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PROBLEMS AND SOLUTIONS. 
upon the sides of the triangle of reference) touches the nine-point circle, is the sextic 
curve 
+ \y cos B (z cos C — x cos A) 
+ jz cos C (x cos A - y cos B) ^ 
( y 
z 
Veos B 
cos G 
( 2 
x 
Veos G 
cos H 
( œ 
y 
Veos A 
cos B 
It would be an interesting problem to trace this more general curve.] 
[Vol. L., p. 192.] 
3481. (Proposed by Professor Cayley.)—Find, in the Hamiltonian form 
dr) dH dvr dH 
dt dvr ’ dt dr) 
the equations for the motion of a particle acted on by a central force. 
[Yol. LV., 1891, p. 27.] 
10716. (Proposed by Professor Cayley.)—In a hexahedron ABGDA'B'C'D' the 
plane faces of which are ABGD, A'B'G'D', A'ADD', D'DCG', G'CBB', B'BAA', the 
edges A A', BB', GO', DD' intersect in four points, say A A', DD' in a; BB', CG' 
in /3; CG', DD' in 7; A A', BB' in 8: that is, starting with the duad of lines 
aft, 78, the four edges AA', BB', CG', DD' are the lines a8, (38, (3y, ay which join 
the extremities of these duads. Similarly, the four edges AB, CD, A'B', C'D' are 
the lines joining the extremities of a duad; and the four edges AD, BC, A'D', B'G' 
are the lines joining the extremities of a duad. The question arises, “Given two 
duads, is it possible to place them in space so that the two tetrads of joining lines 
may be eight of the twelve edges of a hexahedron ? ” The duad a/3, 78 is considered 
to be given when there is given the tetrahedron a/3<y8, which determines the relative 
position of the two finite lines a/3 and 78. 
[Vol. LXL, 1894, pp. 122, 123.] 
3162. (Proposed by Professor Cayley.)—By a proper determination of the co 
ordinates, the skew cubic through any six given points may be taken to be 
® : y