section, and in the introduction of rules for determining their centres of gravity, he has submitted some features of so new and useful a purpose, as to entitle him to the attention of those upon whom he confidently relies for patronage.

New York, April 1st, 1858.

Elipsoid of Revolution (Spheroid).. 203 | Ullaging of Casks

EXPLANATIONS OF CHARACTERS

Used in the following Calculations, etc., etc.

4

Equal to, as 12 inches1 foot, or 8×8=16×4.
Plus, or more, signifies addition; as 4+6+5=15.
Minus, or less, signifies subtraction; as 15-5=10.
Multiplied by, or into, signifies multiplication; as
8×9=72. axd, a.d, or ad, also signify that a
is to be multiplied by d.

Divided by, signifies division; as 72÷9=8.
Is to,

So is,
To,

signifies Proportion, as 2:4::8:16; that is, as 2 is to 4, so is 8 to 16.

Radical sign, which, prefixed to any number, signifies that the square root of that number is required; as 9, or Vaxb. The degree of the root is indicated by the number placed over the sign, which is termed the index of the root, or radical; as V, V, etc.

added or set superior to a number, signifies that that number is to be squared, cubed, etc.; thus 42 means that 4 is to be multiplied by 4; 43, that it is to be cubed, as 43 is 4x4x4-64. The power, or number of times a number is to be multiplied by itself, is shown by the number added, as 2 3 4 5 etc.

The vinculum, or bar, signifies that the numbers are to be taken together; as 8 2+6=12, or 3x5+3=24.

Decimal point, signifies, when prefixed to a number, that that number has for its denominator some power of 10; as .1 is,.155 is 155 etc. Difference, signifies, when placed between two quantities, that their difference is to be taken.

L

1440

Δ

() [ ]

por π

Signify Degrees, minutes, seconds, and thirds.

Signifies angle.

Signifies perpendicular.

Signifies triangle,

Signifies square, as inches.

Signify inequality, or greater than, and are put be-
tween two quantities; as ab reads a greater
than b.

Signify the reverse; as a reads a less than b.
Signifies therefore or hence.
Signifies because.

Parentheses and brackets signify that all the fig-
ures within them are to be operated upon as
if they were only one; thus (3 + 2) × 5 = 25;
[3+2]x5=25.

Is used to express the ratio of the circumference of a circle to its diameter = 3.1415926, etc.

A A A" A" Signify A, A prime, A second, A third, etc.

Signify that the formula is to be adapted to two distinct cases.

— 1, a—2, a—3, etc. Denote inverse powers of a, and are equal to

sin. -1a, cos. -1a, etc. Signify the arc or angle, the sine or cosine, etc., of

which is a, the arc or angle being expressed in terms of the radius, as the unit, unless otherwise stated. If A° denotes the arc or angle in

Set superior to a number, signify the square or cube root, etc., of the number; as 2 signifies the square root of 2.

Set superior to a number, signify the square or cube root, etc., of the 4th power, etc., etc.

Set superior to a number, signify the tenth root of the 17th power, etc., etc.