XXT.] ACCORDANCE OF THEORIES. 553 



salts, &c., are useful in chemical manufactories, custom- 

 house gauging, &c. ; observations of rainfall are requisite 

 for questions of water supply ; the refractive index of 

 various kinds of glass must be known in making achro- 

 matic lenses ; but in all such cases the use made of the 

 measurements is not scientific but practical. It may be 

 asserted, that no number which remains isolated, and 

 uncompared by theory with other numbers, is of scientific 

 value. Having tried the tensile strength of a piece of iron 

 in a particular condition, we know what will be the strength 

 of the same kind of iron in a similar condition, provided 

 we can ever meet with that exact kind of iron again ; but 

 we cannot argue from piece to piece, nor lay down any laws 

 exactly connecting the strength of iron with the quantity 

 of its impurities. 



Quantities indicated by Theory, but Empirically Measured. 



In many cases we are able to foresee the existence of 

 a quantitative effect, on the ground of general principles, 

 but are unable, either from the want of numerical data, 

 or from the entire absence of any mathematical theory, to 

 assign the amount of such effect. We then have recourse 

 to direct experiment to determine its amount. Whether 

 we argued from the oceanic tides by analogy, or deduc- 

 tively from the theory of gravitation, there could be no 

 doubt that atmospheric tides of some amount must occur 

 in the atmosphere. Theory, however, even in the hands 

 of Laplace, was not able to overcome the complicated 

 mechanical conditions of the atmosphere, and predict the 

 amounts of such tides ; and, on the other hand, these 

 amounts were so small, and were so masked by far larger 

 undulations arising from the heating power of the sun, 

 and from other meteorological disturbances, that they 

 would probably have never been discovered by purely 

 empirical observations. Theory having, however, indi- 

 cated their existence and their periods, it was easy to 

 make series of barometrical observations in places selected 

 so as to be as free as possible from casual fluctuations, and 

 then, by the suitable application of the method of means, to 

 detect the small effects in question. The principal lunar 



