594 Dr. 0. Chree : Applications of 



and perhaps suggest improvements in the design of coils. The 

 first requirement is evidently the existence of sufficient energy 

 at break, and this implies a considerable mass of iron, well 

 magnetized, and not forming a circuit too nearly closed. The 

 full utilization of this energy is impeded by want of suddenness 

 in the break, by eddy-currents in the iron, and (in respect of 

 spark-length) by capacity in the secondary. It is to be pre- 

 sumed that in a well-designed coil these impediments should 

 operate somewhat equally. It w T ould be useless to subdivide 

 the iron, or to reduce the secondary capacity, below certain 

 limits, unless at the same time the break could be made more 

 sudden. Jt would not be surprising if it were found that the 

 tentative efforts of skilful instrument-makers have already led 

 to a suitable compromise, at least in the case of coils of mode- 

 rate size. The design of larger instruments may leave more- 

 to be accomplished. 



LVIII. Applications of Elastic Solids to Metroi 

 By 0. Chree, ScD., LL.D., F.R.S. 



- y [Concluded from p. 558.J ^ ^ 



V Standards of Length, J, 



§ 19. TF a rectangular prism of horizontal length L be placed 

 JL on a perfectly smooth and horizontal plane, we find 

 from (36) for the elastic increment in the length at a height 



k + z above the plane (h being the vertical dimension of 



the prism) the formula 



SL/L=-(l-2 1? )(p/E)+ W (p-p')(/i/2E)-^{ W -(lr- J j)p'}/E,(66> 



Here p represents, as before, the pressure in the liquid or 

 gaseous medium surrounding the prism at the level of the 

 C.G., i. e. at the height h/2 above the plane. This result 

 should apply to an ordinary standard yard, and to most 

 commercial standards of length, if supported throughout the 

 entire length on a perfectly smooth table. If, as in the 

 standard yard, the scale is divided on the upper surface 

 z = h/2, we have for its elastic stretching 



sL/L=-<irpW!) 



= -P/3£, (67)*- 



* [Oct. 1901. — A formula apparently equivalent to this is given with- 

 out proof by Mr. Chaney, on pp. 86, 87 of the Proces Verbaux of the 

 International Committee of Weights and Measures for 1899. It is given 

 as applicable to the standard yard, without explicit reference to the- 

 niethod of support, and is illustrated numerically.] 



