320 NATURE OF CAPITAL AND INCOME [Cmap. XVII 
sive layers to the top, as seen in Figure 31. Here AB, 
the capital-value of the lowest layer, is the discounted 
value of the income from that layer, namely the teeth 
a, a, a”, but this income in turn is the discounted value 
of the income represented by the teeth intervening be- 
tween P and Q from the layer next above, and this income 
in turn is the discounted value of the income between P’ 
  
  
  
  
  
Fic. 31. 
and @ on the layer still above. In this representation 
the curves are shown as all terminating in the base line; 
but the representation may readily be extended to the case 
of an income infinitely continued. 
§9 
In Chapter XVI it was shown that certain modifications 
needed to be introduced into our theory of the determina- 
tion of capital-value when the element of uncertainty was 
introduced. We are fresh from the discussion of these, and 
they need no extended mention here. The main point to 
be kept in mind is that when the element of chance is 
taken into account, sudden breaks occur in the capital curve, 
so that instead of following the simple order previously 
indicated, beginning at zero and ending at zero, with inter- 
mediate teeth alternately rising and falling along the dis- 
count curve, it suffers additional interruptions at points 
where the estimates of future chances are changed. 
The most important point in the life history of such a