of the Earths Atmosphere. 281 



together. Both sets of curves are inverted so that an increase 

 in the solar prominence frequency is followed by a decrease in 

 the annual temperatures of the Lake Regions of the United 

 States. 



It is not our purpose to discuss these problems here other 

 than as illustrating certain principles in the discussion of 

 departures and residuals in solar and meteorological data 

 derived from observations. Similar data, as stated, are being 

 collected in every branch of physics pertaining to the atmos- 

 pheres of the sun and the earth. In stellar and planetary 

 astronomy the problems of variations and departures, called 

 perturbations, are comparatively easy, because the effects of 

 the laws of gravitation are studied in rigid masses that can be 

 reduced to ideal points. In astrophysics and meteorology 

 these problems become enormously difficult, because the masses 

 are gases flowing in complex paths that cannot be traced 

 directly, as one follows a comet or a planet in the heavens, but 

 only indirectly in the accumulated effects of a general circula- 

 tion, and its local disturbances, that is in the barometric 

 pressures, the temperatures, the densities, and the velocities of 

 the atmosphere, at the numerous meteorological stations, these 

 being located only in the lowest stratum of the moving fluid. 

 The problem is so exceedingly difficult in itself that we may 

 fairly be permitted to employ such means of discussion as are 

 obviously suitable in order to avoid an inevitable failure in 

 reaching a valuable result. The problems of solar and ter- 

 restrial synchronism can be discussed by two general methods, 

 (1) a strictly rigid mathematical analysis, and (2) a statistical 

 method combined with an interpretation guided by graphic 

 traces. The former is preferred by some as applying definite 

 principles, and allowing no chance for accommodation by a 

 biassed judgment; the latter is preferred by many as the only 

 method for a first approximation to a clear understanding of 

 relations too complicated to be unravelled by any mathematics 

 now in existence. Some criticise the former method as allow- 

 ing no room for the practical judgment, and the latter method 

 is criticised by others as allowing too much room for the judg- 

 ment, especially on the part of those who seek a special result. 

 The truth seems to be that the former method is allowable for 

 the adjustment of the constants and terms of an equation 

 wherein the physical processes are already approximately 

 understood. The latter method is necessary and allowable in 

 those preliminary researches which seek to discover what the 

 law in question is, rather than in the refinement of it. The 

 first method always leads to zero-results in dealing with solar 

 and terrestrial phenomena. The latter offers some hope of 



