1824.] Mr. Powell on Solar Light and Heat. 85 



the bulb (as before) = 0-45 inch ; the diameter of the section 

 near the focus = d, = 0*3 inch ; its square -09. 



In order to obtain the true ratio of the heating effects, we 

 have to apply the case of the formula (B). By experiment, we 



have - = - n : by measurement a, = •0706. 



r, 20 J 



And s = 6361 .*. s — a, = -5655. 

 Here also the case of the formula (C) applies, and we have 



^-^ = 2 ; thus on the whole since p = p x , and k= &, 

 /< ^ _ / 2 x -0706 __ \ i_ i_ J_ 

 h, ~ \ -5655 ~ j 4 ' 20 = " 80' 



Hence also we have for the intensities of light in the two 



cases, 



I <?,* j09 _ J_ 



f — "d 5 " ~~ VM ~ 87 * 



In obtaining this ratio, however, there are evidently several 

 sources of error ; the loss of many rays before they arrive at the 

 focus ; the less intensity towards the central part of the cone 

 (where the thermometer was placed), on these, and, perhaps, 

 other grounds, it would be necessary to reduce the ratio 

 obtained. 



The former ratio (as also in other instances) is subject to 

 some uncertainty, owing to the difficulty of observing accurately 

 the rise of the thermometer under the strong impression of focal 

 light ; but upon the whole it is evident that here also an equality 

 of ratio may be inferred as nearly as the nature of the operations 

 will allow. 



If there be an exterior heat about the focus, this should affect 

 the above ratio ; but since the proportion obtaining is very 

 close, we may infer that the ratio of the intensities of light is 

 really greater than that of the heating effects, but that the pro- 

 portion is preserved by the sum of the heating effect of the focal 

 light, together with the exterior heat. The above experiment 

 cannot be considered sufficient to enable us to determine such a 

 point, but I hope shortly to be able to give it a more complete 

 examination. 



(32.) In like manner we might proceed to compare the effects 

 of the rays in their natural diffuse state, and when brought to a 

 focus, if we had any tolerably accurate method of allowing for 

 the quantity of light lost in passing through the lens, and in not 

 converging accurately to the focus. The former datum might, 

 perhaps, be supplied from Sir W. Herschel's determination 

 (Phil. Trans. 1800), and the latter we might probably estimate 

 by successively diminishing the aperture till the focal effect on 

 the thermometer becomes diminished. The least aperture with 

 which it continues undiminished, compared with the whole, 

 would give nearly the proportion of rays brought to the focus. 



(33.) In the preceding instances we have compared the pro- 



