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Summary form only given. Cassinian curve as shown below has been in existence for quite a long time yet not used in applications of practical interest since engineers do not know them well. No hand book gives the result of K (1//spl sqrt/2) as the perimeter of the Cassinian when β = 1. Greenhill discusses this curve five times in his book  and gives different results that might have confused the readers. To solve this problem we introduce a series of elegant transformations and change the variable ρ4 into d2 COS2θ + e2 sin2 θ throughout and end with a perturbation formula from our provious work. In this way we developed a new class of waveguides named as Cassinian Waveguides. The merits of these waveguides are listed.