I think that your '51 3600 has a short enclosed torque tube in the front and an open driveshaft on the rear. If so, here is an easy way to tell which rear end you have without pulling the pumpkin to find the stampings on the ring gear.
Park your truck on a safe, level surface. Chock the left rear wheel (fronts, too, if you have enough chocks). Put the truck in neutral. Release the emergency brake. Jack up the right rear wheel just enough to allow you to easily turn it. Make a chalk mark on the drivesaft or u-joint yoke. Turn the tire and count the number of turns while watching the chalk mark. Using the ratios Tim gave you above, if it takes about 4.5 tire rotations to give the driveshaft one complete turn, it is a 4.57. It it takes just over 5 tire rotations, it is a 5.14.
This wouldn't work if you had a limited slip, but they weren't available until '59.
Matt
PS--There is also a possibility that you could find that you have a 4.10. They were available from '67 to '72 on the same rear end. Certainly not available back in '51, but a previous owner could have made the easy swap to get better top end. Only three possibilities if you have the original Eaton rear end---4.57 or 5.14 from the factory or 4.10 with a later change.
