Dec. 18, I879] NATURE 153 ing a correspondence between the t points of the cubic T associated with the quadrilateral T, and the similarly determined u point, and proceeds to examine all the cases in which this correspondence is uniform, i.e., when to a point of each curve corresponds a single point of the other curve. He then shows that all other cases may be reduced to this case of uniform correspondence. His conclusion, after a discussion of these equations of condition, is that there are 1lO

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... other solutions besides those deduced from the uniform correspondence cases. He establishes coincidences wit:h most of the cases discussed in Mr. Kempe's paper, and arrives at one new case, viz., when Mr. Kempe's triangles reduce to straight lines coinciding with the sides respectively of T and U. Our object has been to draw attention to what we look upon as a valuable pendant to the lastnamed gentleman's Researches in Linkworks.