244 



SCIENCE. 



[N. S. Vol. VII. No. 164. 



of a-half, a-third, etc., years, but these appear 

 to be less marked than the multiples of years. 



There are also weather periods which are 

 even multiples of days. The most marked of 

 these are 3, 4, 5 and 8 days. On account of 

 limited space I can only illustrate one period, 

 and because of accessible data I have selected 

 the 4-day period. Taking the observations of 

 temperature at 8 a. m. and 8 p. m., made at the 

 Blue Hill Meteorological Observatory during 

 1895, and obtaining the departures from the 

 normals, the residuals were classified into 4- 

 day periods. The means of each six periods 

 were then obtained and are given in the follow- 

 ing table : 



■jon- MEAN DEPARTURES IN DEGERES 



FAHRENHEIT. 



Jan. 20-Feb. 12 —3 —3 —1 +2 +3 +3 +2 —1 



Feb. 13-Mar. S +2+2 —1 —2 —1 +1 +2 



Mar. 9-April 1 +2 +2 +1 —1 —1 —1 — ] +1 



Apr. 2-AprU 25 +2 +1 —2 —2 —1 +1 +2 +3 



Apr. 26-May29 +3+1 —2—3 —3—1 +3+4 



May 30-June 12 +2 +3 +2 +1 —1 —2 —2 —1 



June 13-July 6 0+1 0—1 0+1 



July 7-July 30 0+1 +1 +1+1 



July 31-Aug. 23 0—10 0—1 0+1 



Aug. 24-Sept. 16 +3+1 0—2 —2—1 +1+2 



Sept. 17-Oct. 10 +2 +3 +2 —2 —2 —1 



Oct. 11-Nov. 3 +2 +3 +2 —1 —2 —2 



Nov. 4-Noy. 27 +2 +1 —1 —2 —1 +1 +2 +2 



Nov. 28-Dee. 21 +1 +3 +2 +1 —1 —2 —2 —1 



This table shows that throughout the year plus 

 departures are found on the first day of the 

 period, with but one exception ; while on the 

 third day, out of twenty-eight recorded means, 

 twenty-one were minus departures. This 

 period, has continued equally well marked and 

 mainly with the same phase during the last 

 three years. The range of temperature in the 

 period is about four degrees, while the mean 

 daily range of temperature from hourly records 

 at Blue Hill is about 10° F. Under certain 

 conditions there is a semi-diurnal oscillation in 

 the temperature (Annals of Harvard College 

 Observatory, Vol. 20, p. 123). 



One further illustration will be sufiicient, per- 

 haps, to show the universality of the harmonic 

 law. For this I have selected the 22-year or 

 double-sunspot period. Mr. R. C. Mossmann 

 gives a table in the Transactions of the Royal So- 

 ciety of Edinburgh, Vol. XXXIX., p. 187, show- 

 ing for Edinburgh the departures of tempera- 

 ture from normal, from 1764 to 1896, smoothed 

 by continuous five-year groups. These means 



show little or no trace of an eleven-year period, 

 but in Blr. Mossmann's plotted curve of the an- 

 nual means show six distinct waves of a length 

 of about 22 years. Thus the minima of the 

 waves occurred as follows : 



Observed Minima 1772 1781 1815 1838 1860 1879 

 22-year cycle 1771 1793 1815 1837 1859 1881 



With the exception of 1784 these dates differ 

 but little from that of an exact 22-year cycle, 

 and approximate very closely the dates of mini- 

 mum in the same cycle in New England, in 

 Iceland and in Paris {Nature, Vol. 51, p. 436). 

 The annual averages in Mr. Mossmann's table 

 were classified into six periods of 22 years, be- 

 ginning with 1766, and averages were obtained 

 from each year of the cycle. These, in tenths 

 of a degree Fahr. , are as follows : 



Year of cycle 1 2 3 4 5 6 7 8 9 10 11 

 Means +2 +3 +1 —1 —3 —6 —6 —5 —3 —1 +1 



Mean error + 57765454583 

 Year of cycle 12 13 14 15 16 17 18 19 20 21 22 

 Means +2 +3 +7 +5 +6 +6 +2 +1 +0 +1 +1 



Mean error± 334 2 1224353 



These means show a well marked period, and 

 at the epochs of maximum and minimum the 

 means are considerably larger than their mean 

 errors. At the time of maximum, between the 

 14th and 17th year of the period, the means are 

 nearly three times as large as their mean errors, 

 an unusually favorable showing in the case of a 

 meteorological cycle. Dr. Schreiber's curves of 

 the eleven-year period in rainfall, published in 

 the Abhandlung des Konigl. sachs. meteorolo- 

 gischen Institutes, Plate IV., show that the 

 eleven-year period at Dresden and Freiberg is 

 made up of two primary waves of nearly equal 

 magnitude and two secondary waves midway 

 between the primary. 



The harmonics in the case of periods of other 

 lengths were pointed out in the American 

 Journal of Science, Vol. XLVIII., p. 231. The 

 application of these weather cycles to forecast- 

 ing is interfered with : (1) by the multiplicity of 

 the cycles and their independent variations in 

 amplitude according to some unknown law ; 

 (2) the oscillations of the cycles (including the 

 annual and daily cycles) simultaneously in 

 different phases in different parts of the world 

 (see American Meteorological Journal, Vol. I., 

 p. 528) ; (3) the sudden inversion of the phase 



