TRANSLATIONS AND SELECTED ARTICLES. 35 
-at right angles both to the plane of the area and of the path, the 
‘projection being always in the same sense.” 
Another theorem suggested by the above is this : 
“Tf the centre of gravity of a plane area move in a curve, the plane 
of which is perpendicular to that of the area, and the plane of the 
area is always inclined at the same angle to the path, the volume 
generated is equal to the product of the path and the projection of 
the area on a plane normal to the path at the point.” 
Another case to which the statement of Guldin’s property applies 
is,— 
“If a plane area move so that its centre of gravity describes a 
plane curve, to which the plane of the area is always normal, the 
-volume generated is equal to the product of the area and the path.” 
The area in this case must be limited to lie wholly on one side of 
the evolute of the path at each point. 
Another extension is the following : : 
“If a plane area revolve about an axis parallel to its plane, the 
volume generated is equal to the product of the path of its centre of 
“gravity, and the projection of the area on a plane passing through 
the axis and the centre of gravity.” 
Here also the limitation exists, that the area must lie wholly on one 
side of the plane drawn through the axis at right angles to the ne 
of the area. 
Similar extensions exist, mutatis mutandis, to the second of Guldin’ 8 
properties. Iam not aware that any of the preceding have been pre- 
- viously noticed. : 
TRANSLATIONS AND SELECTED ARTICLES. 
ON THE ORIGIN OF HAIL. 
An exceedingly elaborate and interesting article on this subject, 
from the pen of Frederick Mohr, has appeared in the September 
number of Poggendorff’s Annalen, and as that periodical is not often 
to be met with in this country, an abstract of the treatise may not 
be without interest to the readers of the Canadian Journal. 
The fall from'the heavens of massés of ice, sometimes nearly a 
