VII] OF SACHS'S RULE 297 



(2) The three surfaces may be all alike: as when a soap- 

 bubble floats upon soapy water, or when two soap-bubbles are 

 joined together, on either side of a partition-film. In this case, 

 the three tensions are all equal, and therefore the three angles 

 are all equal ; that is to say, when three similar liquid surfaces 

 meet together, they always do so at an angle of 120°. Whether 

 our two conjoined soap-bubbles be equal or unequal, this is still 

 the invariable rule ; because the specific tension of a particular 

 surface is unaffected by any changes of magnitude or form. 



(3) If two only of the surfaces be ahke, then two of the 

 angles will be alike, and the other will be unlike; and this last 

 will be the difference between 360° and the sum of the other two. 

 A particular case is when a film is stretched between solid and 

 parallel walls, like a soap-film within a cylindrical tube. Here, so 

 long as there is no external pressure applied to either side, so long 

 as both ends of the tube are open or closed, the angles on either 

 side of the film will be equal, that is to say the film will set itself 

 at right angles to the sides. 



Many years ago Sachs laid it down as a principle, which has 

 become celebrated in botany under the name of Sachs's Rule, 

 that one cell- wall always tends to set itself at right angles to another 

 cell-wall. This rule applies to the case which we have just illus- 

 trated; and such validity as the rule possesses is due to the fact 

 that among plant-tissues it very frequently happens that one 

 cell-wall has become solid and rigid before another and later 

 partition-wall is developed in connection with it. 



(4) There is another important principle which arises not out 

 of our equations but out of the general considerations by which 

 we were led to them. We have seen that, at and near the point 

 of contact between our several surfaces, there is a continued 

 balance of forces, carried, so to speak, across the interval; in 

 other words, there is physical continuity between one surface and 

 another. It follows necessarily from this that the surfaces merge 

 one iiito another by a continuous curve. Whatever be the form 

 of our surfaces and whatever the angle between them, this small 

 intervening surface, approximately spherical, is always there to 

 bridge over the line of contact* ; and this little fillet, or " bourrelet," 



* The presence of this httle liquid '"bourrelet," drawn from tlie material of which 



