SURFACES OF DISCONTINUITY 



655 



of triangles is employed, viz., that the area of a triangle 

 whose sides are a, h, c in length is 



l[(a + 6 + c) (6 + c - a) (c + a - 6) (a + 6 - c)]K 



54' Consideration of the Case When the New Homogeneous Mass 

 is Bounded by Spherical Lunes 



To follow the reasoning in the last two paragraphs of this sub- 

 section (pp. 296, 297) one must visualize somehow the form of D in 



Fig. 9 



this case. First imagine (Fig. 9) a thread stretched between two 

 points I and m; mark two points between I and m on the thread 

 and call them di and c?2. The thread represents the original 

 line of discontinuity, and three surfaces B-C, C-A , A— Ball con- 

 taining the thread divide the space round the thread into three 

 portions, each of which contains one of the fluids^, B, C which 

 are supposed to be in equilibrium at these surfaces. Now 

 consider a plane drawn at right angles to the thread with 

 di and c?2 lying on opposite sides of it. Let the thread cut the 



