relates to the regulation of diet. The ideal diet is clearly that which,
without burdening the viscera uselessly, furnishes all necessary nutritive
elements, with due consideration for special physiological conditions in
any given case. Under the head of _Aliment_ the physiological properties of
various foods have already been considered theoretically in respect of
their capacity to supply physical waste in nitrogenous and non-nitrogenous
matter. (See _Aliment_.) No single substance contains the elements needed
to replace this waste in their requisite proportions, and a mixed diet is
therefore necessary. For instance, to secure the required amount of carbon
a man would need to eat about 4 lb. of lean beef, while 1 lb. would yield
all the nitrogen required; thus, apart from the labour of digesting 4 lb.
of beef, the body would be compelled to get rid of the excess of nitrogen.
Bread, on the other hand, has carbon in abundance, but is deficient in
nitrogen; so that by uniting 2 lb. of bread with 3/4 lb. of lean meat, the
due proportion of carbon and nitrogen is satisfactorily supplied. Milk and
oatmeal taken together also contain nitrogenous and non-nitrogenous
substances in nearly the required proportions. A certain proportion of
saline matter is also necessary. The nature of the food most suitable for a
healthy man is dependent in part upon general conditions, such as climate
and season, and in part upon special conditions of individual habit. The
inhabitants of the Arctic regions need large quantities of oleaginous food;
those of the Tropics live chiefly on starchy products. With increased
activity and exertion, as in training, an increase in the nitrogenous foods
becomes necessary. In a state of health we need not draw hairbreadth
distinctions as to the superior salubrity of the several sorts of diet, the
quantity rather than the quality of food being the main consideration.
Those persons who have been most remarkable for health and long life have
generally been contented with two moderate meals a day, which are certainly
quite sufficient during a state of health. In various countries the
breakfast generally consists of tea, coffee, or cocoa, with a certain
proportion of bread and butter; persons with delicate digestive powers, or
who lead a sedentary life, cannot with safety or comfort eat animal food
_constantly_ to breakfast. At dinner all made-dishes highly spiced, such as
curries, turtle-soup, &c., as provoking appetite, are hurtful; and the
custom of late dining is not to be commended. Stewed and boiled meats are
more difficult to digest than meat cooked by fire alone. The flesh of young
animals seems to be more difficult of digestion than that of old; and the
flesh of tame than that of wild animals. All sorts of fat meat must be
taken in smaller quantities. Hence, also, ham, bacon, and salted meats
cannot be eaten in such quantities as the tender flesh of poultry. Fish has
the advantage of being easily soluble. All boiled vegetables are in general
easy of digestion; raw vegetables and salads are rather more difficult.
Fruit should be taken in the forenoon rather than after a hearty meal. The
moderate use of fermented liquors is far from being invariably an evil, but
the smaller the quantity habitually used the better in the majority of
cases.
In all diseases attended with much fever or quickness of pulse the stomach
loathes animal food, and there is generally a great increase of thirst, to
quench which water, either quite cold, or iced, or tepid, or rendered acid,
may be freely indulged. Infusions, too, of barley, sage, balm, &c., may be
taken. In chronic diseases attended with hectic fever, milk is the most
proper diet. The best food for infants is, of course, their mother's milk;
but whenever they begin to cut teeth a little animal food, such as
soft-boiled eggs, beef-tea, and even chicken minced very fine, may be
given. Many infants suffer from having too much sugar given them in their
food.--BIBLIOGRAPHY: R. H. Chittenden, _Physiological Economy in
Nutrition_, and _Nutrition of Man_; Hutchison, _Food and Dietetics_; Lusk,
_The Science of Nutrition_.
DIETRICH (d[=e]'tri_h_), Christian Wilhelm Ernst, a German painter and
engraver, born in 1712, died in 1774. He studied under his father, and
afterwards under Alexander Thiele at Dresden, where he became court-painter
and professor in the academy. He adopted several different manners,
successfully imitating Raphael and Mieris, Correggio, and Ostade.
DIETRICH OF BERN (d[=e]'tri_h_), the name under which Theodoric the Great,
King of the Ostrogoths, appears in the old German legends. Bern stands for
Verona, his capital.
DIEU, or D'YEU (dy_eu_; ancient INSULA DEI), an island off the west coast
of France, department of Vend['e]e. It is inaccessible on the west side,
but on the east has a tolerable harbour defended by batteries. The chief
industry is fishing. There are four lighthouses on the island. Pop. 3809.
DIEU ET MON DROIT (dy_eu_ e mo[n.] drw[:a]; 'God and my right'), the
battle-cry of Richard I at the battle of Gisors (1198), signifying that he
was not subject to France, but owed his power to God alone. The battle-cry
was then adopted as the motto of the arms of England, and revived by Edward
III in 1340, when he claimed the crown of France. Except during the reigns
of Elizabeth and Anne, who used the motto _Semper eadem_, and of William
III, who personally used _Je maintiendray_, it has ever since been the
royal motto of England.
DIEZ (d[=e]ts), Friedrich Christian, German philologist of the Romance
languages, born in 1794, died in 1876. Having qualified himself as a
lecturer at Bonn, he was appointed professor of the Romance languages there
in 1830. His work stands in much the same relation to the Romance dialects
which the researches of Grimm occupy with respect to German dialects. In
addition to various works on the poetry of the Troubadours, he published a
very valuable _Grammatik der Romanischen Sprachen_ (1836-42, translated
into English by Cayley in 1863), and an _Etymologisches W[:o]rterbuch der
Romanischen Sprachen_ (1853).
DIFFERENCE, a stock-exchange term. When stock is bought or sold merely as a
speculation for the rise or fall, with no intention of the buyer to 'take
up' the stock, or of the seller to deliver it, the 'difference' is the
movement in price which may take place between the date of the transaction
and the following 'settling-day'. If the price falls, the buyer has to pay
the difference upon 'carrying over' his purchase to the next account; if it
rises, the seller is at the loss. Since the first weeks of the European War
all stock-exchange transactions have been made, in theory at least, for
cash, and speculative business of this nature has been consequently much
reduced.
DIFFERENCES, FINITE, a calculus much used in actuarial work, which deals
with a series of numbers by considering the differences of the successive
terms.
If u_1, u_2, u_3, ... are the terms of the series, then u_2 - u_1, u_3 -
u_2, u_4 - u_3,... form another series called the series of first
differences. The notation used is u_2 - u_1 = [Delta]u_1, u_3 - u_2 =
[Delta]u_2,...
These first differences may themselves be differenced, giving the second
differences [Delta]u_2 - [Delta]u_1, [Delta]u_3 - [Delta]u_2, ..., which
are written [Delta]^2u_1, [Delta]^2u_2,...
Similarly, we form the third differences [Delta]^3u_1 = [Delta]^2u_2 -
[Delta]^2u_1, and so on.
As an example, let the original series be the cubes of the natural numbers.
1 8 27 64 125 216 / 343 512
7 19 37 61 91 / 127 169
12 18 24 30 / 36 42
6 6 6 / 6 6
0 0 / 0 0
Here we begin by writing down the series of cubes as far, say, as 216;
beneath these we write the first differences 8 - 1 = 7, 27 - 8 = 19, &c. We
thus obtain the part of the table to the left of the diagonal line.
We observe that the third differences are constant, each being 6. (It is
easy to prove generally that the nth differences of the series, 1^n, 2^n,
3^n,..., are constant.) Knowing the third differences, we can now extend
the table as far as we wish to the right of the diagonal line. We get first
6 + 30 = 36, 36 + 91 = 127, 127 + 216 = 343. We infer that 7^3 = 343.
Since u_1 - u_0 = [Delta]u_0, we have u_1 = u_0 + [Delta]u_0 = (1 +
[Delta])u_0.
Similarly, u_2 = (1 + [Delta])u_1 = (1 + [Delta])^2u_0; and, generally,
u^x = (1 + [Delta])^xu_0
= {1 + x[Delta] + (x(x-1)/(1x2)) x [Delta]^2 + ...}u_0
= u_0 + x[Delta]u_0 + (x(x-1)/(1x2)) x [Delta]^2)u_0 + ...
a formula much used by calculators, and known as Newton's interpolation
formula.
The above symbolic method of proof only applies when x is a positive
integer, but the result is used in practice even for fractional values of
x, as in most cases the high differences become negligible.
If n is a positive integer, it is easy to prove that
[Delta]^nu_x = u_{x+n} - nu_{x+n-1} + ((n(n-1))/(1x2))u_{x+n-2} - ...
If the nth differences vanish, or are negligible, this gives
0 = u_{x+n} - nu_{x+n-1} + ((n(n-1))/(1x2))u_{x+n-2} -... +(-1)^nu_x,
another useful interpolation formula, by which we can calculate any missing
term of a series.--BIBLIOGRAPHY: G. Boole, _Finite Differences; Textbook of
the Institute of Actuaries_.
DIFFERENTIAL EQUATION, an algebraical relation involving derivatives or
differentials. Examples:
d^2z/dt^2 = g: ydx + xdy + zdz = 0.
An _ordinary_ differential equation involves only one independent variable,
a _partial_ differential equation involves more than one. Examples of
ordinary equations:
d^2y/dx^2 + (1/x)dy/dx + y = 0; d^2x/dt^2 + a(dy/dt) + px + qy = 0.
Examples of partial differential equations:
x(dz/dx) + y(dz/dy) = nz; d^2u/dx^2 + d^2u/dy^2 + d^2u/dz^2 = 0.
Equations, whether ordinary or partial, can also be classified as _linear_
or _non-linear_. A linear equation is a rational integral equation of the
first degree in the dependent variable or variables and their derivatives.
The equation
x^2 d^2y/dx^2 + x dy/dx + (x^4 + 1)y = 0
is linear, but
(dy/dx)^2 = xy and y dy/dx = x^2
are non-linear. The _order_ of an equation is the order of the highest
derivative or differential which it contains. Of the three equations last
written, the first is _linear of the second order_, the other two are of
the _first order and second degree_. To _integrate_ a differential equation
or system of equations is to find a relation or relations among the
variables, equivalent to the given equation or equations. Thus the integral
of
d^2z/dt^2 = g is z = 1/2gt^2 + At + B,
where A and B are _arbitrary constants_. An ordinary equation of the _n_th
order with one dependent variable has exactly _n_ arbitrary constants in
its complete integral, or solution. In a practical problem the arbitrary
constants are determined by the _initial_, or _boundary_, _conditions_. The
solution of d^2z/dt^2 = g, e.g. is completely determinate if the values of
z and dz/dt when t = 0 are given. The solution of _partial_ equations may
involve arbitrary _functions_, which become definite when proper initial or
boundary conditions are assigned. Thus the equation du/dx = du/dt has for
its complete solution u = [phi](x + t), where [phi] may be a function of
any form whatever; if now we are given that, when t = 0, u = a given
function f(x), we obtain f(x) = [phi](x), so that the solution required is
u = f(x + t). Certain ordinary linear equations of the second order are
specially important, both from the beauty of their theory and from their
usefulness in Mathematical Physics. Some of these equations are: Bessel's
equation, Legendre's equation, the hypergeometric equation, Mathieu's
equation, Lam['e]'s equation. Linear partial equations of the second order
are fundamental in Physics. Such are: Laplace's equation,
d^2V/dx^2 + d^2V/dy^2 + d^2V/dz^2= 0;
the wave equation,
d^2V/dt^2 = c^2(d^2V/dx^2 + d^2V/dy^2 + d^2V/dz^2);
the equation of conduction of heat,
dV/dt = k(d^2V/dx^2 + d^2V/dy^2 + d^2V/dz^2).
These involve one dependent variable only. Equations with several dependent
variables occur in Elasticity, Electrodynamics, and Hydrodynamics. A
notable feature of the hydrodynamical equations is that they are not
linear.
No general rules exist enabling us to deal with a differential equation
taken at random, and only a few types have been completely solved. Of
soluble equations, the most important are those which are _linear with
constant coefficients_.
_Example 1._ d^2x/dt^2 - 7dx/dt + 12 = 0. To solve this, try x = e^{mt}. We
find e^{mt}(m^2 - 7m + 12) = 0. Thus m = 3 or 4. It is now easy to show
that x = Ae^{3t} + Be^{4t} is a solution, where A and B are arbitrary
constants. This is the general solution. We can determine A and B if the
values of x and dx/dt are given for a definite value of t, say t = 0.
_Example 2._ d^2y/dt^2 = c^2 d^2y/dx^2. Try y = e^{lx + mt}. We find m^2 =
c^2l^2, or m = +/-cl. Hence y = Ae^{l(x + ct)} + Be^{l(x - ct)} is a
solution for all values of A, B, l; so, also, is the sum of any number of
terms of similar forms. We may infer that the general solution is
y = f(x + ct) + F(x - ct),
where f and F are arbitrary functions. It is only in exceptional cases that
an equation can be solved, as in these two examples, by an analytical
formula; indeed, differential equations are the most fertile source of new
functions in analysis. But, as in the analogous cases of algebraic
equations and definite integrals, it may be quite possible to find, by
methods of approximation, an arithmetical solution which is sufficient for
the purpose in hand.--BIBLIOGRAPHY: H. T. H. Piaggio, _Differential
Equations_; J. M. Page, _Ordinary Differential Equations_; A. R. Forsyth,
_A Treatise on Differential Equations_; E. T. Whittaker and G. N. Watson,
_Modern Analysis_.
DIFFRAC'TION, a term applied to the bending that rays of light undergo in
passing close to the edge of an opaque body. Thus when a beam of direct
sunlight is admitted into a dark room through a narrow slit, and falls upon
a screen placed to receive it, there appears a line of white light bordered
by coloured fringes; these fringes are produced by diffraction, and in the
case given it may be seen that the red or long-wave rays are diffracted
more than the blue rays. See _Interference_.
DIFFU'SION, the gradual mixing of gases, liquids, or solids when brought
into direct contact. When a block of lead is placed on a block of gold,
with their smooth surfaces in close contact, it is found that, after
several weeks, gold has diffused into the lead, and lead into the gold. In
the case of gases, when a jar of oxygen and a jar of hydrogen are connected
together by a tube or opening of any kind, they rapidly become mixed; and
their mixture does not depend on gravity, but takes place in opposition to
that force, as may be shown by placing the jar of hydrogen gas above the
other. Oxygen is sixteen times heavier than hydrogen, bulk for bulk, but
the heavier gas moves upwards and the lighter downwards, and the process of
intermixture, or _diffusion_, goes on till the two gases are apparently
equably distributed throughout the whole space. After that they have no
tendency whatever to separate. Similarly, if two vessels, one containing
oxygen and the other hydrogen, be connected by a tube which is stuffed with
a plug of porous material, such as plaster of Paris, the gases gradually
diffuse one into the other through the porous plug. The two gases, however,
do not pass through the porous separator at equal rates, but in _inverse
proportion to the square roots of the densities of the gases_. Thus in the
case of two vessels, one containing hydrogen and the other oxygen, which is
sixteen times as heavy as hydrogen, the hydrogen will pass towards the
oxygen jar four times as quickly as the oxygen will pass towards the
hydrogen jar. Kindred phenomena occur when two liquids that are capable of
mixing, such as alcohol and water, are put in contact, the two gradually
diffusing one into the other in spite of the action of gravity. In some
cases, however, as where ether and water are employed, the diffusion is
only partial, this result arising from the fact that these two liquids are
not miscible in all proportions. When solutions of various solid bodies are
placed in contact, interdiffusion also takes place. On the results of his
examination of the phenomena of diffusion of liquids and salts across
porous membranes or _septa_, Graham founded a method of separating
_colloid_ from _crystalloid_ bodies, which he called _dialysis_.
DIGAM'MA, a letter which once belonged to the Greek alphabet, and which
remained longest in use among the Aeolians. It resembled our letter F, and
hence was called _digamma_, that is, double [Gamma]. It appears to have had
the force of _f_ or _v_. Its existence was first pointed out by Richard
Bentley.
DIGBY, Sir Everard, an English gentleman, born of a Roman Catholic family
in 1578. He enjoyed some consideration at the court of Elizabeth and James
I, by whom he was knighted. Having contributed money to the Guy Fawkes
conspiracy, he was tried and hanged in 1606.
DIGBY, Sir Kenelm, eldest son of the preceding, born in 1603, died in 1665.
He studied at Oxford, was knighted in 1623, and on the accession of Charles
I was created a gentleman of the bedchamber, a Commissioner of the Navy,
and a governor of Trinity House. He soon after fitted out at his own
expense a small but successful squadron against the French and Venetians.
In 1636 he became a Roman Catholic, and was imprisoned as a Royalist during
1642-3, when he was allowed to retire to the Continent. At the Restoration
he returned to England, became a member of the Royal Society, and was much
visited by men of science. He wrote numerous works: a _Treatise on the
Nature of Bodies_, a _Treatise on the Nature and Operation of the Soul_,
and _Of the Cure of Wounds by the Powder of Sympathy_.
DI'GEST, a name originally given to a collection or body of Roman laws,
digested or arranged under proper titles by order of the Emperor Justinian.
Hence applied to any somewhat similar collection.
DIGES'TER, a strong vessel of copper or iron, on which is screwed an
air-tight cover with a safety-valve, the object being to prevent loss of
heat by evaporation, and to enable boiling to take place at a high
pressure. Water may be thus heated to 400degF.; at which temperature its
solvent power is so greatly increased that bones are converted into a
jelly.
DIGES'TION is that process in the animal body by which the aliments are so
acted upon that the nutritive parts are prepared to enter the circulation,
and separated from those which cannot afford nourishment to the body. The
organs effecting this process are called the _digestive_ organs, and
consist of the stomach, the great and small intestines, &c. (see
_Intestine_, _Stomach_), the liver, and pancreas. When the aliments, after
being properly prepared and mixed with saliva by mastication, have reached
the stomach, they are intimately united with a liquid substance called the
_gastric juice_, by the motion of the stomach. By this motion the aliments
are mechanically separated into their smallest parts, penetrated by the
gastric juice, and transformed into a uniform pulpy or fluid mass. The
gastric juice acts upon the albuminous parts of the food, converting them
into peptones, which can pass through organic membranes and thus enter the
blood. This action is aided by the warmth of the stomach. The pulpy mass,
called _chyme_, proceeds from the stomach, through the pylorus, into that
part of the intestinal canal called the small intestine, where it is mixed
with the pancreatic juice, bile, and intestinal juice. The pancreatic juice
converts starch into sugar, albumins into peptones, and emulsionizes fats,
so that all these kinds of food are rendered capable of absorption. The
process is aided by the intestinal juice. The bile also acts upon fats, and
thus the food is formed into the _chyle_, which is absorbed into the system
by the capillary vessels called _lacteals_ (see _Chyle_; _Chyme_), while
the non-nutritious matters pass down the intestinal canal and are carried
off.--BIBLIOGRAPHY: F. Hare, _Food Factor in Disease_; Taylor, _Digestion
and Metabolism_.
DIGIT (dij'it; Lat. _digitus_, a finger), in arithmetic, any one of the ten
numerals, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Digit is also a measure of a
finger's breadth, equal to 3/4 inch.
DIGIT, in astronomy, is the measure by which we estimate the quantity of an
eclipse. The diameter of the sun or moon's disk is conceived to be divided
into twelve equal parts, called _digits_; and according to the number of
those parts or digits which are obscured, so many digits are said to be
eclipsed.
DIGITALIN (dij-i-t[=a]'lin), a vegetable alkaloid, the active principle of
the _Digit[=a]lis purpur[)e]a_ or foxglove. It has a bitter taste, and is a
strong poison, but is used medicinally, especially for the heart. See next
article.
DIGITA'LIS (dij-), a genus of plants, nat. ord. Scrophulariaceae,
containing about twenty species of tall herbs, natives of Europe and
Western Asia. The purple foxglove (_D. purpur[)e]a_) is a common wild
flower in Britain, and several species are grown in gardens. Various
preparations from the foxglove receive this name, and are used in medicine,
principally in cases of heart disease.
DIGITIGRA'DA (_digitus_, finger, toe, and _gradi_, to walk), a section of
the Carnivora, so called from their walking on the ends of their toes; as
the dog, cat, and their allies. See _Plantigrade_.
DIGITO'RIUM, a small portable dumb instrument having a short keyboard with
five keys like those of a piano, used by piano-players for practice, to
give strength and flexibility to the fingers.
DIGNE (d[=e]ny), a town, France, capital of the department of Basses-Alpes,
picturesquely situated on a mountain slope, 60 miles north-east of
Marseilles. In 1629 a plague reduced the population from 20,000 to 1500.
Pop. 7317.
DIJON (d[=e]-zh[=o]n; Lat. _Castrum Divonense_), a town in Eastern France,
capital of the department of C[^o]te-d'Or, in a fertile plain, at the foot
of a range of vine-clad slopes, formerly surrounded by ramparts, which now
furnish beautiful promenades. At some distance it is surrounded by a series
of forts. Some of the buildings belong to the period when Dijon was capital
of the dukedom of Burgundy, the chief being the cathedral of St.
B['e]nigne, a building of vast extent with a lofty wooden spire above 300
feet high; the churches of N[^o]tre Dame and St. Michael; the ancient
palace of the Dukes of Burgundy, now used as the h[^o]tel de ville and
museum; and the _palais de justice_, formerly the Parliament House of
Burgundy. Dijon is the birth-place of Bossuet. It has important educational
institutions and a valuable library. Industries: woollens, hosiery,
candles, mustard, vinegar, chemicals, paper-hangings, tanneries, foundries,
machine factories, cotton- and oil-mills. The trade is considerable,
particularly in the wines of Burgundy. Pop. 76,847.
DIKE, or DYKE (connected with the Gr. _teichos_, wall), a word variously
used in different localities to represent a ditch or trench, and also an
embankment, rampart, or wall. It is specially applied to an embankment
raised to oppose the incursions of the sea or of a river, the dikes of
Holland being notable examples of work of this kind. These are often raised
40 feet above the high-water mark, and are wide enough at the top for a
common roadway or canal, sometimes for both. The Helder Dike, one of the
largest, is about 6 miles in length and costly in upkeep. See _Embankment_.
DIKE, or DYKE, in geology, a term applied to intrusive igneous masses, such
as basalt, which fill up veins and fissures in the other rocks, and
sometimes project on the surface like walls through their superior
resistance to weathering.
DILAPIDATION, in English ecclesiastical law, is where an incumbent of a
church living suffers the parsonage-house or outhouses to fall down, or be
in decay for want of necessary repairs; or it is the pulling down or
destroying any of the houses or buildings belonging to a spiritual living,
or destroying of the woods, trees, &c., appertaining to the same. An
outgoing incumbent (or his heirs) is liable for dilapidation to his
successor. In general, the term is applied to the act of allowing or
causing any lands, houses, &c., to become waste or to decay.
DILEM'MA (from Gr. _di-_, double, and _l[=e]mma_, proposition, assumption),
in logic, a form of argument used to prove the falsehood or absurdity of
some assertion, as in the following instance: If he did so he must be
either foolish or wicked; but we know he is neither foolish nor wicked;
therefore he cannot have done so. The two suppositions, which are equally
untenable, are called the 'horns' of the dilemma.