The unit of weight is the gram. 1 gram=.03527 oz. Avoirdupois.

USE OF FORMULAS

A formula, as used in technical books and papers, may be defined as a rule in which letters and symbols are used in place of numbers or words. A formula, then, is a short way of expressing a rule, and is more convenient, as it shows at a glance the operations to be performed.

For example, the volume of a rectangular solid is equal to the product of its three dimensions, length, width, and height. The same statement would be expressed by the formula, V=LWH.

The signs of addition, subtraction, multiplication and division are used in formulas in the same way as in arithmetic except that the sign of multiplication between two letters is usually omitted; as V-LWH means V=LXWXH.

In working out or solving a formula, the numerical values of all but one of the letters must usually be known. These values are substituted for their respective letters and the value of the remaining letter may then be easily found.

Example.

Find S.

In the formula Sgt2.

Let g=32, t=5.

Solution. By formula, S of 32X52=16×25=400.

=

Every formula is in reality an algebraic equation, and a knowledge of some of the simpler principles of equations will be of great assistance in working out formulas.

The equation may be illustrated by reference to a scale pan with equal arms. If equal weights, say five pounds, are put in each pan, they will just balance. If two pounds is

added to one pan, two pounds must be added to the other pan, and if three pounds is taken from one pan, three pounds must also be taken from the other or the pans will not balance.

The same is true of the

equation; whatever oper

ation is performed on one side, the same operation must be performed on the other side.

The following operations may be performed on an equation without changing its value.

I The same number may be added to each side..

II The same number may be subtracted from each side.
III Each side may be multiplied by the same number.
IV Each side may be divided by the same number.

V The same root may be taken of each side.
VI Each side may be raised to the same power.

TRANSPOSING TERMS

Example. Five added to five times a certain number is equal to 15. What is the number?

Solution.

Let x=the unknown number. Then the state

ment of the equation will be 5x+5=15.

But since by (II) 5 may be taken from each side, the statement then becomes, 5x=10.

By (IV) x=2.

In the above example the statement: