84 Mr. Powell on Solar Light and Heat. [Aug. 



Let d = diameter of aperture, 



f = focal length of lens, No. 1. 

 And d',f, those of lens, No. 2. 

 I, and I', = the respective intensities of the rays collected in 

 the sun's image, or focal luminous disk. 

 Then we have 



I __ <ft./ a 



By measurement I found 



In Lens, No. 1, d = 3-25 in. .-. d* = 10-56, 

 /=7-5 •••/* = 56-25, 

 In Lens, No. 2, d' = 1-75 in. .-. d' a - = 3-06, 

 / = 3 .-./* = 9. 



TT I 10-56 x 9 95-04 ' 1 . 



HenCe F " 306 x 56-25 = Tfi^ = TTl ^^ 



If we admit the validity of certain experiments which seem t,o 

 prove the existence of an exterior heat surrounding the luminous 

 cone of rays, this would affect the bulb in each case by a small 

 quantity in addition to the direct effect of the light. But since 

 the total effect has been shown to be very closely in proportion 

 to the intensity of focal light, it would follow that this exterior 

 heat must be in extent, or in energy, exactly in the same pro- 

 portion, supposing its absolute value sufficiently great to produce 

 a perceptible effect. 



These experiments prove for the two particular intensities 

 under examination, that the proportion of heating to illuminating 

 intensity is closely maintained. It might be satisfactory to 

 extend the comparison with lenses of other powers, qualities, 

 &c. but as the above result is not of a nature which requires the 

 admission of any new principles, and agrees with what we should 

 be prepared to expect, I conceive it unnecessary at present to 

 carry the examination any further. 



(31.) With a similar object in view in some subsequent expe- 

 riments, I employed such a difference of intensity as is afforded 

 by two sections of the luminous cone formed by a lens, one 

 being made near the lens, and the other near the focus. 



In two such positions, one, at ±- inch from the lens, the 

 other near the focal point, or at about seven inches distance, the 

 thermometer, blackened as before, was placed successively. 

 The rise in 30 seconds was (mean of three trials), 



At ± inch from lens 2° = r 



Near focus 40 = r, 



To obtain the proportions of light in the two cases, I measured 

 the diameter of the luminous circle formed by the larger section 

 when the rays were intercepted by a plane at the distance of 

 one-quarter of an inch below the lens. The diameter was very 

 nearly 2-8 inches = d } whose square = 7*84 ; the diameter of 



