METHOD OF VARIATIONS. 67 



Professor Piazzi Smyth and Mr. E. J. Stone, that the 

 temperature of the earth's surface as indicated by sunken 

 thermometers gives some evidence of a like period. The 

 existence of a periodic cause having once been established, 

 it is quite to be expected, according to the principle of 

 forced vibrations, that its influence will be more or less 

 considerable in all meteorological phenomena. 



Perhaps the most mysterious part of these investiga- 

 tions is that which refers the phenomena to the planetary 

 configurations as an ulterior cause. Professor Balfour 

 Stewart, with Messrs. Warren de la Kue and Loewy, 

 by laborious researches discovered a periodic change of 

 584 days in the sun spots, coincident with changes in the 

 relative positions of the Earth, Jupiter, and Venus. It 

 has since been rendered probable by the researches of 

 Dr. Kirk wood and others, that Schwabe's eleven -year 

 period is due to the action of Mercury. Several other 

 periods of more or less importance have been supposed to 

 exist, but the subject is yet open to much more inquiry. 



Integrated Variations. 



In considering the infinite variety of modes in which 

 one effect may depend upon another, we must set apart in 

 a distinct class those which arise from the accumulated 

 effects of a constantly acting cause. When water runs out 

 of a cistern, the velocity of motion depends, according to 

 Torricelli's theorem, on the height of the surface of the 

 water above the vent ; but the amount of water which 

 leaves the cistern in a given time depends upon the 

 aggregate result of that velocity, and is only to be 

 ascertained by the mathematical process of integration. 

 When one gravitating body falls towards another, the 

 force of gravity varies according to the inverse square 

 of the distance ; to obtain the velocity produced we 



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