You want to measure the specific gravity of a liquid. To do this, you first weigh a beaker of the liquid on a scale $\left(W_{L o}\right)$. You then attach a string to a solid body that is heavier than the liquid and while holding the string you immerse the solid body in the liquid and measure the weight of the beaker containing the liquid with the solid submerged $\left(W_{L S}\right)$. You then repeat the same procedure using the same weight but with water instead of the "unknown" liquid. The corresponding weight of the water without the weight submerged is $W_{W_{o}}$ and with the solid submerged is $W_{W_{s}}$. Show how the specific gravity of the "unknown" liquid can be determined from these four weights, and show that the result is independent of the size, shape, or weight of the solid body used (provided, of course, that it is heavier than the liquids and is large enough that the difference in the weights can be measured precisely).