On the Spheroidal State of Water in Steam-boilers. 283 



In opposition to these views, it will perhaps be urged that a 

 satellite might be projected in such a manner that the eccentri- 

 city of the orbit it begins to describe would be different from 

 that given by the above theorem. But without mathematical 

 proof, which is altogether wanting, it cannot be asserted that 

 the orbit would retain that eccentricity under the influence of a 

 distui'bing force, or that there would be a mean motion either 

 of the radius-vector or of the apse. If such were the case, there 

 would seem to be no reason for the failure of the method of inte- 

 gration which was applied in the first instance to the equation (C). 

 In all probability, the motion in the case supposed would not 

 settle down to a permanent state till the eccentricity of the orbit 

 had reached the value which accords with the theorem. 



If any hesitation to admit the truth of the theorem be felt, 

 because none of the many eminent mathematicians who have 

 treated of the lunar theory have arrived at the same conclusion, 

 I may urge that by no previous method of investigation has the 

 motion of the moon's apse been found in a direct manner. The 

 indirect methods hitherto adopted to determine the motion of 

 the apse precluded the possibility of arriving at any determina- 

 tion of the value of the eccentricity. It appears to me that I 

 have indicated the initial steps of a new solution of the problem 

 of the moon's motion, which it might be worth the while of 

 those who have time for such researches to trace to its conse- 

 quences. 



Cambridge Observatory, 

 March 20, 1854. 



XLIII. On the Spheroidal State oflVater in Steam-boilers. 

 By A. Normandy, Esq. 

 To Dr. Tyndall, F.R.S. ^c. 



67 Judd Street, Brunswick Square, 

 Dear Sir, March 20, 1854. 



CONVINCED as I am that water frequently assumes the 

 spheroidal state in boilers, in consequence of which these 

 most important vessels, on which the very existence of the steam- 

 engine, that is, of most of the comforts of civilized life, depend, are 

 too often converted by mismanagement or ignorance into frighful 

 engines of death and destruction, I venture now to trouble you 

 with a few observations in addition to those which you were 

 kind enough to listen to the other day, in the hope that, should 

 the facts which I am about to relate appear to you as conclusive 

 as they do to me, you may be induced, in your lectures on heat, 

 to call once more the attention of the audience, should you deem 

 fit to do so, to this, I believe, fruitful but almost unsuspected, 

 or at any rate scarcely credited source of explosion. 

 U2 



