404 Leigh Page, 



vector. Contravariant vectors and polyadics will be provided 

 with superior suffices, while covariant ones will be distinguished 



by inferior suffices. A dyadic, like Do, which is partly contra- 

 variant and partly covariant, will have suffices of both types. 

 More generally, if 



is covariant. Now, the form of Laplace's equation suggests that 

 the exact law of gravitation may be expressed by equating to zero 

 a covariant dyadic involving the g's and their first and second 

 derivatives, the equation being linear in so far as the second 

 derivatives are concerned. Our problem, then, is to build up a 

 dyadic satisfying these requirements. 



Now the square of the linear element ds is 



^//= -^ ^ dx i/xr}. (45) 



Therefore, if the self conjugate dyadic G o is defined by 



it follows that 



Go Si,'' ok ko, 



'^'"'=^a/3'- '^'"'^ '^P'^- (-^^^ 



