USEFUL FACTS AND FORMULAS.
One turn of the crank runs off 1 foot of film.
One foot of film contains 16 pictures.
The audience sees about 960 different pictures in every minute that a
film is being run.
The relative number of revolutions made by two pulleys connected
together by belting or friction is in proportion to their diameters.
The relative number of revolutions made by two gears connected together
is in proportion to their number of teeth.
A theater seat occupies from 4 to 5 square feet.
One 25-watt tungsten lamp or its equivalent provided for every 20 seats
will give fairly good illumination in a small theater.
3 to 5 watts per cubic foot will be required to heat small spaces by
electricity.
_Ohm’s Law._
Direct current equals e.m.f. divided by resistance.
Alternating current equals e.m.f. divided by impedance.
Electromotive force, d.c., equals current time resistance.
Electromotive force, a.c., equals current time impedance.
Resistance equals e.m.f. divided by current.
Impedance equals e.m.f. divided by current.
The joint resistance of two conductors connected in parallel is equal
to the product of their resistances divided by their sum:
_r_ = (_r_₁ × _r_₂) ÷ (_r_₁ + _r_₂})
The joint resistance of any number of resistances connected in parallel
is the reciprocal of the sum of the reciprocals. The reciprocal of a
number is 1 divided by that number:
1
_r_ = --------------------------
1 1 1
---- + ---- + ---- + .....
_r_₁ _r_₂ _r_₃
The total resistance of a number of resistances in series is equal to
the sum of all of them:
_r_ = _r_₁ + _r_₂ + _r_₃ + .....
The heating of a rheostat is proportional to the square of the current
it carries.
Drop in voltage is proportional to the product of the current and
resistance for a direct-current circuit, and the product of current and
impedance for an alternating-current circuit.
If a reactance is used in place of a rheostat in an alternating-current
circuit, the loss of energy is greatly reduced.
If the same intensity of illumination is to be provided for pictures of
different sizes, the amperage must vary about as:
(_W_ × 1.2)²
where _W_ is the width of picture on screen.
For a given power the current in conductors is:
_W_
for direct current _I_ = ---
_E_
_W_
for single-phase a.c. _I_ = -------------
_E_ × _p. f._
_W_
for two-phase a.c. _I_ = .5 × -------------
_E_ × _p. f._
_W_
for three-phase a.c. _I_ = .58 × -------------
_E_ × _p. f._
in which _I_ is the current in amperes, W is the watts, E is the
voltage, and p. f. is the power factor.
_Lens Formulas._
To find the size of a picture obtainable under given conditions and
lens: _Multiply distance from center of lens to screen by one dimension
of slide or film and divide by e.f. focal length of lens, taking all
measurements in inches._
Example: Slide 2-3/4 inches. Length of throw 360 inches. e. f. 10 inches
2-3/4 × 360 ÷ 10 = 99 inches.
To find focal length needed for a given slide or film to produce a given
size of picture: _Multiply slide or film dimension by length of throw
and divide by dimension of picture, taking all measurements in inches._
Example: Same dimensions as above:
2-3/4 × 360 ÷ 99 = 10 inches.
To find length of throw needed to obtain a certain size of picture:
_Multiply required picture dimension by focal length of lens and divide
by slide or film dimension._
Example: Same dimensions as above:
99 × 10 ÷ 2-3/4 = 360 inches.
To find slide size necessary to produce a certain size of picture under
fixed conditions: _Multiply focal length of lens by size of picture and
divide by length of throw._
Example: Same dimensions as above:
10 × 99 ÷ 360 = 2-3/4 inches.
_Measurement of Surfaces._
To find the area of a parallelogram: _Multiply the base by the
altitude._
To find the area of a triangle when base and altitude are given:
_Multiply the base by the altitude and take half the product._
To find the area of any angular surface: _Divide it into triangles and
find the area of the different triangles and add them together._
To find the circumference of a circle: _Multiply the diameter by π; or
3.1416._
To find the diameter of a circle when the circumference is given:
_Divide the circumference by π, or 3.1416._
To find the area of a circle when the radius is given: _Multiply the
square of the radius by 3.1416._ When diameter is given: _Multiply the
square of the diameter by .7854._
To find the radius of a circle when the area is given: _Divide the area
by 3.1416 and extract the square root of the quotient._
_Measurement of Solids._
To find the lateral area of a right prism: _Multiply the perimeter of
the base by the altitude._
To find the lateral area of a right cylinder: _Multiply the
circumference of the base by the altitude._
To find the volume of a cylinder or prism: _Multiply the area of the
base by the altitude._
To find the lateral area of a right pyramid: _Multiply the perimeter of
the base by the slant height and take half the product._
To find the lateral area of a cone: _Multiply the circumference of the
base by the slant height and take half the product._
To find the volume of a pyramid or cone: _Multiply the area of the base
by the altitude and take one-third of the product._
To find the surface of a sphere: _Multiply the square of the diameter by
3.1416._
To find the volume of a sphere: _Multiply the cube of the diameter by
one-sixth of 3.1416 or .5236._
In a right-angled triangle, the sum of the squares of the base and the
perpendicular equals the square of the hypotenuse. To find the length of
the hypotenuse: _Extract the square root of the sum of the squares of
the base and the perpendicular._
To find the base or the perpendicular: _From the square of the
hypotenuse subtract the square of the other given side and extract the
square root of the remainder._