622 



NATURE 



[April 27, 1893 



In the summer months (May, June, and July) the temperature 

 curve during the day hours, from 8 a.m. to 8 p.m., hardly 

 differs from a curve of sines, the first component being more 

 than ten times as large as any of the others, which therefore 

 influence the temperature, relatively, very little. 



The relation of the epoch of the first maximum of the com- 

 ponent of the third order to the time of sunrise is decidedly 

 marked, the former occurring, on the average, about 12°, or 

 48m. after sunrise ; the mean deviation of the interval from that 

 amount being only 7", or 28m. 



The periodical variation in the position of the maximum leads, 

 during the winter months, to a positive maximum of this com- 

 ponent about I p.m., which is combined with negative maxima 

 four hours earlier and later, which correspond to the reduced 

 temperature in the mornings and afternoons of the shorter days. 

 In like manner, in the summer months, when this component 

 has a negative maximum about i p.m., instead of a negative 

 minimum, as in winter, there will be \.vio positive maxima, one 

 four hours earlier, the other four hours later, corresponding to the 

 higher temperature in the mornings and afternoons of the longer 

 days. 



It will be seen that thesepositionsof the midsummer and mid- 

 winter maximum phases correspond respectively to days of 16 

 hours with nights of 8 hours, or days of 8 hours and nights of 

 16 hours, and that at these seasons, when the variations of tem- 

 perature, due to these differences, are greatest, the amplitudes of 

 this component are also the greatest. At the equinoxes, with 

 l2hour days and nights, the component becomes a minimum ; 

 and at this season the change in the position of the maximum 

 takes place as already noticed. 



It might be supposed that an analogous relation between the 

 fourth component and the occurrence of days of 18 hours, com- 

 bined with nights of 6 hours, and vice versd, is likely to arise. 

 But the data are not forthcoming to test this. 



In the summer months the time of mean temperature is nearly 

 where the first component becomes zero, the second and third 

 components then balancing one another. 



In the winter the time of morning mean temperature is later 

 than in summer, and occurs when a positive value of the first 

 component is equal to a negative value of the second. 



The time of afternoon mean temperature throughout the year 

 is somewhat either before or after 7 p.m., and almost exactly 

 coincides with the time when the first and second components 

 are equal, with opposite signs. 



In the summer the time of absolute minimum is between the 

 hours of 3 a.m. and 6 a.m., during which the whole of the 

 components are negative. 



Sunrise in December is about an hour and a half before the 

 time of mean temperature ; while in June it is more than four 

 hours earlier. 



Sunset in December is rather more than three hours beforeihe 

 time of mean temperature ; in June it is about half an hoxxt after 

 that time. 



The rationale of some of the empirical rules for obtaining the 

 mean daily temperature from a limited number of observations 

 is supplied by reference to the harmonic expressions for the 

 hourly deviations of temperature from the mean value. 



In the first place, it will be seen that by adding together the 

 harmonic expressions for any two hours twelve hours apart, the 

 whole of the odd components disappear, and that the sum is 

 twice the mean value, added to twice the sum of the even com- 

 ponents of the selected hours, which are equal. 



By taking the mean of observations at any four hours, at 

 intervals of six hours, both the odd components and those of 

 the second order will disappear, and the result will only differ 

 from the true mean by the amount of the fourth component for 

 the selected hours. 



So, if the mean of any three hours at equal intervals of eight 

 hours be taken, the sums of the first, second, and fourth com- 

 ponents will disappear, and the result will only differ from the 

 true mean by the amount of the third component for the selected 

 hours, which in no case can be so much as |°. 



2. Temperature at the Seven Observatories. 



The examination of the tables will show that in their main 

 characteristics the results closely resemble those for Greenwich, 

 and it will not be necessary to discuss them in any detail. 



The amplitude of the component of the first order is, how- 

 ever, in all cases less than that observed at Greenwich, the 



lowest values being those for Valencia and Falmouth, no doubt 

 due to their position on the sea coast, for which stations the 

 means for the years are 2°'28 and 2°'35 compared with 5''io 

 at Greenwich. 



The Kew values most resemble those at Greenwich, but the 

 mean maximum at Kew is more than l° less, and the mean for 

 the year ^° less. 



The mean values of /u^ for the seven observatories lie be- 

 tween 205" and 220°, that for Greenwich being 214". The 

 means of the summer values are about 3" or 4" less than the 

 mean of the year, and of the winter values as much above it, 

 as in the case of Greenwich. 



The amplitude of the first component conforms approxi- 

 mately, but not so closely as at Greenwich, with the sine of 

 the sun's meridian altitude, but with a flattening of the curve 

 in the summer months, and a tendency at some of the stations 

 to a maximum value in May. 



The components of the second and third orders, beyond which 

 the analyis is not carried for these observatories, conform in all 

 important respects to those for Greenwich, the numerical val- 

 ues of the latter being, however, in all cases somewhat higher. 

 The epochs of maximum follow the same laws, with an increased 

 divergence of the summer epoch from that of the winter at the 

 more northern stations. 



In order to test, and in some degree throw light, on the char- 

 acter and significance of the harmonic components of temperature 

 that have been under discussion, and bearing in mind that they 

 cannot be considered to represent separate effects of physical 

 forces operating at the assumed periods of the components, I 

 have, at the suggestion of Prof. G. Darwin, calculated the 

 harmonic components from a curve representing an intermittent 

 heating action such as that of the sun, continued only during a 

 portion of the day, and commencing and ending abruptly at 

 sunrise and sunset. 



All cooling effects have been disregarded, and the sun's direct 

 heating action is assumed to be proportional to the sine of his 

 altitude, the power of a vertical sun being taken to be 10. Hav- 

 ing calculated the sun's altitude for each hour of the day, for 

 midwinter, the equinox, and midsummer, for certain selected 

 latitudes, the corresponding heating effects have been computed 

 to which the usual method of analysis has been applied. 



The comparison of the results thus obtained with the corre- 

 sponding components derived from actual observation at places 

 having nearly the same latitudes as those selected, establishes 

 their close similarity, and the conclusion is unavoidal)le, that, 

 although both in the actual and hypothetical cases the harmoni- 

 components when combined are truly representative of the pecu- 

 liar forms of the curves from which they were derived, this affords 

 no evidence of the existence of recurring cycles of action cor- 

 responding to the different components, but that the results are, 

 to a great extent, due to the form of the analysis. 



The diurnal curve of temperature is not symmetrical in rela- 

 tion to the mean value, the maximum day temperature being 

 much more in excess than the minimum night temperature is in 

 defect. To adjust the first component, which is symmetrical 

 about its mean value, to the actual unsymmetrical curve, it 

 must be modified by the other components. That of the second 

 order, which has one of its maxima not far removed from the 

 minimum of the first order, supplies the chief portion of the 

 compensation due to this cause. 



Further, from the character of the analysis, when the diurnal 

 curve is symmetrical on either side of the hour half way between 

 noon and midnight— that is, when the day and night are equal 

 in length— the third component becomes zero. Any departure 

 from this symmetry introduces a component of the third order, 

 with the result that with a day shorter than 12 hours one maxi- 

 mum will fall in the day between 6 a.m. and 6 p.m., and the 

 other two in the night between 6 p.m. and 6 a.m. ; while with 

 a day longer than 12 hours, two maxima will occur in the day 

 and only one in the night. In the former case the negative por- 

 tions of the component correspond with the reduced morning 

 and afternoon temperatures of the short day, and in the latter 

 the two positive phases correspond with the higher temperature 

 of the mornings and afternoons of the longer day. 



These conclusions are in conformity with those previously 

 indicated. 



The available data are insufficient to enable us to say whether 

 the corresponding results connected with the fourth component 

 are as fully supported by observation as in the case of the third, 

 but the facts so far as they go confirm this view. 



NO. 1226, VOL. 47] 



