Thus far the various operations have been separately considered, and we
now pass on to a consideration of the methods of working for solving the
various formulæ met with in technical calculations. We propose to
explain the methods of dealing with a few of the more generally used
expressions, as this will suffice to suggest the procedure in dealing
with other and more intricate calculations. In solving the following
problems, both the upper and lower scales are used, and the relative
value of the several scales must be observed throughout. Thus, in
solving such an expression as √((74·5)/(15·8)) = 6·86, the division is
first effected by setting 15·8 on B to 745 on A. From the relation of
the two parts of the upper scales (page 37) we know that such values as
7·45, 745, etc., will be taken on the _left-hand_ A and B scales, while
values as 15·8, 1580, etc., will be taken on the _right-hand_ A and B
scales. Hence, 15·8 on the R.H. B scale is set to 745 on the L.H. A
scale, and the result read on D under the index of C. Had both values
been taken on the L.H. A and B scales, or both on the R.H. A and B
scales, the results would have corresponded to _x_ = √((7·45)/(1·58)) =
2·17, or to _x_ =√((74·5)/(15·8)) = 2·17, _i.e_., to (6·86)/(√(10)).
Hence if a wrong choice of scales has been made, we can correct the
result by multiplying or dividing by √(10) as the case may require. If
the result is read on D, set to it the centre index (10) of B and read
the corrected result under the index of C.
To solve _a_ × _b_^2 = _x_. Set the index of C to _b_ on D, and over _a_
on B read _x_ on A.
To solve (_a_^2)/(_b_) = _x_. Set _b_ on B to _a_ on D by using the
cursor, and over index of B read _x_ on A.
To solve (_b_)/(_a_^2) = _x_. Set _a_ on C to _b_ on A, and over 1 on B
read _x_ on A.
To solve (_a_ × _b_^2)/(_c_) = _x_. Set _c_ on B to _b_ on D, and over
_a_ on B read _x_ on A.
To solve (_a_ × _b_)^2 = _x_. Set 1 on C to _a_ on D, and over _b_ on C
read _x_ on A.
To solve ((_a_)/(_b_))^2 = _x_. Set _b_ on C to _a_ on D, and over 1 on
C read _x_ on A.
To solve √(_a_ × _b_) = _x_. Set 1 on B to _a_ on A, and under _b_ on B
read _x_ on D.
To solve √((_a_)/(_b_)) = _x_. Set _b_ on B to _a_ on A, and under 1 on
C read _x_ on D.
To solve _a_ (_b_)/(_c_^2) = _x_. Set _b_ on C to _c_ on D and over _a_
on B read _x_ on A.
To solve _c_√((_a_)/(_b_)) = _x_. Set _b_ on B to _a_ on A, and under
_c_ on C read _x_ on D.
To solve (√_̅a_)/(_b_) = _x_. Set _b_ on C to _a_ on A, and under 1 on C
read _x_ on D.
To solve (_a_)/(√_̅b_) = _x_. Set _b_ on B to _a_ on D, and under 1 on C
read _x_ on D.
To solve _b_√_̅a_ = _x_. Set 1 on C to _b_ on D, and under _a_ on B read
_x_ on D.
To solve √(_a_^3) = _x_. Treat as _a_√_̅a_.
To solve _a_√(_b_^3) = _x_. Treat as _a_√_̅b_ × _b_.
To solve (√_̅a_^3)/(_b_) = _x_. Treat as (√_̅a_ × _a_)/(_b_).
To solve √((_a_^3)/(_b_)) = _x_. Treat as (√_̅a_ × _a_)/(√_̅b_) =
√((_a_)/(_b_)) × _a_.
To solve √((_a_ × _b_)/(_c_)) = _x_. Set _c_ on B to _a_ on A, and under
_b_ on B read _x_ on D.
To solve (_a_ × _b_)/(√_̅c_) = _x_. Set _c_ on B to _b_ an D, and under
_a_ on C read _x_ on D.
To solve √((_a_^2 × _b_)/(_c_)) = _x_. Set _c_ on B to _a_ on D, and
under _b_ on B read _x_ on D.
To solve (_a_^2 × _b_^2)/(_c_) = _x_. Set _c_ on B to _a_ on D, and over
_b_ on C read _x_ on A.
To solve (_a_√_̅b_)/(_c_) = _x_. Set _c_ on C to _b_ on A, and under _a_
on C read _x_ on D.
To solve ((_a_ × √_̅b_)/(_c_))^2 = _x_. Set _c_ on C to _a_ on D,
and over _b_ on B read _x_ on A.