SPECIFIC GRAVITY AND DISPLACEMENT OF SOME SALINE SOLUTIONS. 17 



Section I. — Introduction. 



§ 1. The Principles of Archimedes* — It is well known that the mechanics of floating 

 bodies, and the laws which govern their equilibrium, were established and enunciated 

 by Archimedes, the Sicilian, in the third century before our era. The following pro- 

 positions, demonstrated in the first book of his treatise on this subject, embody the 

 fundamental principles of the hydrometer : — 



(a) The surface of any fluid at rest is the surface of a sphere whose centre is the 

 same as that of the earth. 



(h) Of solids, those which, size for size, are of equal weight with a fluid will, if 

 let down into the fluid, be immersed so that they do not project above the surface, 

 but do not sink lower. 



(c) A solid lighter than a fluid will, if immersed in it, not be completely submerged, 

 but part of it will project above the surface. 



{d) A solid lighter than a fluid will, if placed in the fluid, be so far immersed that 

 the weight of the solid will be equal to the weight of the fluid displaced. 



((?) If a solid lighter than a fluid be forcibly immersed in it, the solid will be 

 driven upwards by a force equal to the difl"erence between its weight and the weight 

 of the fluid displaced. 



{/) A solid heavier than a fluid will, if placed in it, descend to the bottom of the 

 fluid, and the solid will, when weighed in the fluid, be lighter than its true weight 

 by the weight of the fluid displaced. 



Archimedes considered only one solid and one fluid, and his laws regulate exactly 

 what takes place in such a system when the solid is totally immersed in the fluid ; 

 or, if only partially immersed in it, when the non-immersed portion of the solid is 

 immersed in no other fluid — in other words, when the experiment is being made in 

 a vacuum, or in a medium the density of which is insensible. When, however, the 

 experiment is being made in air, it is not necessary to postulate that its density 

 is insensible ; Archimedes' laws still hold good, only the solid falls to be considered 

 as divided into two, one of which is completely immersed in the one fluid (the 

 liquid), and the other is completely immersed in the other fluid (the air). If the 

 solid was immersed in three fluids, as, for instance, water, oil, and air, and floated 

 at rest when part of it was immersed in each of these fluids, it would fall to be 

 divided into three portions, each of which is totally immersed in one of the three 

 fluids, Archimedes' laws would still be applicable, and the final total effect would 

 be the sum of the partial effects. 



§ 2. Hydrometer suitable for Demonstrations on the Lecture Table. — I constructed 

 an instrument of this kind for use in lectures which I gave as assistant in the 



* The IVorhs of Archimedes, editedin Modern Notation, by T. L. Heath, Sc.D., Cambridge University Press, 1897, 

 pp. 253-268. 



TRANS. ROY. SOC. EDIN., VOL. XLIX., PART I. (NO. 1). 3 



