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"If y be the object the image appears to a normal eye situated behind the system L with passive accommodation at a very great distance under the angle w'. Since H' P= F O, = y, from the focal length of the simple microscope is the image side focal length." —Encyclopaedia Britannica, 1910

Optical Position and Size of Image Through Magnifying Glasses

"If y be the object the image appears to a normal eye situated behind the system L with passive accommodation…

"Since the valve must move a distance equal to the outside lap before admission can take place, it is evident that the eccentric can no longer be at right angles to the crank at the beginning of the stroke, but must be ahead of the right—angle point by an amount equal to AOC." —Derr, 1911

Valve with Lap of Steam Engine at Extreme Left with Exhaust Ports Open

"Since the valve must move a distance equal to the outside lap before admission can take place, it is…

"If the inside lap is increased, the valve must move farther before released occurs and the crank angle would be greater than illustrated. On the return of the valve to the dotted position, the port will close earlier and make an earlier compression. Decreasing inside lap will cause earlier release and later compression." —Derr, 1911

Steam Engine Valve with Lap Steam Where Slide Valve Moved to Open Position

"If the inside lap is increased, the valve must move farther before released occurs and the crank angle…

"If a jet with the velocity V strikes the bucket at an angle a, its velocity A B could be resolved into two components —one C B at right angles to the shaft, and one C A parallel to the shaft. The one at right angles to the shaft, commonly known as the velocity of whirl, would produce a rotative impulse equal to Vcosa, and V1, the velocity of the vane necessary for maximum efficiency." —Derr, 1911

Jet Steam Stream Hitting Curved Vane

"If a jet with the velocity V strikes the bucket at an angle a, its velocity A B could be resolved into…

A squared nanogram star with 8 points. The star is created by using two four sided squares on top of one another at an angle.

Squared Eight Point Nanogram Star

A squared nanogram star with 8 points. The star is created by using two four sided squares on top of…

Used for mowing and reaping, consisting of a long curved blade fixed at an angle to a long bent handle.

Attachment Scythe

Used for mowing and reaping, consisting of a long curved blade fixed at an angle to a long bent handle.

Indicator that establishes the horizontal when a bubble is centered in a tube of liquid

Construction Level

Indicator that establishes the horizontal when a bubble is centered in a tube of liquid

Portable locks used to protect against theft, vandalism, sabotage, espionage, unauthorized use, and harm. They are designed to protect against some degree of forced and surreptitious entry.

Early Use Padlock

Portable locks used to protect against theft, vandalism, sabotage, espionage, unauthorized use, and…

The four fundamental forms of resistance: A, to tension; B, to compression parallel to fiber; C, to compression at right angle to fiber; D, to transverse tension; F, fiber of wood. Arrows indicate direction of force.

The Forms of Resistance

The four fundamental forms of resistance: A, to tension; B, to compression parallel to fiber; C, to…

"The highest of the White Mountains is Mount Washington. We can go in an ordinary train to the foot of this mountain, and from there can ride to its summit over one of the oddest little railroads in the world. The mountain is more than a mile high, and this little railroad goes right up to its top. In some places the track is so steep that it looks more like a ladder than a railroad, and the cars which go up it are at times at such an angle that you would think they would slide to the bottom."—Carpenter, 1898

Railroad Up Mount Washington

"The highest of the White Mountains is Mount Washington. We can go in an ordinary train to the foot…

A side angle view of a potato warehouse.

Potato Warehouse

A side angle view of a potato warehouse.

This span roof frame is one of the most popular. The sashes are held open at any angle required. These frames are best suited to remain where placed permanently.

Span-Roof Frame

This span roof frame is one of the most popular. The sashes are held open at any angle required. These…

Phyllanthus chantrieri flowers are brick-red with pale yellow hairs. The flowers bloom in summer. Branches form a right angle with the stem.

Phyllanthus Chantrieri

Phyllanthus chantrieri flowers are brick-red with pale yellow hairs. The flowers bloom in summer. Branches…

<I>Artabotrys uncinatus</I> is a climbing shrub with branches at a wide angle. The leaves are oblong and taper to a point. The flowers have six petals and are brownish red.

Artabotrys Uncinatus

Artabotrys uncinatus is a climbing shrub with branches at a wide angle. The leaves are oblong and taper…

A cross-over where two different lines of trolley wire cross at right angles.

Cross-over

A cross-over where two different lines of trolley wire cross at right angles.

A cross-over where two different lines of trolley wire meet at acute angles.

Cross-over

A cross-over where two different lines of trolley wire meet at acute angles.

When pipes are bent at ninety degree angles, a rounded bend is best as shown along with a radius as large as possible to increase discharge.

Pipe Diameter

When pipes are bent at ninety degree angles, a rounded bend is best as shown along with a radius as…

A gimbals is a contrivance designed to keep a marine compass, chronometer, lamp, or other instrument in the horizontal position on board ship, notwithstanding the rolling and pitching of the vessel. The instrument is suspended in the diametral axis of a ring, which is again suspended in the diametral axis of another ring, the two axes being at right angles to one another. This illustration shows a diagram of a gimbals, showing the angle of the ship (A), the perpendicular axes of the rings, and the compass suspended horizontally in the gimbals (B).

Gimbals (Diagram)

A gimbals is a contrivance designed to keep a marine compass, chronometer, lamp, or other instrument…

In Joinery, a common dovetail joint is the most efficient for joining two boards that meet at a right angle. The edges of each board are cut into a series of alternate projections and indentations, which fit into each other, and which by the bevel of their sides prevent the boards from drawing apart.

Common Dovetail Joint

In Joinery, a common dovetail joint is the most efficient for joining two boards that meet at a right…

A kaleidoscope is an optical instrument invented by Brewster about 1815. It became very popular as a toy. It consists essentially of a tube, within which are fixed longitudinally two mirrors at a certain angle ACB -- any even submultiple of 360º, in practice generally 60º -- an eyepiece at one end, and an object box containing fragments of colored glass at the other. On shaking the instrument, an infinite series of always symmetrical patterns is presented.

Kaleidoscope

A kaleidoscope is an optical instrument invented by Brewster about 1815. It became very popular as a…

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances from two fixed points is the square of half the distance between the points. It is a particular case of the Cassinian oval and resembles a figure 8. When the line joining the two fixed points is the axis of x and the middle point of this line is the origin, the Cartesian equation is the fourth degree equation, (((x^2)+(y^2))^2)=2(a^2)((x^2)-(y^2)). The polar equation is (ℽ^2) = 2(a^2)cos(2θ). The locus of the feet of the perpendiculars from the center of an equilateral hyperbola to its tangents is a lemniscate. The name lemniscate is sometimes given to any crunodal symmetric quartic curve having no infinite branch. The name is also sometimes given to a general class of curves derived from other curves in the way that the above is derived from the equilateral hyperbola. With these more general definitions of the lemniscate the above curve is called the lemniscate of Bernoulli.

Lemniscate

A Lemniscate is, in general, a curve generated by a point moving so that the product of its distances…

A 90 degree angle connector.

Angle Connectors

A 90 degree angle connector.

Ritchie Liquid Compass. US Naval compasses have the degree around the rim marked from 0 to 360, east being 90, south being 180, etc.

Compass Card

Ritchie Liquid Compass. US Naval compasses have the degree around the rim marked from 0 to 360, east…

An example of a simple machine. In the figure, AC is the included plane, CB is the height of the plane, BA is its base, and BAC is the angle of inclination or elevation. The power necessary to sustain any weight on an included plane is to the weight as the height of the plane to its length, or as CB to CA.

Inclined Plane

An example of a simple machine. In the figure, AC is the included plane, CB is the height of the plane,…

A positive slope line making a 60 degree angle with the x-axis.

Straight Line

A positive slope line making a 60 degree angle with the x-axis.

Finding the angle between two lines whose equations are in intercept form.

Angle

Finding the angle between two lines whose equations are in intercept form.

Transforming from one set of rectangular axes to another with the same origin, but different direction.

Rectangular Axes

Transforming from one set of rectangular axes to another with the same origin, but different direction.

Angles on a modified coordinate plane.

Oblique Axes

Angles on a modified coordinate plane.

Double angle milling cutter.

Double Angle

Double angle milling cutter.

A scriber block is used to layout lines at a set height from the base, thus its second name surface height gauge or just "surface gauge". The work piece is held against an angle plate so that it is perpendicular to the surface plate, the scriber block is then adjusted to the required height and used to scribe a line parallel with the table, by sliding the block along the table's surface.

Scriber Block

A scriber block is used to layout lines at a set height from the base, thus its second name surface…

Cast metal box parallel with finished surfaces used to for set-ups in machining, layout, and inspection.

Box Parallel

Cast metal box parallel with finished surfaces used to for set-ups in machining, layout, and inspection.

A fleet of three ancient Anglo-Saxon ships, each with wind filling the lone sail. Each ship has a dragon head at the bow. The front ship has a curled, dragon tail at the stern. Several men occupy the decks of the ships. The ship of the right has a head on a pike displayed at its bow. A crow sits on and pecks at the head. Another crow sits on the mast of that ship.

Anglo-Saxon Ships with Wind in the Sails

A fleet of three ancient Anglo-Saxon ships, each with wind filling the lone sail. Each ship has a dragon…

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." &mdash;Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

"Nautically, a block with two sheaves, whose axes are at right angles to each other, used for the buntlines of the courses." &mdash;Whitney, 1889

Shoe Block

"Nautically, a block with two sheaves, whose axes are at right angles to each other, used for the buntlines…

"The curve of sines, in which the abscissas are proportional to an angle, and the ordinates to its sine." -Whitney, 1889

Sinusoid or Sine Wave

"The curve of sines, in which the abscissas are proportional to an angle, and the ordinates to its sine."…