87 



such that if a strain of any one of those types be impressed on the 

 body, the elastic reaction is balanced by a stress orthogonal to the 

 five others of the same system. 



It is next shown that there is necessarily one, and in general only 

 one, such system of six types of strain for an elastic solid which are 

 all mutually orthogonal ; and the types belonging to this system are 

 called the Six Principal Strain Types of the body. 



The characteristic of a Principal Strain Type is, that the stress re- 

 quired to keep a body in a state of strain of such a type, is of the same 

 type as the strain. The six Principal Elasticities of a body are the 

 six coefficients by which strains of the six Principal Types must be 

 multiplied to find the stress required to maintain them. 



In conclusion, reasons are given for believing that natural crystals 

 may exist for which there are six unequal Principal Elasticities, and 

 consequently six different, and only six different, Principal Strain- 

 types. 



A corollary regarding the property which certain liquids and cry- 

 stals possess of causing a rotation in the plane of polarization of light 

 passing through them, and Faraday's optical property of transparent 

 bodies under magnetic force, is inferred, and is more fully considered 

 in a subsequent communication to the Royal Society. 



II. " On the Construction of the Imperial Standard Pound, and 

 its Copies of Platinum ; and on the comparison of the Impe- 

 rial Standard Pound with the Kilogramme des Archives/' 

 By W. H. MILLER, M.A., F.R.S., Professor of Mineralogy 

 in the University of Cambridge. Part I. Received April 



16, 1856. 



(Abstract.) 



The Commissioners appointed in 1838 to consider the steps to be 

 taken for the restoration of the standards of weight and measure, to 

 replace those which were destroyed by the burning of the Houses of 

 Parliament, found provisions for the restoration of the lost standards 

 prescribed to them by Sections 3 and 5 of the Act 5th George IV., 

 whereby it is directed that, in case of the loss of the standards, the 

 yard shall be restored by taking the length which shall bear a certain 



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