TRANSACTIONS OF SECTION A. 64 9 



On. the Expression of the Co-ordinate of a Point in terms of the Potential 

 anal Line of Force at the Point. 5y 'Professor W. M. Hicks, M.A. 



On the Pressure at a Point inside a Vortex-ring of Uniform Vorticity. 

 By Professor W. M. Hicks, M.A. 



9. Transformation of the Stereographic Equatorial Projection of a sphere 



by means of a certain form of the Peaucellier Cell. 



By Professor A. W. Phillips. 



The machine is made of bars of metal. A is a fixed point, B traces the original 

 projection, and C the new projection.: 



If the point A is fixed on the equator in the Stereof/raphic Equatorial Projection, 

 and B traces the meridians and parallels of this projection, then C will trace the- 

 meridians and parallels of the Stereographic Meridian Projection. 



(The proportions of the machine are made such that the projections of one 

 half of the sphere in the two pictures are contained in circles of the same size.) 



Outlixe of Machine. 



If the point A is fixed on the parallel of 6° south of the equator in the original 

 projection, and B traces the parallels and meridians as before, then C will trace the 

 parallels "and nmnchimS of the Stereographic Horizontal Projection, in which the 

 North Pole will he 6° from the Northern horizon. 



The above propositions are proved by transforming the equations of the parallels 

 and meridians in the original projection by means of the relation between p and p' 

 with respect to the fixed point A. The transformed equations agree with the 

 equations of these lines in the Meridian and Horizontal projections. 



10. A Geometrical Theorem in. connection with the Three-cusped Hypocycloid. 



By R. F. Davis. 



11. On the Discriminating Condition of Maxima and Minima in the 

 Calculus of Variations. By E. P. Culverwell, M.A. 



Jacobi's method of reducing 8 2 U = o"- /(.r, y,~, . . . —¥)(%« to limiting 



J \ d.v dx»J 



variations, alonjr with a term f 0'~— — -^ dx. where 6 depends on Sy and its 



° rd( d"<>\~\- - 



L \&\ 



differentials, is open to objection, not only because of its great length, but also as 

 it appears to assume that the first In differential coefficients of hy must be con- 



