70 



MR. GEORGE C. SIMPSON ON THE 



are given : one each for the winter, spring, summer, and autumn three months and 

 another for the year taken as a whole (fig. 3). It will at once be seen that the two 



A.M. 



11 12 1 

 MID-DAY. 



Fig. 3. 



10 11 12 



curves for the winter and spring lie entirely above the curve for the year and those 

 for the autumn and summer entirely below. 

 The equations to the five curves are* : 



Winter three months, P = 180 + 64 sin (0+189) + 26 sin (20+155) + 4 sin (30+200), 

 Spring P = 177 + 57 sin (0+176) + 37 sin (20+ 151) + 13 sin (30+ 195), 



Summer P = 97 + 16 sin (0+141)+ 9 sin (2(9+144)+ 4 sin (3(9+ 126), 



Autumn P = 103 + 23 sin (0+170)+19 sin (20+184)+ 2 sin (30+131), 



Whole year . . . . P = 139 + 39 sin (0+177) + 23 sin (20+158)+ 5 sin (30+178). 



From these equations we see that there are two periods which must be taken into 

 account ; the amplitude of the third period falls without the limits of the accuracy of 

 the instrument. Of these, the greater is a whole-day period and the lesser a half- 

 day period. We also see that the phase of the main period undergoes a regular shift 

 from a maximum in the winter to a minimum in the summer, which means that the 

 evening maximum is earlier in the winter than the summer, thus following the sun. 

 The phase of the second period does not vary regularly, and on account of its 



* These equations are worked out to mean local time, taking 12 o'clock midnight as the zero and 15 to 

 represent an hour. All other time used in this paper is mid-European, which is 42 minutes behind mean 

 local time. 



