1896.] Mr Hargreaves, Distribution of Solar Radiation, etc. 69 



(3) Distribution of Solar Radiation, and its dependence on 

 Astronomical Elements. By R. Hargreaves, M.A., formerly 

 Fellow of St John's College. 



(Printed in full in Transactions, Vol. xvi.) 



{Abstract.) 



This investigation was undertaken with the object of providing 

 exact data for the discussion of the influence of changes in certain 

 astronomical elements on the distribution of solar radiation on the 

 surface of the earth. It is well known that secular changes of 

 climate, of such extent as to give rise to the terms Glacial and 

 Genial epochs, have been attributed by some authors to this 

 cause. In view therefore of the interest which this question 

 has for geologists and others, who might be repelled by the 

 mathematical analysis, this is preceded by a somewhat full 

 outline, and numerical results are given in connection with each 

 point. 



The paper begins with the expression of the amount of heat 

 due to the earth in any latitude, on the assumption of a dia- 

 thermanous atmosphere, by means of a harmonic series which is 

 carried numerically as far as the term with one quarter of a 

 year for period. Denoting by H/r* the amount of radiation on 

 unit-surface in unit-time exj)osed perpendicularly to the sun's 

 rays at distance r, the element of heat-supply is 



— r (L + Li sin 9 + L 2 cos 26 + X 4 cos 40 +...), 



6 being the orbital angle of the sun measured from the spring 

 equinox. 



If the orbit of the earth (or any other planet) was circular 

 6 would be proportional to mean time. The actual conversion 

 to mean time is given later, but various conclusions can be drawn 

 from the present form. The constant h is introduced by the 

 relation r 2 dd/dt = h; when a year is unit of time, its value is 2irab. 

 As the minor axis is dependent on eccentricity, but only varies 

 within very narrow limits, the effect of this general divisor is 

 very slight. The coefficients L , L,, Z 4 ... are functions of 

 latitude, and obliquity of the ecliptic, the same for both hemi- 

 spheres, expressed in finite terms by complete elliptic integrals 

 of the three kinds, and also in series of zonal harmonics. The 

 coefficient of the annual variation L l has the simple form 



7T . . 



— sm A, sin e, 



with opposite signs in the two hemispheres. 



