SECONDARY RUPTURES. 69 



t 



ideas a concrete form, suppose that a hot cube of homogeneous matter 

 were to be cooled from one side only, and that the cooled surface under- 

 went contraction. This contraction would produce tension throughout 

 the cooling surface, excepting at the edges, so that the surface would 

 assume the form of a very shallow dish, as illustrated in the following 

 diagram : 



Figure 12. — Contraction of il/ass cooling from one Side. 



Since the tension would be zero at the edge, it would clearly be greatest 

 at the center, and here rupture would take place in the surface film when 

 the tension reached the limiting value. The tension at the center might 

 he relieved by cracks of various characters. A single straight crack would 

 relieve it only in one direction, and would, in fact, tend to increase ten- 

 sion in the direction of the crack, because the crack must gape, and its 

 edges would therefore slightly exceed its median line in length. This 

 form of rupture is therefore impossible under symmetrical conditions. 

 The same objection applies to two cracks forming a letter T. Complete 

 relief at the center would be afforded either by an X _ shaped crack or by 

 one in the form of a Y- Of these, the latter has the smaller total length 

 for a given intersected area. Now, the cracks will clearly form in such a 

 manner as to afford the greatest amount of relief per unit length of crack, 

 and hence the rupture will take the shape of the letter Y- This will 

 afford total relief at the center and partial relief at surrounding points. 

 This relief, under symmetrical conditions, must be equally distributed, 

 and therefore the three cracks must make with one another angles of 

 120°. 



This simple inference is confirmed by observation. Thus, if one alb iws 

 a vessel containing melted wax to cool slowly, an excessively thin trans- 

 parent film forms on the surface. Then a minute opaque Y becomes 

 visible near the center. This is due to the cracking of the film and the 

 great acceleration of the process of solidification on the sharp exposed 

 edges. So, too, a slight blow on glass often produces cracks in the same 

 shape. Cracks in asphalt pavements frequently show a tendency to the 

 same form; so do those in drying mud, and many of the divisional sur- 

 faces in columnar lava meet one another at angles approaching 120°. 



As the coaling progresses the cracks must extend from the center; but 

 the longer they are the less is the relief which they afford in the circle 

 circumscribing their extremities and, unless the cooling area is small, 



