MancJiester Memoirs, Vol. I. (1906), No. 8. 



19 



pared, in order to complete the solution, I shall state the 

 results. 



With the object of making use of the simplifications 

 already found, I consider the actual motion as obtained 

 by means of a correction on a hypothetical motion dying 

 away from the surface motion by the exponential law 

 resulting from the substitution in the surface motion of 

 H(J.e., he'^'') in place of h, the correcting terms being of 

 the type H\Jfi-H% etc. 



For example, from (7) 



and I consider this as 



2m + ^* + -^-W + i^H"' + ".^H'){Ii' - H'') 



and similarly with the other quantities. 



By this method the chief terms (using the word 

 " chief" not in a physical sense, but in reference only to 

 the analytical method) in the values of A, M, N, are 

 deduced from values derived from those of (23) by 

 substituting // in place of /i throughout. 



The correcting terms are readily calculated from (17) 

 and (20), and are 



