DIAGONAL. polyhedral vertices. ( u"4 — 3- (4 — 2) ■ Thus the cube has 6
- 4 diagonals.
-]■■
1 '■^'^'
DIAGONAL SCALE. A system of lines by
means vt which fractional parts of a unit,
usually hundrcilths, may be laid down or meas-
ured with eompassos (q.v.). Such scales are of
particular value in plotting maps from given
data. (8ee Surveyixc.) In the fijnire the line
from to 10 represents one inch. The diagonal
line which ends at cuts off on the lines above
fractions of an inch, .j^^, ^Ic, tst • ^^^ *° °°'
The next diagonal line cuts off ■jViSij'Blr
of an inch : the next -f^'^, -jsV- ... of an
inch ; and so on. A pair of compasses may be
set by such a scale so that its points are 1.01,
1.02,' . . . l.U, 1.12, . . . 1.21, 1.22,
. . . 1.90 inches apart, and thus be used to
plot. chains and links on a map of a given scale.
DIAG'OKAS (Gk. Aia-/6pa(). A Greek poet and
philosopher. He was born in -Slelos. an island
of the Cyclades. and flourished in the fifth cen-
tury B.C., but beyond his reputation for atheism,
little is known regarding his career. He is
said to have been a disciple of Deniocritus of
Abdera, and to have resided during the more
important part of his life in Athens, where
he won considerable distinction as a lyric poet.
but only the scantiest fragments of his verses
survive. He is better known to the later world,
however, as an atheist, and as such is alluded
to by Aristophanes in the Clouds ( n.c. 423 ) ,
and the Birds (B.C. 414). Tiether he was
a thorough-going disbeliever in the gods and
religion or simply a scoffer at the current re-
ligious practices and superstitions cannot now
be determined, but in any case he was banished
eventually for his opinions, and died in Corinth.
Besides his lyrics, he is said to have written a
work in two books. (
Greek characters), exposing the
sacred Mysteries (q.v.). Consult Zellen, P/iitos-
ojihir (Iff (Iriechen i. (1802).
DIAGRAM (T.at. diarjratnma, Gk. iiaypa/ifia, figure from fiaypai^civ, diagraphcin, to describe, from dt&j dia. through + yp('i<!>civ, graphcin, to write). A figiire so drawn that its geometric relations may illustrate the relations between other quantities. The area of a rectangle is the product of the numbers representing its length and breadth; the diagram of a rectangle is the visible symbol, corresponding to the equation az=bl; and. by analogy, the rectangle may be used to symbolize any quantity which is the product of two factors. Similarly, a pnrallclopi- ped may symbolize any quantity which is the product of three factors. The purpose of many mathematical diagrams 19.-; DIAGRAM. is simply illustration, and it is necessary only that the idea be clearly presented, accuracy of drawing being relatively unimportant — e.g. those showing electric connections require only a prop- er representation of the parts in their association w ith one another. Other diagrams, as those drawn for workmen by architects and engineers, are in- tended to furnisli magnitudes or distances by actual measurement, and their execution cannot be too accurate. A pru/ilc diagram shows such an outline as would lie formed, for example, if a hill were cut through l)y a vertical plane, and the material on one side of the plane were removed. Evi- dently a succession of such profiles might be laid on the same sheet of paper, the lines being dis- tinctly drawn, and the whole would serve to com- pare several vertical profiles of the same mass. It is not necessary that vertical and horizontal measurements should conform to the same scale, provided each series of measurements is consist- ent in itself. Thus fieographic profiles, which include upon a single sheet the outlines of entire continents and ocean beds, usually luive the ver- tical measurements on a scale several times aa great as that used for horizontal distances; otherwise the diagram would be made incon- veniently long, or the heights would be incon- spicuously small. A topographer's contour map exhibits a series of curves, such as would be formed if a series of horizontal sections were made, and the outlines carefully drawn on paper. The drawing really shows the horizontal projec- tions of the contour lines upon a surface parallel to the system. In mechanical drawings, particu- larly those designed to guide workmen in the construction of machinery, several connected views of the same oljject are required, each view giving some information which the others can- not furnish. Suppose three planes perpendicular to one another, like the bottom, one side, and one end of a rectangular box. and let an object, as a hexagonal nut. be placed within the tri- hedral angle thus formed. Looking from the front, we see an image of the nut projected against the back of the box: from the side, a different image is seen against the end of the box ; from above, a third form appears against the bottom, while from some or all of these fig- ures the necessary measurements may be ob- tained. If now the end of the box is swmig out- ward into the plane of its back, and then both together are laid back into the plane of the bottom, we have the three coexistent drawings in one plane, and they may be transferred to, or be constructed on, one sheet of paper. In many cases the same points will find representa- tion upon each diagram, and the fact may be indicated by the same letter: while the eye may be led from one position of the point to another by lines distinctively drawn to show that they are merely guides and not parts of the outline. See Geomktuy, Descriptive. Many devices have been invented by which diagrams illustrating natural phenomena may be automatically described. The physical ex- periment which produces the parallelogram of forces is a familiar example. As a more general illustration, suppose a spring di/nanwmeter (q.v.) placed ifhcre it may ri'ceivc tin- dratight of a horse when moving a carriage. Let the move- ment of the spring b" shown by an index whose motion is back and forth along a line in the
