Sweden. 
505 
properties of surfaces of the second degree with three unequal 
axes. And accordingly (in the Philosophical Magazine for 
September, 1844), I have examined what are the results of 
that process, when the centre of the surface is made the origin 
of transformation, and in this way I have been led to discover 
the properties of two cylinders, remarkably related to the sur- 
faces of the second degree. 
«5. But, more generally still, we may transform those 
focal properties, placing the centre of our auxiliary sphere at 
any point of space ; and thus the following leading problem is 
suggested and solved : 
** Given any surface of the second degree, and a point any- 
where situated, to trace on the surface all the plane curves, 
which, viewed from the given point, shall appear to be circles. 
‘* The brief indications given in the present note will, of 
course, require large developments; and these, with the per- 
mission of the Academy, | shall endeavour to supply on some 
future occasion. My object in what I have now said has been 
merely to direct attention in a general way to several consider- 
able groups of the properties of curves and surfaces of the 
second degree, which may, with advantage, be studied as re- 
sults of the Polar Transformation.” 
DONATIONS. 
Mémoires présentés par divers Savants al Académie Royale 
des Sciences de l'Institut de France. Tome IX. (Sciences 
Mathématiques et Physiques.) 
_ Mémoires de l Académie Royale des Sciences de U Institut 
de France. Tome XIX. Presented by the Institute. 
On the Silurian Rocks and their Associates, in Parts of 
A brief Review of the Classification of the sedimentary 
. Rocks of Cornwall. By Sir Roderick I. Murcheson.  Pre- 
sented by the Author. 
