180 Proceedings of the Eoyal Society of Edinburgh. [Sess. 
6dp can be written down at once by the rules given above. It will be 
found that there are four resulting forms of the integral function u 
according as <p belongs to one or another of the classes of strains. The 
method can easily be applied to various vectors of higher degree. For 
example, let cr — . . . S/Bn-i/BnP, the summation including 
terms with all permutations of the subscripts. This is a form to which 
many (but not all) homogeneous vectors can be reduced. By applying 
(40), it appears that the vector t may have as possible values, either 
the point-vector p, or any of the constant vectors /3, or a variety of 
linear vector functions commutative with (p, the differential of cr. 
{Issued separately July 8, 1915.) 
