DECIMAL EQUIVALENTS OF 64ths.

The decimal fractions printed in large type give the exact value of the corresponding fraction to the fourth decimal place. A given decimal fraction is rarely exactly equal to any of these values, and the numbers in small type show which common fraction is nearest to the given decimal. Thus, lay off the fraction .1330 in 64ths. The nearest decimal fractions are .1250 and .1406. The value of any fraction in small type is the mean of the two adjacent fractions. In this instance the mean fraction is .1328, and as.1330 is greater than this, .1406 or will be chosen. In the same manner the nearest 64ths corresponding to the decimal fractions .3670 and .8979 are found to be 2 and 3, respectively.

MENSURATION.

In the following formulas, the letters have the meanings here given, unless otherwise stated.

D = larger diameter;

d

=

smaller diameter;

= radius corresponding to D;

" = radius corresponding to d;

p = perimeter or circumference;

area of convex surface area of flat surface which can be rolled into the shape shown;

area of entire surface = C+ area of the end or ends; area of plane figure;

=

3.1416, nearly ratio of any circumference to its diameter;

V volume of solid.

The other letters used will be found on the cuts.

The above letters refer to angles.

For a right-angled triangle, c being the

c = length of side opposite an acute angle of an oblique-angled triangle.

C = length of side opposite an obtuse angle

of an oblique-angled triangle.

C = Va2+b2+2be.

For a triangle inscribed in a semicircle; i. e., any rightangled triangle,

TRAPEZOID.

A =

h(a+b).

TRAPEZIUM.

Divide into two triangles and a trapezoid.

A = bh' + a(h' + h) + \ ch;

=

or, A [bh' + ch+a(h' + h)].

Or, divide into two triangles by drawing a diagonal. Consider the diagonal as the base of both triangles, call its length 7;

call the altitudes of the triangles h1 and h2; then A = l (h1 + h2).

*The perimeter of an ellipse cannot be exactly determined without a very elaborate calculation, and this formula is merely an approximation giving fairly close results.