3S2 Professor Sir James Dewar [Jan. 18, 



simply squeezino; the indiarnbber bulb quite flat, the nozzle havinir 

 already been dipped in soap solution, and the glass plate well- 

 moistened with solution. The single and double columns already 

 described may be shown in the same simple manner (Fig. 24). By 

 using the horizontal projection lantern these figures are plainly 

 shown on the screen. 



The forms taken by these clusters are governed by the conditions 

 for equilibrium of the surface tensions at the intersections of the 

 films. Not more than three films can meet in any one line, and if 

 they are planes they will be equally inclined to one another at angles 

 of 120°, while, if they are curved, then the law of equal inclinations 

 holds between the tangent planes at all points of contact. Taking 

 first the case of tAvo l)ubl)les which have coalesced into two segments 

 united by a circular plane film, the tangent planes at any point of 

 the line of contact of the curved surfaces will be inclined at 120' to 

 each other and to the circular plane. It follows that the radius of 



the plane central film is ^-2-of the radius of the two equal spherical 



segments, the distance between their centres of curvature being equal 

 to this radius, which is greater than the radius of the original separate 

 bubbles in the ratio of 4/4 : 1*5 or I'O : 0*9452. Therefore the 

 internal excess pressure (which is inversely as the radius of curvature) 

 is reduced 4 • 5 per cent, by the coalescence. Measurements made on 

 two bubbles gave under 5 per cent. 



Three spherical segments in contact are each approximately five- 

 sevenths of a whole sphere. The internal pressures therefore are 

 now reduced to the proportion of \/7 : 4/5 or 1 : 0-^i93o. Now 

 0-893o = (0'9452)^, so that the process appears to proceed by a 

 geometrical progression, each linkage reducing the internal pressures 

 in an equal proportion. 



Concentric Half Bubbles. 



An interesting application of the method of film formation by 

 regulated drops was made in order to obtain a group of concentric 

 hemispherical bubbles. It was desired to obtain them with a uniform 

 difference of radii of 1 cm. between successive film surfaces. They 

 were blown on the under side of the top glass plate of a smaller 

 cubical vessel (30 cm. length of edge). A special form of nozzle was 

 made with its rim flush with the surface on which the bubbles were 

 to be blown. The part containing the narrow neck was of ebonite, 

 and had a shoulder carefully fitted to the aperture in the glass plate. 

 The dropping funnel and glass blowing tube were fitted tightly into 

 the neck of the ebonite nozzle. Fig. 25 shows the arrangement 

 with a group of ten half Ijubbles, the horizontal lines indicating the 

 levels reached l)y black zones on the fourth day. 



