12 The Astronomer Royal on a supposed Failure of 



Atmospheric air Hydrogen Vacuum. 



The apparatus ,- — -* ~s 



contained. under a pressure of 1 atmosphere. 



Loose cotton 7-2° C* 11-0° C. 70° C. 



„ „ 7-7 11-0 



„ „ 7-5 11-0 7-0 



„ „ 7-5 7-1 



„ „ 6-0 



Eider-down 60 



After these results it cannot be doubted that hydrogen con- 

 ducts heat, and that in a higher degree than all other gases. 

 This is the more unexpected, since although the conductibility is 

 not directly dependent on the density of bodies (for example, pla- 

 tinum conducts worse than copper or silver), yet the metals, the 

 densest of all bodies, are the best conductors, and in general the 

 looser and less dense substances conduct worse than the denser 

 ones. If hydrogen exhibits in this respect a deviation, a new 

 proof is afforded of that similarity to the metals, so often main- 

 tained from its chemical relations. 



[To be continued.] 



II. On a supposed Failure of the Calculus of Variations. 

 By G. B. Airy, Esq., Astronomer Royalf. 



PROFESSOR JELLETT, in his comprehensive Treatise on 

 the Calculus of Variations, has alluded twice (pages 161 

 and 365) to the problem " To construct upon a given base A B 

 a curve such that the superficial area of the surface generated by 

 its revolution round A B may be given, and that its solid con- 

 tent may be a maximum/' The curve found by Professor Jel- 

 lett's treatment is a semicircle, and the solid therefore is a sphere. 

 On this he remarks, page 365, " The solution is not given by 

 the sphere, inasmuch as its superficial area is a determinate 

 function of AB [that is, supposing the sphere of the solution to 

 have its diameter equal to and coinciding with AB], and cannot 

 therefore be made equal to any other given quantity." And in 

 page 366 he concludes, " The method therefore fails altogether." 

 Mr. Todhunter has cited this solution and remark of Professor 

 Jellett, in his invaluable ' History of the Calculus of Variations/ 

 page 410. Mr. Todhunter points out the form of the solution 

 when the solid required has circular ends, but docs not allude 

 further to the case considered by Professor Jellett. And thus 

 the matter is left, as an apparent failure of the Calculus. 



* The temperatures are counted from 15° C. upwards, 

 t Communicated by the Author. 



