THE FOUR EXrEHI.^IENTAL METHODS. iioO 



phrase) a function not of A alone but of A and something else : its 

 changes will be such as woukl occur if part of it remained constant, 

 or varied on some o.ber principle, and the remainder varied in some 

 numerical relation t,> the variations of A. In that case, when A dimin- 

 ishes, a will seem to approach not towards zero, but towards vsomc 

 other limit : and when the series of variations is siicli as to indicate 

 what that limit is, if constant, or the law of its vai'iation if variable, 

 the limit will exactly measure how much of a is the effect of some 

 other and independent cause, and the remainder will be the- effect of A 

 (or of the cause of A). - 



These conclusions,"^ however, must not be drawn, without certain 

 precautions. In the first place, the possibility of drav/ing them at all, 

 manifestly supposes that we are acquainted not only with the variations, 

 but with the absolute quantities, both of A and a. If we do not know 

 the total quantities, we cannot, of course, detei'mine 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 that 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 can never be more than a gu6Ss, and of 

 the most hazardous sort, not a legitimate induction; for since wc 

 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 distance does or does not follow the diminution of 

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

 quantities would vanish simultaneously. \ 



In contrast with this, let u-s consider a case in which the absolute 

 quantities 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 opposition to first appearances; all terrestrial object^;, when 

 in motion, gradually abate their velocity and at last stop ; which 

 accordingly the ancieiits, with their inductio per enumerationcm sim- 

 pliccm, imagined to be the law. Every moving body, however, 

 encounters various obstacles, as fi-iction, the resistance of the atmos- 

 phere, &c., which we know by daily experience to be causes capable 

 of destroying motion. It w^as suggested tlitit the whole of the retard- 

 ation might be owing to these causes. How was this inquii*ed into ? 

 If the obstacle^ could have been entirely retuoved, 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, 

 admitted only of the Method of Concomitant Variations. This accord- 

 ingly being employed, it was found that every diminution of the 

 obstacles diminished the retardation of the motion : and ina.s'much as 

 in this case (unlike the case of heat) the total quantitie's both of the 

 antecedent and of the consequent were known ; it was practicable to 

 estimate, with an approach to accuracy, both the amount of the retard"- 

 ation 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 fi-om a fixed point, and moved a little out of the 



