148J MEMOIR ON THE RESULTANT OF A SYSTEM OF TWO EQUATIONS. 443 
As a specimen of a mode of verification, it may be remarked that the Resultant 
qua invariant ought, when operated upon by the sum of the two operations, 
3o9 6 + 2bd c + cd d and 2pd q + qd r , 
to give a result zero. The results of the two operations are originally obtained in the 
forms in the first and second columns, and the first column, and the second column, 
with all the signs reversed, are respectively equal to the third column, and conse 
quently the sum of the first and second columns vanishes, as it ought to do. 
Next to explain the second method, viz. the calculation of the resultant from the 
expression in the form of a determinant. 
Taking the same example as before, the resultant is 
a, b, c, d 
a, b, c, d, 
P, q, r 
P, q, r 
p, q, r 
56—2