The Astronomer Royal's Reply to Professor Challis. 143 



according to the quantity of steam contained in it, and the 

 condensing power of the elevation to which it should be raised. 

 In this part of the world cumuli generally come from the 

 westward, because the winds from that quarter are more fully 

 charged with steam than those from any other quarter. But 

 they may be sometimes seen coming from the eastward over 

 the Yorkshire hills, and these may have originated either in 

 the elevating power of the sun, or of the hills. The passage 

 of small cumuli across the heavens does not produce a sensi- 

 ble effect on the barometer. An alteration may be observed 

 in the flatness of the top of the mercury when one of consi- 

 derable size has been passing. Very large ones, 'dark at the 

 under side, sometimes lower the mercury a little; but it seems 

 to require one of great extent sufficient to cover the horizon, 

 to cause a decided fall in the barometer. 



XXIV. Reply to Prof. Challis, on the Investigation of the Re- 

 sistance of the Air to an Oscillating Sphere. By G. B. Airy, 

 Esq., Astronomer Royal. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



t DID not intend to trouble you again on the subject of dis- 

 ■*• cussion between Professor Challis and myself. But the 

 remarks of my esteemed friend, in his communication to your 

 July Number, have tended so much to confuse the matter, and 

 some of the doctrines which he has brought forward are (if I 

 understand them rightly) so dangerous to the purity of ma- 

 thematical reasoning, that I must crave your permission to 

 place this series of remarks in your Journal. T promise that 

 I will not occupy any more of your valuable space by con- 

 tinuing this discussion. 



On the new equations discovered by Professor Challis as 

 having claims for consideration, and marked by him (2.), (4-.), 

 (5.), page 65, 1 have only to remark, that I certainly supposed 

 every person who knows anything of partial differentials (Pro- 

 fessor Challis and myself included) to be fully aware that 



fi,fi i 



where there are n independent variables there are — '— 



such equations. But Professor Challis's language seems to 



imply that he is hardly aware that n— I of the equations are 

 sufficient for nearly every purpose, and that they do contain 

 absolutely and completely all the equations of the next order 

 involving different independent variables in each differentia- 



