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, 1 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. 



Memoir es presentes par divers Savants a V Academ ie Roy ale 

 des Sciences de rinstitut de France. Tome IX. (Sciences 

 Mathematiques et Physiques.) 



Memoires de V Academic Royale des Sciences de rinstitut 

 de France. Tome XIX. Presented by the Institute. 



On the Silurian Rocks and their Associates, in Parts of 

 Sweden. 



A brief Review of the Classification of the sedimentary 

 Rocks of Cornwall. By Sir Roderick I. Murcheson. Pre- 

 sented by the Author. 



