﻿426 Sir W. Thomson on Approach caused by Vibration. 



Nov. 23, 1870. 



Dear Sir, — The repulsion of a hydrogen balloon observed by 

 Shellbach, of which you tell me in your letter of the 16th inst., 

 is temptingly suggestive of the conclusion you tell me he has 

 drawn, that there is attraction or repulsion accordingly as the 

 density of the interior gas is greater or less than that of the 

 surrounding air. There are, no doubt, curiously close analo- 

 gies between some of the circumstances of motion in contiguous 

 fluids of different densities and the distribution of magnetic 

 force in a field occupied by substances of different inductive ca- 

 pacities. Thus, if in a great space occupied by frictionless in- 

 compressible liquid denser in some portions than in others, a 

 solid be suddenly set in motion, the lines of the fluid motion 

 first generated agree perfectly with the permanent lines of mag- 

 netic force in a correspondingly heterogeneous medium under 

 the influence of a bar-magnet, to be substituted for the move- 

 able solid and placed with its magnetic axis in the line of the 

 solid's motion. As to amounts, the fluid velocity multiplied 

 into the density is simply equal to the resultant magnetic 

 force at each point, if the particular definition of resultant 

 magnetic force in a medium of heterogeneous inductive capa- 

 city, given in the footnote to § 48 of my paper on the u Ma- 

 thematical Theory of Magnetism"*, be adopted. But here the 

 analogy ends ; the rigidity in virtue of which a solid moveable 

 in a fluid medium differing from it in magnetic inductive capa- 

 city keeps its form, does not exist in the hydrokinetic analogue. 

 If a quasi-rigidity be given to a globe of lighter fluid, as a hy- 

 drogen soap-bubble, by the tension of a containing film, or to a 

 hydrogen balloon by the stiffness and tension of the containing 

 membrane, the circumstances become so complex that no general 

 dictum can be readily pronounced regarding the resulting force 

 from the abstract dynamical theory. It is certain that if the 

 tension of the containing film were sufficiently great even with- 

 out rigidity, or if the containing membrane were sufficiently 

 stiff by rigidity, as a thin shell of solid, the balloon would be 

 attracted as a perfectly rigid globe quite irrespectively of the 

 density of its contents. 



But it seems, from Shellbacks results, that the membrane of 

 the hydrogen balloon may have stiffness enough to keep the 

 figure very approximately spherical., but yet not too much to 

 allow the smaller density within to exercise its influence and to 

 give attraction instead of repulsion f. The question is highly 



* Philosophical Transactions, June 21, 1849. Published in Part I. for 

 1851. 



f [Note added 13th April, 1871.] The details of Schellbach's experi- 

 ments described in the preceding article, which were unknown to me when 



