412 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



given for every ten days, since otherwise the diagram would be too 

 crowded with lines. 



However, I thought I must include the curves for April 1 and 

 September 28, although they would remain unused in connection 

 with the twenty-day interval beginning with January 1st, since 

 these are the dates which among those contained in Singer's table 

 seem to come nearest to the dates of the minimum and maximum 

 heat content of the ground. 



It is, moreover, quite possible that this condition is more pre- 

 cisely fulfille ;"1 on the 21st March and 2 2d September. I therefore 

 intentionally adhere strictly to the data available without under- 

 taking further numerical or graphical operations in order to avoid 

 giving the appearance of a greater accuracy than I can truly assume 

 it to have. 



The great symmetry shown by both the curves, and easily recog- 

 nized in fig. 58 by the crowding of the lines at the above given dates 

 is remarkable, in consideration of the non-artificial and direct 

 method of utilization of the data. 



A special explanation of fig. 58 is hardly necessary since the 

 scale of temperatures (Centigrade) is given below on the lower line 

 and the scale of depths in meters on either end. The short dotted 

 lines at either end give the depths in meters at which the ther- 

 mometers were placed ; therefore the intersection of the correspond- 

 ing prolonged horizontal lines with the curves gives the points that 

 were deduced from the observations. 



The dates for which the curves are drawn are given at the top 

 in Arabic numerals for the days and Roman numerals for the 

 months. 



As a contrast to the curve for Munich we give in fig. 59 the 

 tautochrone for Nukuss. 



This offers a special interest because this station situated on the 

 Amu Darja represents a region of remarkably great insolation and 

 radiation with very slight amount of precipitation. 



Moreover the series of observations is one of the very few that 

 give the material needed for the determination of the changes of 

 temperature in the very highest strata. 



However, the temperatures of these upper strata are in fact 

 deduced from only one year of observation, whilst the numbers for 

 the greater depths are the means of three years. 



This fact is remarkably shown in fig. 59 which is constructed 

 directly from the data published by Wild 17 without further interpo- 



