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LII. Applications of Elastic Solids to Metrology, 

 By C. Chree, 'Sc.D., LL.D., F.R.S* 



Contents. 

 Section. 



1. Fundamental Equations. 



2. Suspended and Supported Solids. 

 3, 4. Pressure of surrounding- medium. 

 5-7. Solid surrounded by varying- medium. 



8. Aeolotropic Solids. 



9. Cylinder suspended from the rim. 



10. Solid Cylinder or Prism with axis vertical : Complete Solution. 



11. Flask containing Liquid. 



12-13. Hollow Cylinder containing or surrounded by Liquid. 



14. Spherical Shell containing and surrounded by Liquid. 



15. Cylinder under pressure a quadratic function of z. 

 16-18. General properties, influence of Cavities, Gravitation, &c. 

 19-20. Standards of Length. 



21-25. Applications of Bernoulli-Euler Method. 



26-27. Bar under additional weight. 



28-35. Numerical applications to Standards of Length. 



36-37. Application to deflexion-bars of Magnetometers. 



38. Concluding remarks. 



Fundamental Equations. 



§1. npHE ordinary conception o£ a solid is apt to be that of 

 _L a body whose shape and volume are variable only with 

 temperature. Elastic changes in dimensions are necessarily 

 small in most bodies of limited size, and they are often 

 negligible even in exact metrological work. The present 

 tendency is, however, to aim at an increasing accuracy in 

 physical measurements, and it is open to doubt whether the 

 steps taken in this direction are always guided by a sufficiently 

 lively apprehension that solids are elastic, not rigid. The 

 object of this paper is to exemplify the bearing of elasticity 

 on physical measurements. Some of the points dealt with 

 have met with previous recognition, but so far as my know- 

 ledge goes there has been no previous systematic treatment 

 of them by an elastician. Many of the mathematical results 

 used in this paper depend ultimately on a previous paper f, 

 published in 1892, in which I obtained expressions for the 

 mean strains and for the change in total volume of any r 

 homogeneous elastic solid, acted on by any given system of 

 forces throughout its mass or over its surface. 



When the material is isotropic, E denotes Young's modu- 

 lus, n the rigidity, rj Poissoir's ratio, and k(= JE/(l-2?7)) the 

 bulk modulus. 



* Communicated by the Physical Scciety : read May 10, 1901. 



f " Changes in the Dimensions of Elastic Solids . . ." Camb. Phil. 

 Trans, vol. xiv. p. 313. 



