A new model of percolation on random lattices is introduced. It allows
for simulations on geometries like the sphere for which there do not
exist periodic lattices of arbitrary fineness. Horizontal crossing pro
babilities pi(h) are measured on rectangles of various aspect ratios r
. These measurements agree with Cardy's prediction though there are sm
all discrepancies for rectangles with large aspect ratio. Further cros
sing probabilities are measured on a cylinder. These probe the hypothe
sis of conformal invariance stated in Bull. Ams. 30 (1994) 1.