ON SOLAR RADIATION. 37 



degrees per second, and qO the rate of fall of temperature at any excess 6 

 if the radiation were cut off, we have evidently the equation 



dd/dt=r-qti (1) 



the solution of which under the given initial conditions is 



e={l-e-'^>)rlq (2) 



The limiting steady temperature of the disc when t is infinite is 6°=r/q. 



In 1893 some experiments were recorded verifying the elementary 

 theory and the constancy of the coefficient of cooling q. In 1896 a 

 photographic recording device was applied to obtain the curves of heating 

 of the disc by registering the deflections of the D'Arsonval galvanometer 

 on a moving photographic plate. The curves proved to be approximately 

 logarithmic, but the reduction of the results to absolute measure was not 

 attempted. 



Absolute Measurements. — If I be the intensity of radiation to be 

 measured in watts per square centimetre, and A be the area in square 

 centimetres normal to the rays over which the measured portion of the 

 radiation is incident, the quantity of heat received is lA joules per second. 

 This is equal to rSms, where r as already defined is the initial rate of rise 

 of temperature of the disc when exposed to the radiation, J is the number 

 of joules in one calorie, which may be taken as approximately 4"18 ; m is 

 the mass, and s the specific heat of the disc. In applying this method it is 

 tacitly assumed that the whole of the disc is at a uniform temperature at 

 any moment during the rise of temperature ; it is also necessary to know 

 accurately the specific heat s of the material of the disc, and to be able 

 to calibrate the thermo-junction so as to interpret the indications of the 

 galvanometer in degrees of temperature. Further, the rise of temperature 

 must not exceed two or three degrees in order that q, the coefficient of 

 cooling, may be taken as constant, and the rate of rise must be sufficiently 

 slow to jDermit of accurate measurement, and of the uniform diffusion of 

 heat throughout the disc. 



After some preliminary experiments with the apparatus it became 

 evident that these conditions were not sufficiently satisfied by the disc 

 and thermo-junction employed in the experiments already recorded. The 

 disc was about two centimetres in diameter and half a millimetre thick. 

 The aperture for admitting the radiation was about one centimetre. 

 Under these conditions it was not possible without the use of lenses to 

 ensure a sufficiently uniform distribution of the radiation over the surface 

 of the disc, and the rate of rise of temperature was too rapid for accurate 

 measurement. The disc was supported on a short iron wire nearly 

 two millimetres thick, which conducted heat away from the centre of the 

 disc so rapidly that the temperature of the junction was always very con- 

 siderably below that of the disc. Owing to its form the thermo-junction 

 could not be accurately calibrated, and the sensitiveness of the copper-iron 

 couple, though suitable for powerful sources such as direct solar radiation, 

 was far too small for accurate work with sources of constant intensity 

 such as were required for absolute measurement. 



The Galvanometer supplied with the instrument was of the Ayrton 

 Mather type, with a resistance of about 7 '5 ohms, and gave a deflection of 

 about 2 millimetres at 1 metre per microvolt, equivalent to about 

 20 millimetres per degree with a copper-iron junction. In orcler to 



