246 New Method of solving Equations of partial Differentials, 

 -f if <p (e log * ~ log M , s logy ~ log M ) 



There are several equations which are not of a form to 

 which this method is immediately applicable, but which be- 

 come so by a slight transformation. For instance, in the 

 equation 



d x dy w 



where X, Y, Z are functions of x, y, and z, respectively, 

 assume 



d z 



/dz 



which may be solved in the same manner as Example 3. 

 The equation 



/ . \ dz , . v dz 



may be transformed so that this method shall be applicable, 

 by taking x+y = w, and x and u for the independent varia- 

 bles. It then becomes 



dz _ dz 



u -j 2x -3 — = %. 



dx du 



As this article has already been extended to some length, 

 I shall defer to a succeeding Number the application of my 

 method to equations of the second and higher orders. It is 

 in those chiefly that it claims a superiority to the method of 

 Lagrange ; and in cases to which his does not apply it gives, 



