296 THE FOEMS OF TISSUES [ch. 



we determine the three angles of our triangle (Fig. 101), and we 

 therefore know the relative magnitudes of the three surface 

 tensions, which magnitudes are proportional to its sides; and 

 conversely, if we know the magnitudes, or relative magnitudes, 

 of the three sides of the triangle, we also know its angles, and these 

 determine the form of the section of the drop. It is scarcely- 

 necessary to mention that, since all points on the edge of the 

 drop are under similar conditions, one with another, the form of 

 the drop, as we look down upon it from above, must be circular, 

 and the whole drop must be a solid of revolution. 



The principle of the Triangle of Forces is expanded, as follows, 

 by an old seventeenth-century theorem, called Lami's Theorem : 

 "If three forces acting at a -point he in equilihrium, each force is 

 -proportional to the sine of the angle contained between the directions 

 of the other two.''^ That is to say 



P:Q:R: = sm QOR : sin FOR : sin POQ, 



P Q _ R^ 



®^ sin QOR ~ sin ROP ~ sin POQ ' 



And from this, in turn, we derive the equivalent formulae, by 

 which each force is expressed in terms of the other two, and of the 

 angle between them : 



P2 = ^2 + 2^2 + 2QR cos [QOR), etc. 



From this and the foregoing, we learn the following important 

 and useful deductions : 



(1) The three forces can only be in equilibrium when any one 

 of them is less than the sum of the other two : for otherwise, the 

 triangle is impossible. Now in the case of a drop of olive-oil 

 upon a clean water surface, the relative magnitudes of the three 

 tensions (at 15° C.) have been determined as follows: 



Water-air surface ... ... 75 



Oil-air surface ... ... ... 32 



Oil-water surface ... ... 21 



No triangle having sides of these relative magnitudes is possible ; 

 and no such drop therefore can remain in equilibrium. 



