258 PROCEEDINGS : BOSTON SOCIETY NATURAL HISTORY. 
f 
deviations from the rule. Of this the Braintree train affords a good 
example. Considering only the fragments large enough to he 
represented in stone walls, I find it is possible to divide the portion 
of the train studied into four sections by lines normal to the axis 
of the train. In the first of these, which has, say, a width of two 
miles, an immense number of small boulders were found, with a few 
of large size, the average diameter being, perhaps, about ten inches. 
In the second section, the width of which I will assume to be about 
five miles, a great reduction in the number of boulders was noted, 
especially among those lying at the extremes of the range in size. 
The small fragments still predominate, however, bringing the aver¬ 
age down to some six or eight inches. The third section with a 
width of some ten miles shows a still more marked diminution in 
the number of boulders, but the size, instead of decreasing as before, 
seems to have increased, the average length now being a foot or 
more. In the fourth section which comprises the remainder of the 
train the decrease in the number of boulders should be less rapid. 
The average size, which reached its maximum in the preceding 
section, should again begin to decrease and continue with consider¬ 
able uniformity until the boulders finally disappear or reach the 
moraine. 
For an explanation we must again refer to the nature of the 
ledges. From their possession of a marked cleavage it is evident 
that by far the larger number of fragments would be small in size ; 
a considerable, but much smaller number, of medium size; while 
fragments of any considerable size would be rare. A ratio of 100 
of the smaller fragments to 20 of the medium and 1 of the large 
is by no means improbable. According to this ratio there would 
be in every 1000 boulders torn from the ledges 827 of the smaller 
size represented by x , 165 of medium size represented by k lx and 
8 of the larger size, varying perhaps from 3x to 5x, but represented 
on an average by 4x. The amount of loss by erosion will be assumed 
to be equal to the volume x for each arbitrary section passed over 
(not necessarily the sections referred to in the preceding paragraph). 
The effect will be as indicated below. 
Boulders of Sec. 1 : 
44 
4ft 
a 
2: 
<4 
a 
4 4 
Q . 
O . 
u 
u 
(4 
4: 
827 (x) +165 (2x) + 8(4x) 
165 ( x)+8(3x) 
8 (2x) 
8 ( x) 
Av. 1.19 
Av. 1.09 
Av. 2.00 
Av. 1.00 
