268 M. G. Wertheim on the double Refraction 



surement with certainty, being of the same order in point of 

 magnitude as the possible errors, no conclusion can be drawn 

 from them. 



Our method causes all these uncertainties to disappear; we 

 have already remarked, that with our parallelopipeds, which pos- 

 sess on an average a section of 500 square millimetres perpen- 

 dicular to the direction of the force, a difference of 1 kilogramme 

 in the force translates itself into a sensible difference of tint. 

 Let us say, for the sake of more certainty, 2 kilogrammes; 

 supposing the coefficient of elasticity of the substance to be 

 only 5000, the result is that a difference in the charge of 4 grms. 

 per square millimetre, and a shortening or elongation of less 

 than a millionth of the height, are sensible and measurable, 

 while such quantities completely escape the direct modes of ex- 

 periment. We can even double or triple the sensibility of our 

 process by doubling or trebling the length of the pieces ; for 

 with the same charge the tint remains the same, while the 

 mechanical linear change will be only one-half or one-third 

 of what it was. At the same time, we have the advantage 

 of operating, not with bars several metres in length, but with 

 small cubes, which enables us to avoid numerous causes of 

 error. 



Dividing the values of P and of T by the length La, I have re- 

 duced them to what they would be for a parallelopiped I millimetre 

 in length, or what is the same thing (according to 1 and 2), to what 

 they would be for a cube 1 millimetre the side ; the weights have 

 been plotted on the axis of the abscissae, each division of which re- 

 presents a kilogramme. The double refractions corresponding are 

 represented by the ordinates, each division of which corresponds to 

 a difference of path of ^^^th of a millimetre in the air. It is to 

 these curves which we must have recourse whenever we wish to 

 determine with precision the lengthening or shortening which 

 corresponds to a feeble charge ; but we observe at the same time 

 how little this curve deviates from the straight line which repre- 

 sents the ordinary coefficient of elasticity. 



I have calculated, for all the pieces contained in the table, the 

 ratios of the successive values of P and T. Assuming each 

 value of P,\^ equal to 10 ; here follow the means of these quo- 



2 



tients*, which for the same difference of path differ very little 

 from^each other : 



* I have not comprised in this mean the tractions which refer to the 

 pieces 10 and 12, and which show that, in the sense in which the pressures 

 become too small, the tractions, on the contrary, augment in an extraordi- 

 narv manner. 



