568 On Reflexion and Refraction of Elastic Waves. 



them. Fortunately the numerical details are introduced into 

 my paper more for the purposes of illustration than for the 

 calculation of definite results, so that the main argument is 

 not affected. Yours truly, 



C. G. Knott. 



. Rose Polytechnic Institute, 



Dr. C. G. Knott, Terre Haute, Ind., 



Edinburgh University. Sept. 24, 1899. 



Dear Sjr, — I have just found time to look over your paper on 

 " Elastic Waves," and find a reference to some determi- 

 nations of elastic moduli of rocks made by me in connexion 

 with some work which Prof. Milne and I were engaged on 

 in Japan. The moduli are given correctly in my tables 

 (Smithsonian Physical Tables, 2nd Edition, 1897) and also 

 in the ' Quarterly Journal of the Geological Society ' for 

 1883. They do not seem to agree with the numbers you 

 quote in your paper, and it may save trouble if I state them. 

 They are, in grammes per square centimetre, as follows : — 



E. n. 



Granite . . . 416 xlO 6 128x10" 



Marble . . . 400 x 10 6 119 x 10 6 



Tuff . . . . 189x10° 102 XlO 6 



Clay-rock . , 329 x 10 6 177 x 10 6 



Slate .... 686 XlO 6 229 x 10 6 



With regard to the velocity of propagation of elastic waves, 

 I find, on looking up the original paper, that the column 

 headed " Calculated velocity of normal wave in centimetres 

 per second " should have been headed " Calculated velocity of 

 normal wave, along a bar of the rock, in centimetres per 

 second/' This, no doubt, explains part of your difficulty. 

 The statement is made in the paper that we intended to 

 calculate the bulk-modulus from the results of the experiments 

 and then calculate the theoretical velocity of propagation of 

 earthquake-waves in rock media. The intention seems to 

 have been all right, but I find no record of the performance. 

 It is probable that the results were not considered satisfactory. 

 In the case of clay -rock and tuff, the value of Poisson's 

 ratio comes out negative when calculated from the tabular 

 numbers above given on the assumption of continuous iso- 

 tropic material. Undoubtedly, however, the experiments 

 here quoted give no data which we are justified in using, on 

 any such assumption, either for the calculation of k or s (the 

 bulk-modulus or Poisson's ratio) . The nature of the material 

 is not such as to justify any such application. Most of us 

 are familiar with rocks which within certain limits of bending 

 show remarkable flexibility, and hence low Young's modulus. 

 Some of these rocks show considerable uniformity of structure, 

 but it is of the brick and mortar variety. They are not iso- 



