1865.] and Viscosity of Metals. 293 



per square centimetre (as 13'596 is the density or specific gravity* of mer- 

 cury, and 76 centimetres the height of the barometric column corresponding 

 to the pressure defined as "one atmosphere"). Or, again, Young's 

 "modulus," which has generally been called simply the modulus of elasticity 

 of a solid, is the longitudinal traction of a stretched rod or wire of the sub- 

 stance, divided by the extension produced by it. Or, lastly, the " modulus 

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

 tropic solid, is the amount of tangential stress divided T 



by the deformation it produces, the former being mea- 

 sured 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 measure. 



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

 many experimenters; but hitherto there have been very few determinations 

 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, how are moduli of elasticity affected in one substance 

 by permanent changes in its molecular condition ? which was my starting- 

 point for all I 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, I used as 

 vibrator in each case a thin cylinder of sheet brass, turned true outside and 



* The one great advantage of 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, Ayr- 

 shire, Lanarkshire, 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 physical science, 

 that a people tending naturally to be regulated by common sense should voluntarily con- 

 demn 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 emancipated themselves. I have been informed, through 

 the kindness of Professor W. II. Miller, of Cambridge, that he concludes, from a very 

 trustworthy comparison 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. 



