﻿Level of no Strain within a Solid Earth. 131 



shaft turned by the handle indicates that it has turned 



through an angle proportional to 2*405, which is the first 



value of x which satisfies J (a') =0. 



It is advisable to have a pointer and a scale to indicate 



exactly the displacement of the table, so as to test the 

 accuracy with which the cam performs its duties. Of course, 

 when the graduated-circle indication is 2*405, the displace- 

 ment of the table is to be 2*405 ^(2*405) or -1-249 inches. 

 The area recorded on the planimeter in square inches 

 must now be multiplied by 2(2'405) 2 /a 4 [J 1 (2*405)] 2 , and the 

 answer is A x . 



To find A 2 : change the gearing so that when the whole 

 roller-curve passes under the tracing-point of the planimeter, 

 the graduated circle indicates 5*5201, and check the error of 

 the cam by noting that the displacement indication ought 

 now to be" 5*5201 Jx(5*5201) or 1*878 inches. The area 

 recorded by the planimeter in square inches must now 

 be multiplied by 2(5*5201) 2 /a 4 [J 1 (5*520 1)] 2 . If variable 

 frictional gearing is used, it is important that the roller 

 should be placed on roller bearings of small resistance. 



To develop an arbitrary function in Bessels of any other 

 order, or in Fourier's Series, or in zonal harmonics, or in 

 series of functions of any other normal forms, we have only 

 to replace the cam by one of another shape; so that this one 

 simple machine is suited to quite general analytical use. 



XL On the Effect of Sphericity in Calculating the Position 

 of a Level of no Strain within a Solid Earth, and on the 

 Contraction Theory of Mountains. By Rev. O. FlSHEK, 

 M.A., F.G.S* 



IHAYE been permitted to reply to Professor Blake's 

 criticism upon my investigations concerning the relative 

 structure of the continental and suboceanic crust f, and I now 

 hope to do the same to his objections to the calculation of 

 the depth of the " level of no strain * J — a subject which he 

 admits to be important. 



Mr. Blake says that he is surprised that the superficial 

 position of the level of no strain at no more than four miles 

 from the surface " should not be regarded as a reductio ad 

 absurdum that the method or premisses which lead to it must 

 be wrong, both a priori, that any critical change in condition 



* Communicated by the Author, 

 t Phil. Mag. vol. xxxvii. p. 375, April 1894. 

 t 'Annals of British Geology,' 1892, p. iv. 

 K2 



