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# Determination of Volumes by Weighing

The volumes of some bodies of known shape may be determined further by calculation from their linear dimensions; one instance of this has been given in the experiment with the calipers.

A Table giving the relations between the volume and linear dimensions in those cases which are likely to occur most frequently will be found in Lupton's Tables, p. 7. 9. Determination of Volumes by Weighing.

Volumes are, however, generally determined from a knowledge of the mass of the body and the density of the material of which it is composed. Defining 'density' as the mass of the unit of volume of a substance, the relation between the mass, volume and density of a body is expressed by the equation M=Vρ, where M is its mass, V its volume, and ρ its density. The mass is determined by means of the balance (see p. 91), and the density, which is different at different temperatures, by one or other of the methods described below (see pp. 107-112). The densities of certain substances of definitely known composition, such as distilled water and mercury, have been very accurately determined, and are given in the tables (Nos. 32, 33), and need not therefore be determined afresh on every special occasion. Thus, if we wish, for instance, to measure the volume of the interior of a vessel, it is sufficient to determine the amount and the temperature of the water or mercury which exactly fills it. This amount may be determined by weighing the vessel full and empty, or if the vessel be so large that this is not practicable, fill it with water, and run the water off in successive portions into a previously counterpoised flask, holding about a litre, and weigh the flask thus filled. Care must be taken to dry the flask between the successive fillings; this may be rapidly and easily done by using a hot clean cloth. The capacity of vessels of very considerable size may be determined in this way with very great accuracy.

All the specific gravity experiments detailed below involve the measurement of a volume by this method.

Experiment. - Determine the volume of the given vessel.

Enter results thus:

Last Update: 2011-03-27