452 THE PEINCIPLES OF SCIENCE. [CHAP. 



passage across the meridian. Kepler and Descartes too 

 admitted the connection previous to Newton's demonstra- 

 tion of its precise nature. When Bradley discovered the 

 apparent motion of the stars arising from the aberration 

 of light, he was soon able to attribute it to the earth's 

 annual motion, because it went through its phases in a 

 year. 



The most beautiful instance of induction concerning 

 periodic changes which can be cited, is the discovery of 

 an eleven-year period in various meteorological pheno- 

 mena. It would be difficult to mention any two things 

 apparently more disconnected than the spots upon the 

 sun and auroras. As long ago as 1826, Schwabe com- 

 menced a regular series of observations of the spots upon 

 the sun, which has been continued to the present time, 

 and he was able to show that at intervals of about 

 eleven years the spots increased much in size and number. 

 Hardly was this discovery made known, when Lamont 

 pointed out a nearly equal period of variation in the 

 declination of the magnetic " sedle. Magnetic storms or 

 sudden disturbances of the needle were next shown to 

 take place most frequently at the times when sun-spots 

 were prevalent, and as auroras are generally coincident 

 with magnetic storms, these phenomena were brought 

 into the cycle. It has since been shown by Professor 

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

 of the earth's surface as indicated by sunken thermome- 

 ters 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 detected in all 

 meteorological phenomena. 



Integrated Variations. 



In considering the various modes in which one effect 

 may depend upon another, we must set 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 



