196 M. R. Thalen on the Determination of 



fixing the microscope could not exceed 0*02 millim., or 0*1 of 

 a division as a maximum. Notwithstanding the observations in 

 the commonest case exhibited an agreement to hundredths of a 

 division, in the following Tables only tenths of a division were 

 taken, and for the following reasons. 



As will subsequently be shown, the permanent elongations 

 increase considerably with greater loads, and the bars become 

 then extremely susceptible of the stretching forces. Provided 

 now that in using Fuller's machine the tension of the bar has 

 already been so increased that it is able to raise the lever with 

 its load attached, there is yet at each stroke of the pump of the 

 hydraulic press, united with a further raising of the lever, a new 

 elongation of the bar under experiment. As such an elongation 

 occurs, however carefully the pumping (that is, the stretching) 

 may be effected, it is seen that, after all, any given permanent 

 elongation may be obtained. In the agreement between the 

 various experiments, however, it will be found that the scale 

 was continually raised to a given distance above a light moveable 

 index fixed on it. What has been said shows that in the ques- 

 tion of great loads it cannot be of interest to investigate the 

 course of the elongations otherwise than approximately, and an 

 extreme fineness in the measurement would be here merely spe- 

 cious and therefore unnecessary. 



§ 3. Limit of Elasticity. 



In the question of stretching, the theoretically correct de- 

 finition of the limit of elasticity would be this — the highest 

 load for the unit of surface which the bar investigated can bear 

 without its undergoing the slightest permanent elongation after 

 removing the load. But it is clear that the determination of 

 this highest load depends greatly on the goodness of the instru- 

 ments used for measuring lengths, and can be lowered in the 

 same degree as the accuracy and sharpness of the said measuring- 

 apparatus is increased ; for this reason it has been thought ne- 

 cessary to fix a certain permanent elongation as corresponding 

 to the limit of elasticity, and to take this at 0*0005 of the unit 

 of length*. 



Against this new definition it has been justly urged that it is 

 arbitrary. The point upon the curve representing the perma- 

 nent elongation, which according to the said definition fixes the 

 limit of elasticity, is not in the least distinguished from other ad- 

 jacent points, and is therefore quite destitute of any physical 

 significance. But even neglecting the arbitrary way of pro- 

 pounding the definition, and only looking at the possibility of 



* G. Wcrtheim, RecJierches sur Velasticite, premier memoire, p. 55. 



