INTERNAL FRICTION IN ROCKS 629 



vertical stress as compared with lateral stress, this formula repre- 

 sents the facts and that each of the softer rocks possesses a definite 

 modulus of plasticity, this being also true in the harder rocks in the 

 earlier stages of the deformation at least. 



This interesting fact is discussed at length in the accompanying 

 paper by Dr. King, where a mathematical treatment of some of the 

 new data developed in the present investigation is also presented, 

 illuminating certain parts at least of that hitherto unsubdued and 

 almost unoccupied domain — the mathematics of the flow of solids. 



In the present paper, without entering into a mathematical 

 treatment of the subject, the following deductions from the experi- 

 mental data may be indicated. 



If a vertical line be drawn cutting off the "true curve" obtained 

 in the case of any rock when the deformation of the tube amounting 

 to o. 15 has been reached, and if the area inclosed by this line, the 

 "true curve" itself, and the base line of the diagram be measured, 

 this area represents the "work done" to effect the deformation of 

 the rock. This area showing the "work done" in deforming a 

 standard column of Carrara marble in a o. 25-centimeter steel tube 

 in Fig. 7 is shaded. In Fig. 9 the "true curves" obtained in this 

 deformation of all the rocks of the series, in steel tubes having a 

 wall thickness of 0.25 centimeter, are shown, and in Fig. 10 the 

 complete series of "true curves" obtained when the wall thickness 

 of the tube is increased to 0.33 centimeter is set forth. In both 

 figures the curves are cut off at the ordinate 0.15, and the area 

 representing the "work done" in the case of each rock is clearly 

 shown and may be compared. 



Table III sets forth these comparative values in square inches. 

 This table shows quite clearly that with the increased resistance, 

 offered by the thicker-walled steel tube, the amount of work 

 required to effect an equal deformation increased in the case of 

 every rock. It also sets forth the comparative ' value of these 

 increases and also the relative amount of work done to deform the 

 different rocks of the series. 



The table thus shows that the "work done" in deforming a 

 column of marble of the size employed and under the conditions of 

 the experiment, when inclosed in the thinner-walled tube, is to the 

 "work done" when an identical column is deformed, when inclosed 



