R. FE. Browne—Becker’s Theory of Faulting. 353 
work, the accumulated effect will be a material translation of 
the sheet in the direction of rolling. 
tis easy to see that a result the same in character will be 
effected if there is substituted for the toothed cylinder, a cylin- 
der without teeth, the operation being continuous. 
If an edged ruler is applied and drawn from P, toward B the 
effect will depend upon the magnitude of the resistance which 
the sheet offers to the relative motion of the edge of the ruler. 
If the edge be sharp and this resistance greater than the frie- 
tional resistance between sheet and base, the result will be rela- 
tive rest of sheet and edge and slipping of the sheet upon the 
base. If, on the other hand, the edge be blunt and this resist- 
ance less than the frictional resistance between sheet and base, 
the ruler will slip on the surface of the sheet carrying the de- 
pression with it, and it is easily seen that the result will be the 
same in character as in the ease of the rolling cylinder. 
n rolling the cylinder from 
A to B the entire sheet will be 
mately equal to the full amount 
of extension which would result 
from distributing uniformly from A toward B weights of suff- 
cient magnitude to reduce the entire sheet to thickness ¢, 
In explaining the formation of the curved surface the weight 
used by Mr. Becker will be omitted, as it only serves to keep 
the sheets in contact. The cylinder will be substituted for the 
blunt edged rubber. It will scarcely be doubted that these 
changes are admissible and will not affect the general character 
of the curve formed. They are made in order to simplify the 
statements. : 
et fig. 5 represent an indefinite number of highly elastic 
and flexible sheets of paper, having their edges originally in 
the surface A B normal to the 
se upper surface MN. Ifcylinder 
R* is applied with pressure to 
the surface M N, this pressure 
will be transmitted normally to 
the curve of depression formed. 
The area of surface over which 
this pressure is distributed will 
rapidly increase—hence the di- 
minution in thickness of a sheet, 
due to compression, will decrease—with increase of the distance 
from the upper surface M N. If now the cylinder is rolled to 
1 * Let the length of the cylinder be greater than the width of the sheets, and 
et it be so placed that its axis is normal to the longer dimension of the sheets. 
