4.46 INDUCTION. 



stances lasts but a few minutes, was prolonged in Borda's ex- 

 periments 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 

 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 velo- 

 city, 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 counteract- 

 ing 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 predictions of 

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

 Concomitant Variations. The uncertainty, however, of which 

 I am about to speak, is characteristic of that method ; espe- 

 cially in the cases in which the extreme limits of our observa- 

 tion are very narrow, in comparison with the possible variations 

 in the quantities of the phenomena. Any one who has the 

 slightest acquaintance with mathematics, is aware that very 

 different laws of variation may produce numerical results 

 which differ but slightly from one another within narrow 

 limits ; and it is often only when the absolute amounts of 

 variation are considerable, that the difference between the 

 results given by one law and by another becomes appreciable. 

 When, therefore, such variations in the quantity of the ante- 

 cedents as we have the means of observing, are small in com- 

 parison with the total quantities, there is much danger lest 

 we should mistake the numerical law, and be led to miscalcu- 

 late the variations which would take place beyond the limits ; a 

 miscalculation which would vitiate any conclusion respecting 



