178 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. "JO 



VARIATIONS IN HEIGHT OF WATER IN THE LAKES AND RIVERS 



It has been found that the middle European rivers give an indica- 

 tion of somewhat higher level of water at the time of sun spot maxi- 

 mum than at sun spot minimum. The Nile shows also a well marked 

 maximum at the time of sun spot maximum. 



The director of the Swedish Hydrographic Bureau, Dr. Axel 

 Wallen, has, as already been stated, made valuable investigations on 

 the height of the water in the great Swedish lakes. He has analyzed 

 the periodic variations thoroughly and principally according to the 

 method of consecutive means which Schreiber (1896) critically dis- 

 cussed. In his investigation in Wenern (1910), Wallen proceeds 

 from the monthly means (the a- values). By consecutive means 

 over twelve months, the yearly period is estimated. Thus he 

 obtains b-values, which he finds give the average interval between 

 the successive maxima or minima of something over three years. 

 He found then c-values by successive means of forty b-values, 

 whereby the approximately three-year period is eliminated. In a 

 similar way he eliminates further possible periods of eleven and 

 thirty-five years. 



In order to study the single periods more accurately, Wallen com- 

 putes the difiFerences : a = a — b, /3=b — c, etc. He finds then for the 

 height of the water in Wenern a period of thirty-two to thirty-three 

 months with an amplitude of y6 centimeters (reduced). He also 

 finds a double period of about twelve years, which is the sun spot 

 period. Finally he discovers variations through a long series of 

 years with an indication of the Brijckner period. Concerning the 

 sun spot period in the water level, Wallen finds a principal mini- 

 mum nine months before the sun spot minimum and the prinicpal 

 maximum two and a half years after the sun spot maximum. There 

 is a weaker secondary maximum two years after the sun spot mini- 

 mum and a more marked secondary minimum one year before the 

 sun spot maximum. 



In combination with these investigations upon Wenern, Wallen 

 also studied the variations of precipitation and temperature in the 

 surroundings. He determined a sho'rt interval variation of twenty- 

 six months in the precipitation and of two years in the temperature. 

 The eleven-year period is divided for the precipitation about in the 

 same way as for the water level with the two amplitudes within the 

 eleven-year periods about equally great. In the three-year period 

 the extremes of the water level are approximately constant at a 

 half year after those of the precipitation. The temperature shows 



