Ok, found my book, here is the break down... just for this though experiment, lets say air has a specific gravity (sg) of 0, water is 1, sand is 2, rocks are 10 and gold is 20.
In air, you would look at the values minus the value of the air. So... Sand (2-0=2), rocks (10-0=10), and gold (20-0=20). So when you pan in air, gold would be 10 times heavier as sand (20/2=10) and 2 times heavier than rocks (20/10=2)
On to water... Using the SG of 1 for water instead of 0 for air. Sand (2-1=1), rocks (10-1=9), and gold (20-1=19). So when you pan in air, gold would be 19 times heavier as sand (19/1=19) and 2.11 times heavier than rocks (19/9=2.11)
Clear as mud right?!?!

[/QUOTE Your original premise is correct, but you got fouled-up on the "weights". Sand, and rocks both have the same specific gravity...and the SG is what matters, not the weight. On average, sand and gravel have specific gravity about 2.5. Gold is about 19. (Usually alloyed with other stuff.)
So, the difference, in air, is about 7.5:1+/-. The difference in water is calculated by subtracting the water's SG, which is 1. Now the ratio is 18 (gold/1.5(gravel), which comes out to 12:1 Now, if you add a material with a higher SG to the water, so it is absorbed....the SG of the water might get to 1.5. That changes the ratio again....you get 1 for the gravel, and 17.5 for the gold. The ratio has become 17.5:1. The greater the ratio, the easier it is to separate the gold from the gravel. The reason this isn't used, is that there very few liquids heavier than water.
Jim