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the locus of a point, such that tangents being drawn from it 
to two equal intersecting circles, their rectangle may be con- 
stant, and equal to the square of half the common chord, 
If the circles do not intersect, and if the rectangle under 
the tangents be equal to the square of the tangent to either 
- from the middle point between the centres, the locus will give 
the curve derived from an hyperbola, whose real axis is greater 
than the imaginary. 
To get the curve when the imaginary axis is greater than 
the real, we must take the locus of a point, such that lines 
being drawn from it to meet the circumferences of two equal, 
non-intersecting circles, and subtending right angles at their 
centres, their rectangle may be constant, and equal to the 
sum of the squares of the radius, and of half the distance be- 
tween the centres. 
There exist in spherical geometry numerous properties of 
an analogous character. 
The Rev. Charles Graves made a communication relative 
to the new functions employed by him in the interpretation of 
his theory of Algebraic ‘Triplets. 
The three functions a,M, N, defined in p. 60, possess so 
many interesting properties that they seem to deserve distinc- 
tive appellations. The first is symmetrical with respect to its 
two amplitudes, ¢ and y; and its properties are in the main 
analogous to those of the trigonometrical function cosine. On 
the other hand, m and N are not symmetrical functions of 
and x; but either of them may be obtained from the other by 
interchanging the two amplitudes; and they correspondinmany 
respects to the trigonometrical sine. Mr. Graves proposes 
then to call a the cotresine, and and n the ¢resines of @ 
and x: and he designates them respectively by the symbols 
cotr[@, x], tres[, x], tres[x, ¢]- 
As in trigonometry cos @ = cos(2i7 + 9), and sing= 
