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_.