I send a note on the following problem, a solution of which was requested of me by one of the tutors at King's College, Cambridge.

We are given a quadrilateral of four jointed bars ABCD (fig. 83). The bar CD being held fast, find the tangent to the locus of P, the intersection of DA, CB in any position; and verify the following construction for the radius of curvature of the path of P:—

Let PQ be the third diagonal, draw through P a perpendicular to PQ meeting BA, CD in L and L′; through L and L′ draw parallels to PQ meeting AD in M and M′; through M and M′ draw perpendiculars to AD meeting the normal at P in O and O′; then will