Rev. B. Powell's Remarks on a Statement by Dr. Thomson. 329 

 mum : but if it be not possible, it does. Thus if V = 



■■ - — ,— = : we find */ y — v.. . */ 1 + p l = c, and by 



means of this equation we can show that <P (x) is always po- 

 sitive whatever be the function u. Thus we can in this case 

 show analytically that we have obtained that relation between 



r x ' 

 x and y which renders / d xV a minimum; and in a simi- 



x ,i 



lar manner we can solve several other problems. The only 



case in which it is obvious that the general formula for 0' (*) 



cannot change its sign, is when the coefficients of w 2 u' 2 u"° 



&c, are all of them either positive or negative for all values 



of x between the limits of the integral. 



Lincoln's Inn, July 10th, 1830. 



XLIX. Remarks on a Passage in Dr. Thomson's " Outline of 

 the Sciences of Heat and Electricity " London, 1830. By the 

 Rev. B. Powell, M.A. F.R.S., Savilian Professor of Geo- 

 metry, Oxford.* 



N looking into the volume lately published by Dr. Thom- 

 son on Heat &c, my attention was immediately drawn to 

 the chapter on radiant heat, as being a subject on which I 

 have been particularly engaged. And I cannot but feel in- 

 debted to the distinguished author for the notice he has been 

 pleased to take of my researches on this subject: though at 

 the same time I trust he will allow me to make a few remarks 

 on the mode in which the mention of them is introduced. 

 The passage referred to is as follows : 



"The conclusions from the observations ofDela Roche 

 have been called in question by Mr. Powell. He admits 

 that when a hot body becomes luminous it gives out heat 

 capable of passing directly through transparent screens. But 

 this new heat acts more on a smooth black surface than on 

 an absorptive white one. From this he concludes, that it is 

 different from common radiant heat. We have no evidence 

 that it is the same as light. It is great from red-hot metals, 

 though the light be feeble. It exists in the solar rays, 

 and is what produces the photometrical effect in Leslie's 

 Photometer. But this ingenious explanation of Mr. Powell 

 has, I think, been obviated by a very happy and instructive 

 experiment of Mr. Ritchie," &c. &c. p. 156. Then follows a 

 description of Mr. Ritchie's experiments in detail. 



Now to a reader not previously acquainted with the sub- 



* Communicated by the Author. 

 N.S. Vol. 8. No. 47. Nov. 1830. 2 U ject, 



