Publisher's Synopsis
An excerpt from the beginning of the INTRODUCTION:
1. Object of Nomography.
We are all familiar with graph-drawing as a means of solving equations. But ordinary graphical methods are often inconvenient, because a separate graph is required for practically each equation we have to solve. Thus, to solve the quadratic equation
x2+x-2=0
we need to draw the graph y=x2+x and find where it is cut by the line y=2. To solve the equation x2+2x-2=0, we must draw the graph y=x2+2x and similarly for other values of the coefficient of x. The object of Nomography is to enable us to solve all equations of a given type by means of one diagram. Thus all quadratic equations of the type x2+ax+b=0 can be solved by means of one graph which can be drawn once for all. In the same way all cubic equations of, say, the form x3+ax+b=0 can be solved graphically by means of one diagram. Such a diagram is called a Nomogram. It is also the object of Nomography to enable us to find the value of a complicated expression graphically. Let us consider, e.g. , the formula for the pressure R in pounds on a flat plate normal to a passing current of air, viz.,
R=0.0194W*SV2 (lbs.),
where W is the weight of the air in pounds per cubic foot, S is the area of the plate in square feet, and V is the relative velocity of the air in feet per second. If the pressure has to be found for a number of different plates at various velocities, it is obviously convenient to have a diagram which, having been constructed once for all, can be used for any values of W, S, and V that are likely to occur.
In the present volume we shall consider in a simple manner how to construct and use nomograms for multiplication and division in formulae like the one for air pressure, as well as the more general methods applicable to easy algebraic and other equations. As an introduction to the nomograms for multiplication and division we shall consider first the construction and use of nomograms for addition and subtraction.