28 THE UNIVERSITY SCIENCE BULLETIN. 



(a) In Professor Schuster's discussion of the periodogram (6) 

 method of searching for periods we find the following: "There is a 

 limit beyond which it is useless to go. This limit is reached when the 

 values of A and B for two closely adjoining values n^ and n, are 

 no longer independent of each other. The theory of vibration shows 

 that independence begins when there is an ultimate disagreement of 

 phase amounting to about one-quarter of a period." 



(5) Professor Turner has worked out the effects of any period on 

 adjoining periods (86). He divides the data into integral parts and 

 calls any one of these submultiples q; p is a period near q, such that 

 q-\-x^p.x<l. From the Fourier sequence the periods q and q-^-l 

 are independent. Let us consider the seasonal period as q and the 

 ninth harmonic of the sun-spot period as p. In order that x may be 

 as small as 1, we must have q=3. That x be less, requires q^=2. But, 

 quoting Professor Turner, ''q is a fairly large integer for any peri- 

 odicity worth serious consideration." 



(c) The work involved in computing the periods near 12 months 

 for each state is much greater than the value of the results. , I have, 

 however, taken Pennsylvania as typical of the United States and 

 computed periods of 12, 13, 14, 15 and 16 months. 



For 12 months, which is the seasonal period, the amplitude of the 

 variation is 34 per cent; for 13 months it is 11 per cent; for 14 

 months it is 12 per cent; for 15 months it is 10 per cent; and for 

 16 months it is 17 per cent; the amplitude of the ninth harmonic of 

 the sun-spot period is 26 per cent. The mean value of the ninth 

 harmonic during this interval of years was 15.8 months, showing 

 the increase in amplitude at the nearest of the other periods as de- 

 manded by the theory or the periodogram (6) or by the Fourier 

 sequence (8c). 



A serious source of weakness in the state averages published by 

 the United States Weather Bureau and by almost every other 

 meteorological service developed during this investigation. This 

 may well be illustrated by the state of Washington as a fair sample. 

 Within one year the number of stations used in the state average 

 varied between 105 and 130. Over a number of years the range is 

 larger. The eastern part of the state is very much drier than the 

 western. If one is comparing two months' rainfall it becomes im- 

 perative that he know what stations were omitted each month. The 

 month showing the greater fall may be below normal and that show- 

 ing less may be above because of omission of eastern stations in the 

 first and western in the latter. I realize that it is impossible to ob- 



