vn PRINCIPLE OF ARCHIMEDES 97 



meanings of the terms density or absolute density and rehiticc 

 ({Hstty : the first is dependent on the units of mass and volume, 

 the second being merely a numerical ratio does not vary with 

 these units. 



Hydrostatic Method of Determining Relative Densities. 

 It has already been pointed out, and illustrated by experiment, 

 that equal volumes of different materials have different masses, 

 which truth is expressed by saying that they have different 

 absolute densities. Again, the experiments on the principle of 

 Archimedes have shown that some substances are heavier and 

 some lighter than an equal volume of water. Let us use the 

 principle to find exactly how much heavier or lighter certain 

 substances are than an equal volume of water, that is, their 

 Mnth-e densities compared with water as a standard. 



There are two numbers which we wish to determine : (i) The 

 weight of the body of which the density is required, t'.e., its 

 weight in air ; (ii) the weight of an equal volume of water. 



The first number can be obtained directly by hanging the body 

 from a hook at the top of one scale pan, and then placing accurate 

 weights on the other, until the weight of the body is exactly 

 balanced. This only requires practice to be able to accomplish 

 it with the greatest precision. To find the second number, a 

 glass of water is placed upon a small platform (Fig. 41) so that 

 the body under experiment is immersed in it. The loss of weight 

 then experienced is equal to the weight of an equal volume of 

 water. This experiment shows, therefore, the weight of the 

 body and the weight of an equal volume of water. The propor- 

 tion between these two numbers, that is, the first divided by 

 the second, is the relative density of the body. For, 



Relative density - - weight of substance 



weight of equal vol. of water 

 And as 



loss of weight in water = weight of equal vol. of water 

 we can put down 



Relative density = weight of substance 

 loss of weight in water 



EXPT. 88. Find by weighing, and determining the loss of 

 weight in water, the relative densities of a halfpenny, a 

 shilling, and a sovereign. 



EXPT. 89. Find, by the method of the preceding experi- 

 ment, the relative densities of two or three common solids, 



H 



