532 Mr Hargreaves, The Harmonic Expression of the 



The Harmonic Expression of the Daily Variation of Solar 

 Radiation, and the Annual Variation of its coefficients. By 

 R. Hargreaves, M.A., formerly Fellow of St John's College, 

 Cambridge. 



[Read 22 November 1897. Revised 1898.] 



A harmonic series, applied to express the intermittent daily 

 supply of heat from the Sun, consists of a series of terms with the 

 day, half-day, one-third of a day &c. as periods, and an opening 

 term on which the total supply for the day depends. Each 

 coefficient depends on the latitude of the place and on the Sun's 

 declination, and through the latter is subject to an annual 

 variation. 



This annual variation for the opening term was discussed 

 in a previous communication to the Society*. The present paper 

 contains the solution for the general case, and tables are appended 

 giving numerical values for latitudes up to 60°, at intervals 

 of 10°. 



A corresponding analysis of the daily variation of temperature, 

 and the yearly variation of its coefficients, will be found in a 

 volume published by the Meteorological Council, under the title 

 ' Harmonic Analysis of hourly observations of Air Temperature and 

 Pressure at British Observatories ' ; and an account of the method 

 and general results in a paper, bearing the same title, by 

 Lieutenant-General Strachey, published in the Transactions of 

 the Royal Society for 1893. I understand that this is practically 

 the only case in which the Harmonic Analyser has been applied 

 to the second stage, i.e. to express the annual variation of co- 

 efficients of the daily expansion. The preliminary comparisons 

 which I have made of these results of observation, with the 

 calculations of the present paper, are sufficiently promising to 

 justify a detailed study, should time permit. But the time and 

 labour required are very serious, and the reader who gives a 

 casual glance at the collection of numerical tables appended 

 here, will hardly realise the weeks of laborious calculation 

 involved. These tables, with explanations in sections 1 and 5, 

 are all that is needed for meteorological purposes. Section 3 

 gives a brief resume of properties of the coefficients, which in the 

 more general form of the mathematical problem, bear a curious 

 resemblance to the Associated Functions of Laplace. 



| 1. With a diathermanous atmosphere, the amount of solar 

 radiation reaching a unit area of the earth's surface, depends on 



* ' Distribution of Solar Radiation on the Surface of the Earth, and its depen- 

 dence on Astronomical Elements,' printed in Transactions, 1896. 



