﻿Coefficients of Pressure in Thermometry. 375 



There is a final objection to the extension of the result (3) 

 to a thermometer, which has doubtless occurred already to 

 every one familiar with the ordinary shape of that instrument. 

 A mercury-thermometer of ordinary dimensions which makes 

 the slightest pretence to an open scale must have the internal 

 diameter of its bulb a very large multiple of that of its tube. 

 Its resemblance to a cylindrical tube with hemispherical ends, 

 whose diameters must of course equal that of the tube, is 

 thus so remote that even if (3) had been satisfactorily estab- 

 lished for the one body its extension to the other would have 

 been a very long step into the unknown. 



The object of the preceding remarks is solely to show the 

 necessity for further investigation. It is far from my desire 

 to reflect in any way on the author of the proof, whether 

 Dr. Guillaume or another. The discriminating physicist 

 whom the exigencies of the case compel to use imperfect 

 mathematical methods, but who nevertheless reaches results 

 of practical utility, ought not to be classed with the mathe- 

 matical proficient who overlooks errors in his analysis which 

 wholly vitiate his physical conclusions, or who fails to recog- 

 nize fundamental differences between the problem he has 

 actually solved and that which is presented by nature. 

 While the mathematician devoid of physical insight may go 

 badly wrong through some slip which mathematically con- 

 sidered is insignificant, the man possessed of keen physical 

 instincts would almost appear protected by a special pro- 

 vidence which causes even his mistakes to work to his 

 advantage. 



The conclusion to which my own investigations lead is that, 

 on the hypothesis of uniform pressure, (3) is true absolutely, 

 and not merely approximately , for any homogeneous elastic 

 material, isotropic or aeolotropic, limited by an internal and an 

 external surface of any shape or shapes whatsoever', and this I 

 now proceed to prove. 



In any homogeneous elastic material, with any number of 

 elastic constants from 2 to 21, acted on only by surface- 

 forces, the elastic stresses must satisfy the three internal 

 equations 



dxx d xy ,dxz__~ 

 dx dy dz 



day ^ dyy dyz _ Q 



dx dy dz 



d xz dyz ,dzz_ 



dx dy dz * 



y .... (6) 



