NO. 4 sun's variation and temperatures — ABBOT 9 



5. AMPLITUDES OF TEMPERATURE EFFECTS, AND PHASE 



SHIFTINGS 



Owing to the phase shif tings from year to year, just remarked upon, 

 it is necessary to allow for them when computing the true average 

 amplitudes of the temperature effects resulting from the 6.6456 cycle. 

 To do this, I plotted for each month of the year, and for all years from 

 1910 to 1945, the mean march of the temperature effect as determined 

 from the four or five recurrences of the cycle in the given month. 

 Such a graph, for the month of October only, is shown in figure 3. 

 From all the graphs I read off individually the positions in the 20-day 

 tabulations (such as that of table 2) when the three maxima of such 

 a tabulation occurred. Obtaining for these three places the mean of 

 all 36 years, I computed departures from these means for all the cases 

 individually. I found then the nearest integral measures, in days, of 

 the shifts required to bring all the tabulations to approximately iden- 

 tical phases from 1910 to 1945. To fix ideas I give, in table 3, the 

 calculations made of these mean shifts for the month of March. I 

 remark here that there is some uncertainty about these computed phase 

 shiftings. A shift forward by 3 days, for instance, is for my purposes 

 the same as a shift backward of 3I days. 



In table 4, using these mean shifts, I compute the mean marches 

 and amplitudes of the temperature departures for March, due to the 

 6.6456-day cycle. The lacunae in table 4 are due to the shifts made. 

 Owing to them, the extremities of the corresponding curves in figure 

 4 are only approximate, from —5 to —4, and from 13 to 14, From 

 — 3 to -I- 1 2 the curves show accurately the average effect, in March, 

 of the 6.6456-day period. The mean amplitude for March is 4?8 F., 

 but for individual years the mean amplitudes vary, in March, from 

 2° to 18° F. Smallest amplitudes occurred in March in the years 

 191 5, 1926, 1942, and 1944. Largest amplitudes occurred in March 

 in 1921, 1936, and 1943. The corresponding curves will be found in 

 figure 4. Similar tables to table 4 have been computed for all months 

 of the year from Washington temperature records. In figure 5 I give 

 the mean curves for all months, covering the years 191 o to 1945. The 

 reader perhaps is surprised that the mean curves do not certainly in- 

 dicate changes of phase from month to month. It might be expected 

 that the lag of temperature response to solar change would differ with 

 the season of the year. There is indeed a range of about 2 days in 

 the phases of the monthly curves shown in figure 5, but it is not quite 

 certain that this is not introduced mathematically in the correction of 

 phase differences, as shown in table 3. On the other hand there is a 

 very obviously real difference in the amplitudes of variation. The 



