30 Mr. Wilson o?? the 



In effect we solve (A.), (B-)' (C-) and (D.), by n^eans of 

 S', a", S'", S'^ ; the remaining S's (excepting S ° ) are deter- 

 mined in effecting tlie reduction otgY',, to the form of (C.) ; 

 and S "' will be obtained from y = 0, after substituting in it the 

 values of the other H's. 



The above investigations give the formula 



«(1, 1,1, I)(or, «(r')) = 9; . . . (317".) 

 and shows that the general equations of the ninth mid higher 

 degrees may he transformed into others of the same degrees, 

 from "which the second, third, fourth andffth terms disappear; 

 the corresponding foi'mula for m (see the first part of this dis- 

 cussion*) is 



m{\, 1, 1, I) = 11 (or 10). . . . (317.) 



2 Church Yard Court, Temple, 

 November 28, 1846. 



Postscript, Dec. 14, 184-6. — On looking over the proof-slip, 

 I observe that, in this paper, I have not had occasion to use 

 the foregoing notation for the roofs of equations. But the 

 above may be considered to suggest the following permanent 

 notation ; viz. that cc,. should represent a root, and a ''^ the 

 coefficient of the (;'+l)th term of an equation in X ; ^.X a 

 quantity composed of symmetric functions of, and homogeneous 

 and of the ?th degree with respect to, cl\, jt^j, . j.'„ ; that ^ should 

 denote the disposable quantities which enter (explicitly) into 

 the equation for j/ and H, tiie disposable quantities implicitly 

 contained in that equation. When /• is given as a number, we 

 may, however, as above, express the coefficients by accents if 

 r be small, or by Roman numerals if it be large. For facility 

 of reference 1 have termed ' last' volume what was in fact the 

 current one at the time of writing this paper. 



IX. On the Solvent Action of Drainage-Water on Soils. 

 By John Wilson, Esq.f 



IN the autumn of 1S44, being a resident in East Lothian, 

 -■- Avhere the system of ikoroufjh draining is very extensively 

 carried out, it occurred to me that the drainage-water during 

 its percolation of the soil must necessarily dissolve out and 

 carry away a great portion of the soluble constituents of it, 

 which, by the practice as at present followed, arc carried off 

 the land and entirely lost to the farmer. I therefore took 

 advantage of the first fall of rain sufficient to set the drains 



* Phil. M.ng. S. .3. vol. xxix. pp. 181-183. 



t Communicated by the Chemical Society; having been read May 4, 

 1846. 



