TRANSACTIONS OF SECTION A. 



64 J> 



mn 



'ling the 



7. Oil the E.t'pressi'ou nf fhe Cn-nrdinate «/ a roint in terms of the Totential 

 and Line of Force at the Point. 2/^ "Professor W. ^l. Hicks, M.A. 



8. On the PressKro at a Point insiile a Vortex-rivg of Uniform VoriicHij. 

 Bij Professor W. M. Hicks, M.A. 



0. Transformation of the Stereo'/raphic Ei/natorial Projection of a sphere 

 hy means of a certain form of the I'eancellier Cell, 

 jhj Professor A. AV. Phillips. 



Tbeniacliino is made of Lavs of niotal. A is a fixed point, B traces the original 

 ]irqji'clii)n, and C tiie new pvojection. 



If tile })oint A is fixed on tlie erjnator in the S'tereof/raj/hic Eqiiaforial Projection, 

 luid W traces the meridians and paraUcls of tliis projeclion, then V, will trace tin? 

 meridians and ])arallel3 of the Sti'rvofjrapJtic Meridian, Projection. 



{The proi)()rlioiis of the machine are made such that the projections of one 

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



Ouir.ISK (ll.- Al.\( HIXE. 



If the point A is fixed on the parallel of 6° .sonth of the equator in tin; original 

 projection, and V> traces the parallels and meridians as hefore, tiien (J will trace the 

 parallels and irteridihiis of the Stvrco(jraphic Horizontal Projection, in whicli the 

 North Pole will he 5° from the Northern horizon. 



The ahove propositions are proved hy transforming the equations of the parallels 

 and meridians in the original projection hy means of the relation hetween /) and p' 

 with respect to the fixed pomt A. Tlie transformed equations agree with the 

 expiations of these lines in the Meridian and Horizontal projections. 



PI A Geometrical Theorem in comiection n-ith the Three-cusped Ilyjwcijcluld, 



Pij R. ¥. Davis. 



11. On the Discriminating Gondii io^i >f Maxima and Minima in the 

 Calculus of Variations. By E. P. CuLVEinvKLL, J/..1. 



Jacobi's method of reducing 8''U = S-' /(.c, i/,''', • ■ . ' '^V'-' to limiting- 



J \ ' (i.c U.C"J 



variations, along with a term [ ^V-7r:7',7T-^~ ''•'> ^I'ere 6 depends on S// and its 



^ L \dx")\ 



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

 it appeal's to assume that the first 2n diflerential coetticieuts of by must be con- 



I 



