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Some idea of a system of such equations may be given in order to clear the way.
In Professor Chrystal’s Algebra, Chapter XIV., No. 18, p. 303, we have:
“Of the equations
with two similar equations in y, z, where x, y, z are unequal; prove that any two imply the third.” (Cayley.)
1. It may not be generally known how much more rapidly such operations as multiplying or dividing by π, or reducing metres to yards, etc. can be effected by the methods of “Practice” than by direct multiplication and division.
2. For example, the commonly used approximation 
for the value of π, though an excellent first approximation, is only true to three significant figures; but (i) 
is true to five significant figures, and thus yields a second approximation by a correction of the first. The value (ii) 
which is slightly higher, may be used as a useful check.
