Intelligence and Miscellaneous Articles. 379 



the Seine valley comes next (pp. 16-25) ; then London and the 

 Thames (pp. 25-32) ; Brussels and the Senne (pp. 32-41) ; Berlin 

 and the Spree (pp. 42-53) ; St. Petersburg and the Neva (pp. 53- 

 59) ; lastly, Rome and the Tiber (pp. 59-68). Transverse geological 

 sections of these valleys, and vertical sections of the deepest wells 

 and borings in the said cities, illustrate this admirably concise and 

 well-considered little book ; and the general remarks on these inter- 

 esting localities, and the special notes on their water-supply and 

 sanitary conditions, still further enhance the value of M. Karrer's 

 admirable work. We must add that the author supplies copious 

 references to authors and observers, and carefully acknowledges the 

 original sections and notes communicated by his many helpful friends. 



XL VIII. Intelligence and Miscellaneous Articles. 



THE SPONTANEOUS THINNING OF LIQUID FILMS. BY J. PLATEAU. 

 TN" my memoirs ' On the Figures of Equilibrium of a Liquid Mass 

 -*- without Weight,' and in my ' Statics of Liquids submitted to 

 Molecular Forces only,' I have from time to time insisted that the 

 gradual thinning of liquid films is due, entirely in certain cases, and 

 in great part in the rest, to the suction exerted by the small sur- 

 faces with strongly concave transverse curvatures which line the 

 margins of those films. Now, on considering the capillary pressures 

 in themselves, and starting from the principle that the pressure of 

 a plane or relatively but little curved excels that of a strongly con- 

 cave surface, one may ask if the gradual thinning does not consist 

 in this — that the two superficial layers of the film, by their excess 

 of pressure, press out from between them the interposed layer, 

 driving it towards the very concave portions, — or if the superficial 

 layers participate in this motion. To solve this question I have 

 had recourse to the following experiment. A plane film of gly- 

 cerine liquid was formed in a ring of iron wire of 7 centim. dia- 

 meter, supported by three feet, and quite horizontal. While it was 

 still colourless it was sprinkled with a light coat of lycopodium 

 powder ; it was then covered over with a glass bell, and was observed 

 while it was gradually being attenuated, which was ascertained by 

 the appearance and succession of the colours. Now, the lycopodium 

 was seen little by little to gain the margin; about half an hour after, 

 it had accumulated along the ring, and the film was clear of it. 



Thus, in the act of thinning, the superficial layers travel towards 

 the margins of the films ; but as these necessarily adhere to the 

 interposed layer, they could not move without dragging the latter. 

 It must, then, be admitted that the whole of the film partakes of 

 this motion, whether the action be exerted directly upon the super- 

 ficial layers only, or is exerted directly upon the interposed layer 

 also, or, lastly, only upon the latter. 



When the apparatus is not covered with a bell, the slight agita- 

 tions of the ambient air determine extensive irregular movements 

 in the film, which are manifested by the lycopodium. Let us say 

 further that, to distribute the lycopodium powder properly over 

 the film, a little of it is introduced into a small paper tube, and 

 blown into the air at a certain distance from the apparatus : the 

 powder then descends and deposits itself upon the film in a state 



