128 Prof. J. Plateau on the Figures of Equilibrium 



the particular composition of the linear function fq; and that 

 therefore we may write generally this Formula of Quaternion 

 Inversion, 



nf-^n'-nHf+n'"/*!-/ 8 (6) 



3. As it was in the Number of the Philosophical Magazine for 

 July 1844 that the first printed\ publication of the Quaternions 

 occurred (though a paper on them had been previously read to 

 the Royal Irish Academy in November 1843), I have thought 

 that the Editors of the Magazine might perhaps allow me thus 

 to put on record what seems to myself an important addition to 

 the theory, and that they may even allow me to add, in a Post- 

 script to this communication, so much as may convey a distinct 

 conception of the Method which I have pursued. 



Observatory of Trinity College, Dublin, 

 June 27, 1862. 



XIX. Experimental and Theoretical Researches concerning the 

 Figures of Equilibrium of a Liquid Mass without Weight. — 

 Sixth Series. By Professor J. Plateau*. 



Theory of the generation of liquid films. — Laws which regulate 

 systems of films — theory and experiments ; constitution of the 

 froth which forms on certain liquids. — Mods of generation of 

 systems of films. — Conditions under which the system of films 

 formed by a polyhedric skeleton is perfect, imperfect, or abortive. 



IN the present series of researches, I endeavour in the first 

 place to show that the development of liquid films is a 

 simple result of viscosity and cohesion, so far at least as the 

 mere fact of their development is concerned, without taking into 

 consideration the greater or less degree of facility with which it 

 occurs. I take an exceedingly simple example, namely, the he- 

 mispherical film produced at the surface of a liquid by an air- 

 bubble which has risen from the interior of the liquid mass. 

 The bubble cannot approach the surface except by forcing back, 

 in the direction of all the azimuths around its summit, the liquid 

 molecules situated above it ; and it is evident that the relative 

 displacement of the molecules must be so much the more rapid 

 in proportion as the summit of the bubble comes nearer to the 

 surface. But the viscosity of liquids offers to the relative dis- 

 placement of their molecules a resistance which increases rapidly 

 with the velocity of the displacement ; so that, when the distance 



* Translated, with the Author's corrections, from the Annales de Chimie 

 et de Physique, S. 3. vol. lxiv. p. 473 (April 1862), being an abstract of the 

 original Memoir published in the Memoires de VAcademie de Bruxelles, 

 vol. xxxiii. For abstracts of the previous series of researches see Phil. 

 Mag. October 1861, p. 286, note *. 



