Theory of sn function wave guides

we study the conformal transformation z = sn w to see how the constant u an d constant v lines are transformed into the Z-plane curves to be utilized a s boundaries of EM Waveguides, We give two sample curves for the lines v = K ' /2 and u = K/2, The latter is believed to be new: a Cassinian oval curv e of alpha = 1/k and beta = 1/k rootk ' Many curves can be drawn as boundar ies of EM ware guides. formulas for drawing these curves and show that we c an also use a good table of 4 significant figures to draw these curves, (11 ) and (17c) are new.