28 Wisconsin Academy of Sciences, Arts, and Letters . 
In the above table have been included all reports which have 
come under the eye of the writer, or have been communicated to 
him personally, in which the orientation of the fracture systems 
has been indicated, however crudely; and this entirely without 
reference to whether the results favor one theory more than an¬ 
other. One condition only has been imposed, namely, that the 
fracture systems described shall be made up of individual sur¬ 
faces that in steepness approach the vertical—are in general 
steeper than 70°—thus insuring that such tilting as may have 
occurred since their formation has not materially affected the 
plan of their arrangement. 
There are undoubtedly many districts in which no such regu¬ 
larity of arrangement of fracture series can be discovered, but it 
will generally be found that the planes of jointing or of veins or 
dikes, are many of them inclined at comparatively low angles to 
the horizontal. Even where this is not the case, the number of 
directions of joint planes may be so many that no law of ar¬ 
rangement is discernable; as might well be true when the belt 
of rocks has been subjected to successive deformation within the 
zone of fracture either from a single or from several directions. 
If we are to discover any laws governing the orientation of frac¬ 
ture systems, it will be by proceeding from the simple to the 
more complex areas, and there is ample ground for assuming that 
where belts of flat-lying, homogeneous rocks without pre-existing 
fracture planes are deformed within the zone of fracture, there 
is normally produced a vertical prismatic system composed of 
intersecting parallel series. Moreover, observations would ap¬ 
pear to show that even where rocks are far from homogeneous 
and lie in other than horizontal positions, an approximation to 
this result still obtains. While it has not as yet been demon¬ 
strated by experimentation, it is difficult to avoid the conclusion 
based upon field observation, that a second deformation of rocks 
which are already possessed of a simple prismatic system of 
joints through renewal of compression from the original direc¬ 
tion, in the main merely increases the number of series within the 
vertical joint system. 
It is certainly of much significance that the systems of frac¬ 
tures which are developed throughout the area of the United 
