 

 diminution of the quantity of heat 

 according to such a numerical rela- 

 tion that 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 contem- 

 plated in the first law of motion, 

 viz. that all bodies in motion con- 

 tinue to move in a straight line with 

 uniform velocity until acted upon by 

 some new force. This assertion is in 

 open opposition to first appearances ; 

 all terrestrial objects, when in motion, 

 gradually abate their velocity and 

 at last stop ; which accordingly the 

 ancients, with their inductio per enu- 

 mcrationem simplicem, imagined to be 

 the law. Every moving body, how- 

 ever, encounters various obstacles, as 

 friction, the resistance of the atmos- 

 phere, &c., which 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 inquired into? If the ob- 

 stacles could have been entirely re- 

 moved, the case would have been 

 amenable to the Method of Differ- 

 ence. They could not be removed, 

 they could only be diminished, and 

 the case therefore admitted only of 



the Method of Concomitant Varia- 

 tions. This accordingly being em- 

 ployed, it was found that every dimi- 

 nution 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 conse- 

 quent were known, it was practicable 

 to estimate, with an approach to ac- 

 curacy, both the amount of the re- 

 tardation 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 

 towards annihilation, as the cause 

 was. The simple oscillation of a 

 weight suspended from a fixed point, 

 and moved a little out of the perpen- 

 dicular, which in ordinary circum- 

 stances lasts but a few minutes, was 

 prolonged in Borda's experiments to 

 more than thirty hours, by diminish- 

 ing 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 hesi- 

 tation in assigning the whole of the 

 retardation of motion to the influence 

 of the obstacles ; and since, after sub- 

 ducting 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 there- 

 fore of which we have no direct ex- 

 perience, some counteracting cause 

 might develop itself ; either a new 

 agent, or a new property of the agents 

 concerned, which lies dorn\ant in the 

 circumstances we are able to observe. 

 This is an element of uncertainty 

 which enters largely into all our pre- 



