178 DISCOURSE ON THE STUDY 



to the condensation of air, while yet we have the 

 strongest analogies to show that long before it had 

 reached any very enormous pitch the air would be 

 reduced into a liquid, and even, perhaps, if pressed 

 yet more violently, into a solid form. 



(187.) Laws thus derived, by the direct process 

 of including in mathematical formulae the results 

 of a greater or less number of measurements, are 

 called " empirical laws." A good example of such 

 a law is that given by Dr. Young (Phil. Trans. 1826,) 

 for the decrement of life, or the law of mortality. 

 Empirical laws in this state are evidently unverified 

 inductions, and are to be received and reasoned on 

 with the utmost reserve. No confidence can ever 

 be placed in them beyond the limits of the data from 

 which they are derived ; and even within those li- 

 mits they require a special and severe scrutiny to 

 examine how nearly they do represent the observed 

 facts ; that is to say, whether, in the comparison of 

 their results with the observed quantities, the dif- 

 ferences are such as may fairly be attributed to error 

 of observation. When so carefully examined, they 

 become, however, most valuable; and frequently, 

 when afterwards verified theoretically by a deduc- 

 tive process (as will be explained in our next chap- 

 ter), turn out to be rigorous laws of nature, and afford 

 the noblest and most convincing supports of which 

 theories themselves are susceptible. The finest 

 instances of this kind are the great laws of the 

 planetary motions deduced by Kepler, entirely from 

 a comparison of observations with each other, with 

 no assistance from theory. These laws, viz. that 

 the planets move in ellipses round the sun; that 



