temporarily produced in Isotropic Bodies. 259 



/^^x' V \' ^2^' ^3A_' ^4\' ^s\^' ^«x^' ^?\ 



2222 2 22 22 



10-64 10-85 10 10-34 10*42 10'75 11-01 10-88 11-02. 



The latter compressions deduced from a small number of ex- 

 periments are probably too great ; we may assume that the first 

 pressure PjX^ is to the definite values of P and T as 1 is to 1*08; 



2 



consequently, starting from the point where the double refrac- 

 tions become proportional to the charges, we will multiply by 

 this coefficient the numbers inscribed in the sixth column in order 

 to find the constant augmentation of the charge. 



We give the name of coefficient of mechanical elasticity E to 

 the ratio between the charge applied to the unit of surface, and 

 the elongation or compression which it has produced in the unit 

 of length. 



In a similar manner we will give the name of coefficient of 

 optical elasticity C to the ratio between the charge applied to the 

 unit of surface and the double refractions which it produces, 

 taking for the unit of double refraction a diff*erence of path in 

 the air equal to the unit of length. 



Let P be one of the mean values inscribed in the sixth column, 

 we shall have for the coefficient of optic elasticity the following 



expression, C = P x 1*08 x - — ^^r^^s^ — ■ ; the different values of C 



have been carried into the seventeenth column. 



We might have represented by a formula of interpolation the 

 route of the pressures and tractions ; but it might have been 

 demanded whether the proportionality really exists beyond a 

 certain limit, whether the curve becomes confounded with a 

 straight line in all the rest of its course, and whether this takes 

 place even when permanent changes of length add themselves to 

 the temporary changes. 



The actual observations are still too limited to enable us to 

 respond to these questions in an absolute manner ; however, I 

 believe that I have elsewhere demonstrated that the coefficient 

 of mechanical elasticity increases and diminishes with the density 

 of the substance. Now, according to the law of changes of 

 volume, the compression augments the density, while the trac- 

 tion diminishes it ; the curve thus appears to prolong itself at 

 both sides to the two points of rupture, by tearing and by 

 crushing. 



The results which we have just obtained are of no practical 

 importance in constructions ; these differences are too small to 

 be taken into account in the employment of materials, and our 



S2 



