Page 37 - statbility for masters and mates

Laws of ¯otation 25
waterline. Weigh the hydrometer again and let its mass now be My kilograms.
The mass of water displaced by the stem between X and Y is therefore equal to My Mx kilograms. Since 1000 kilograms of fresh water occupy one cubic metre, the volume of the stem between X and Y is equal to
My Mx cu: m. 1000
Let L represent the length of the stem between X and Y, and let `a' represent the cross-sectional area of the stem.
a Volume Length
My Mx sq m 1000 L
Now let the hydrometer ¯oat in water of density dkg/m3 with the waterline `x' metres below Y.
Volume of water displaced My x a 1000
M M M y xyx I
Volume of water displaced Mass of water displaced Density of water displaced
But
or
My II 1000 d
Equate (I) and (II) ;
d M M
My x y x L
1000 1000 L
M M M M
y y x 1000 d 1000
y x 1000 L
My
In this equation, My, Mx and L are known constants whilst d and x are variables. Therefore, to mark the scale it is now only necessary to select various values of d and to calculate the corresponding values of x.