Proceedings of the Royal Society of Edinburgh. 185 



though but an abridgment of a larger one which the author had pre- 

 pared on the subject. Particular circumstances induced him to alter 

 the plan he had originally contemplated, and instead of a complete 

 development in detail of his researches and his views, he has only on 

 the present occasion giv^en so much of his results as were necessary 

 to bring the system of polar spherical co-ordinates to a state analo- 

 gous to that in which plane polar curves has long been stationary, 

 one point of the analogy excepted, viz. where the author has extend- 

 ed the method of treating tangents and normals, and the consequent 

 investigations dependent on these, by giving the polar equations of 

 those lines, instead of merely exa\nining the relation between the 

 radius-vector, and perpendicular upon the tangent. In a note the 

 equations of the tangent and normal, to plane curves, is given from 

 first principles ; and the analogy between plane and splierical curves 

 is shewn to be remarkably close. 



Amongst the properties of spherical curves, the following curious 

 one occurs. 



If the pole of a loxodrome to rhumb « be made the centre of 

 another equal sphere, the visual cone under which the loxodrome will 

 appear, will cut the second sphere (the eye being at centre of first 

 sphere) in a curve, whose equatorial subtangent is constant, and 

 equal to ec : and if conversely, the pole of the spherical logarithmic 

 (the equisubtangential curve just mentioned) be made the centre of 

 an equal sphere, the visual cone of this logarithmic, seen from the 

 centre of its own sphere, will cut the second sphere in a loxodrome 

 whose rhumb is equal to the subtangent of the logarithmic. 



The author expresses his intention of discussing in a separate 

 work the singular points of spherical curves, certain new systems of 

 co-ordinates, and other classes of research, which, on account of the 

 length to which they necessarily extend, were not adapted to the 

 Transactions of the Royal Society. 



3. Experiments and Observations on the Arterialization of 

 the Blood. By William Gregory^ M. D., F. R. S. E. 

 and W. J. Irvine, Esq. 



The object of these experiments was to ascertain some of the cir- 

 cumstances under which the blood changes in colour, from the dark 

 venous to the florid arterial hue. 



Dr Stevens first showed, that the venous clot deprived of its serum 

 by washing, remained dark even when in contact with oxygen ; and 

 that the addition of a saline solution caused it immediately to become 

 jRorid. He stated also, that a strong saline solution would cause thi§ 



