It is used to determine the density of a body experimentally; for if W is the weight of a body weighed in a balance in air (strictly in vacuo), and if W' is the weight required to balance when the body is suspended in water, then the upward thrust of the liquid (I) (2) "F r an Minim ' 'i n or weight of liquid displaced is W-W, so that the specific gravity (S.G.), defined as the ratio of the weight of a body to the weight of an equal volume of water, is W/(W-W').
The components of velocity of the moving origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if u, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ, v =V +v -zP +xR, w=W +w -xQ +yP.
dt-(u)dy- (w-w) dz = d - (U-yR+zQ) dy - (V-zP+xR)d -(W-xQ+yP) d z (8) is the time-rate of change of 49 at a point fixed in space, which is left behind with velocity components u-u', v-v', w-w'.
It is readily seen that W+W i - W 2 is the weight of the liquid displaced by the solid, and therefore is the weight of an equal volume of liquid; hence the relative density is W/(W+Wi - W2).
The meaning of this deflection can be interpreted as follows: If a galvanometer has a resistance R and is shunted by a shunt of resistance S, and the shunted galvanometer is placed in series with a large resistance R' of the order of a megohm, and if the same w w Se J FIG.
C A W W 3 j ?..a... ? ?-- -- - n--- --y ?
Then W-w is the weight of the solid.
Hence, since the weight of the solid itself is W-w, its density must be (W-w)/(wi-w).