192 THE PRINCIPLES OF SCIENCE. 



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 more 

 generally from the theory of gravitation, there could be 

 no doubt that atmospheric tides of some amount, depend- 

 ing on the apparent heights of the sun and the moon, 

 must occur in the atmosphere. Theory, however, even in 

 the hands of Laplace, was not able to overcome the com- 

 plicated mechanical conditions of the atmosphere, and 

 predict the amount 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, it was easy to make series of baro- 

 metrical observations in places selected so as to be as free 

 as possible from casual fluctuations, and then by the suit- 

 able application of the method of means to detect the 

 small effects in question. The principal lunar atmospheric 

 tide was thus proved to amount to between "003 and 

 004 inch a . 



Theory, in fact, yields the greatest possible assistance in 

 applying the method of means. For if we have a great 

 number of empirical measurements, each representing the 

 joint effect of a number of causes, our object will be to 



n Grant's ' History of Physical Astronomy,' p. 162. 



