Specific gravity of soil particles

Consider the following figure.
specific gravity
W1= weight of empty vessel
W2= Weight of vessel + weight of sample
W3=Weight of vessel + weight of sample+Water
W4=Weight of vessel + Water

Here,
Weight of solid = W2-W1

Similarly, from last two figures
W3-W4=Weight of solid- Weight of water
or, W3-W4= W2-W1 -Weight of water
or, Weight of water=(W2-W1)-(W3-W4)(= weight of equal volume of water as that of solid)

Now,
specific-gravity=\frac{weight of solid}{weight of equal volume of water}
i.e. \rho_s=\frac{(W2-W1)}{(W2-W1)-(W3-W4)}

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