Prof. W. Thomson on the Elasticity and Viscosity of Metals. 67 



being -jtotto P er atmosphere, its " modulus of compressibility " or 

 its "volume modulus of elasticity," is 21000 atmospheres, or 



76 x 13-596 x 21000=217 XlO 6 



grammes weight per square centimetre (as 13*596 is the density or 

 specific gravity* of mercury, and 76 centimetres the height of the baro- 

 metric column corresponding to the pressure defined as " one atmo- 

 sphere"). Or, again, Young's "modulus," which has generally 

 been called simply the modulus of elasticity of a solid, is the longitu- 

 dinal traction of a stretched rod or wire of the substance, divided by 

 the extension produced by it. Or, lastly, the " modulus of rigidity," 

 or, as it is conveniently called, simply "the rigidity" of an isotropic 

 solid, is the amount of tangential stress divided 

 by the deformation it produces, — the former being 

 measured in units of force per unit of area applied, 

 as shown in the diagram, to each of four faces of 

 a cube, and the latter by the variation of each of 

 the four right angles, reckoned in circular mea- 

 sure. 



Measurements of Young's modulus have been made for many bodies 

 by many experimenters; but hitherto there have been very few deter- 

 minations of rigidity, notwithstanding the great ease with which this 

 can be done for wires by Coulomb's method. Accordingly, although 

 several accurate determinations of Young's modulus have been made 

 upon wires of different substances hung in the College Tower of the 

 University of Glasgow (which, by giving 80 feet of clear protected 

 vertical space, affords great facilities for the investigation), I shall in 

 this paper only refer to some of the results as bearing on the question, 

 howjare moduli of elasticity affected in one substance by permanent 

 changes in its molecular condition ? which was my starting-point for 

 all 1 have attempted to do experimentally regarding the elasticity of 

 solids. 



To determine rigidities by torsional vibrations, taking advantage 

 of an obvious but most valuable suggestion made to me by Dr. Joule, 



* The one great advantageof the French metrical system is, that the mass of the 

 unit volume (1 centimetre) of water at its temperature of maximnm density (3° "945 

 Cent.) is unity (1 gramme) to a sufficient degree of approximation for almost all 

 practical purposes. Thus, according to this system, the density of a body and 

 its specific gravity mean one and the same thing; whereas on the British no- 

 system the density is expressed by a number found by multiplying the specific 

 gravity by one number or another, according to the choice (of a cubic inch, cubic 

 , foot, cubic yard, or cubic mile) that is made for the unit of volume, and the weight 

 of a grain, scruple, gun-maker's drachm, apothecary's drachm, ounce Troy, ounce 

 avoirdupois, pound Troy, pound avoirdupois, stone (Imperial, Ayrshire, Lanark- 

 shire, Dumbartonshire), stone for hay, stone for corn, quarter (of a hundred- 

 weight), quarter (of corn), hundredweight, or ton, that is chosen for unit of force. 

 It is a remarkable phenomenon, belonging rather to moral and social than to phy- 

 sical science, that a people tending naturally to be regulated by common sense 

 should voluntarily condemn themselves, as the British have so long done, to 

 unnecessary hard labour in every action of common business or scientific work 

 related to measurement, from which all the other nations of Europe have eman- 

 cipated themselves. I have been informed, through the kindness of Professor 

 W. H. Miller, of Cambridge, that he concludes, from a very trustworthy com- 

 parison of standards by Kupffer, of St. Petersburgh, that the weight of a cubic 

 decimetre of water at temperature of maximum density is 1000'013 grammes. 



F2 



