ON THE INTENSITY OF SOLAR RADIATION. 163 



The values of q as determined by different trios did not come out so 

 closely accordant as the calculated final excesses, as might indeed have 

 been expected from the nature of the equations. Still they agreed in 

 showing that to satisfy the insolation observations the coefficient of cool- 

 ing q must be taken distinctly larger, in the ratio of about 5 to 4, than 

 when the thermometer cooled after exposure. When a beam of the rays 

 of the sun falls on the front face of the thermometer a portion of heat is 

 absorbed directly by the mercury under the place where the rays strike. 

 As mercury is opaque the portion thus warmed would in the first 

 instance form a thin stratum adjacent to the surface by which the rays 

 entered. Of course currents of convection would arise in the mercury, 

 and also the fluid metal would conduct the heat.. But if the heat thus 

 tends to get diffused, on the other hand there is a constant renewal of 

 the superficial heating. Now this specially heated stratum, however 

 thin, helps to raise the mean temperature of the surface, but contributes 

 comparatively little to the mean temperature of the mass ; in fact, if it 

 were infinitely thin it would contribute infinitely little. Now the rate of 

 cooling is determined by the average temperature of the surface taken 

 all round, whereas the indication of the thermometer is determined by 

 the average temperature of the whole mass of mercury. Hence the 

 mean temperature of the surface is greater than the mean temperature 

 of the mass ; and therefore, if the rate of cooling is supposed to be 

 determined by the temperature indicated by the thermometer, in other 

 words, to be what it would have been if there had been no such inequality 

 of temperature in different parts of the mass, we must to make up for it 

 take a larger coefficient of cooling. 



Hitherto a single series only of observations has been mentioned. 

 In fact, a considerable number of series were taken, but as the general 

 mode of treatment and the general character of the results are prettj^ 

 nearly the same throughout, it does not seem necessary to mention them 

 except when they were made for the special elucidation of particular 

 points. 



In the first sei-ies the diaphragm used with the lens was the larger 

 one, of ^/2-inch diameter. It seemed desirable to compare the results 

 obtained with this and with the smaller diaphragm of 1-inch diameter. 

 Accordingly, on a day when the sky was clear, series were taken with 

 the two diaphragms in succession. On reducing the results it was fouad 

 that the effect of radiation through the larger diaphragm was as nearly 

 as possible double that through the smaller. 



The object of the quartz plate was to prevent possible irregularities 

 arising from the action of wind, which, it was thought, might cause some 

 interchange between the air inside and outside the cube. It seemed 

 desirable to try the instrument with and without the quartz plate. 

 Comparative series were accordingly taken on a clear and not windy day 

 _with and without the quartz plate. The efl'ect was in round numbers 

 about 10 per cent, less with plate on than with plate off. When the 

 plate is used there is loss by reflection from the two surfaces, besides 

 which there may also conceivably be loss by absorption. The loss by 

 reflection can easily be calculated by Fresnel's formula for the intensity 

 of reflected light. If we disregard the double refraction, and take /x for 

 the refractive index answering to the mean of the heat rays incident, and 

 take account of the rays reflected an even number of times, as well as of 

 those which are not reflected at all, we have for the intensity of the 



