These transformations are fully discussed in the article Sugar.
Arithmetical groups, connected with the theory of quadratic forms and other branches of the theory of numbers, which are termed "discontinuous," and infinite groups connected with differential forms and equations, came into existence, and also particular linear and higher transformations connected with analysis and geometry.
If a system be removed from all communication with anything outside of itself, the whole amount of energy possessed by it will remain constant, but will of its own accord tend to undergo such transformations as will diminish its availability.
The various grades of life on our planet are the natural consequences of certain physical processes involved in the gradual transformations of the earth.
So long as food is supplied the living substance is the seat of transformations which are continually proceeding, being partially decomposed and again constructed, the new food being incorporated into it.
A very complete account of this equation and its various transformations was given by J.
The transformations of these two forms are discussed in Chemistry: Physical.
The Coleoptera can be traced back farther in time than any other order of insects with complete transformations, if the structures that have been described from the Carboniferous rocks of Germany are really elytra.
The wonderful transformations of these insects were first investigated by G.
(1890) and Les Transformations de la royaute pendant l'epoque carolingienne (1892).
On the 5th of June 1806 the Batavian republic completed its chrysalis-like transformations by becoming a kingdom for Louis Bonaparte.
The "Life" calls into existence in the visible world a series of three great Helpers, Hibil, Shithil and Anosh (late Judaeo-Babylonian transformations of the well-known names of the book of Genesis), the guardians of souls.
In 1845 a further contribution to the study of allotropy was made by Anton Schrotter, who investigated the transformations of yellow and red phosphorus, phenomena previously noticed by Berzelius, the inventor of the term " allotropy."
Considering derivatives primarily concerned with transformations of the hydroxyl group, we may regard our typical acid as a fusion of a radical R CO - (named acetyl, propionyl, butyl, &c., generally according to the name of the hydrocarbon containing the same number of carbon atoms) and a hydroxyl group. By replacing the hydroxyl group by a halogen, acid-haloids result; by the elimination of the elements of water between two molecules, acid-anhydrides, which may be oxidized to acid-peroxides; by replacing the hydroxyl group by the group. SH, thio-acids; by replacing it by the amino group, acid-amides (q.v.); by replacing it by the group - NH NH2, acid-hydrazides.
By transformations of the carbonyl group, and at the same time of the hydroxyl group, many interesting types of nitrogen compounds may be correlated.
Intermolecular transformations-migrations of substituent groups from one carbon atom to anotherare of fairly common occurrence among oxy compounds at elevated temperatures.
X u x?X x x HZ which exist between aliphatic and benzenoid compounds make the transformations of one class into the other especially interesting.
Transformations of electrical into chemical energy are witnessed in the processes of electrolysis (q.v.; see also Electrochemistry and Electrometallurgy).
The reverse series of transformations occurs when this final modification is heated.
Functions, operations, transformations, substitutions, correspondences, are but names for various types of relations.
All the forms obtained are invariants in regard to linear transformations, in accordance with the same scheme of substitutions, of the several sets of variables.
The number of different symbols a, b, c,...denotes the the covariants are homogeneous, but not in general isobaric functions, of the coefficients of the original form or forms. Of the above general form of covariant there are important transformations due to the symbolic identities: - (ï¿½b) 2 2)2 = a b - a b; (xï¿½ = as a consequence any even power of a determinant factor may be expressed in terms of the other symbolic factors, and any uneven power may be expressed as the product of its first power and a function of the other symbolic factors.
In algebraical transformations, however, such as (x-a)2 = x 2 - 2ax+a 2, the arithmetical rule of signs enables us to combine the sign-with a number and to treat the result as a whole, subject to its own laws of operation.
A summary of its chemical transformations may be given here, and reference should be made to the articles on the separate compounds for further details.
Fustel de Coulanges, Histoire des institutions politiques de l'ancienne France (Les Origines du systeme feodal, 1890; Les Transformations de la royaute pendant l'epoque carolingienne, 1892); A.
According to Sostratus, author of an elegiac poem called Teiresias, he was originally a girl, but had been changed into a boy by Apollo at the age of seven; after undergoing several more transformations from one sex to the other, she (for the final sex was feminine) was turned into a mouse and her lover Arachnus into a weasel (Eustathius on Odyssey, p. 1665).
The name thermodynamics is given to that branch of the general science of Energetics which deals with the relations between thermal and mechanical energy, and the transformations of heat into work, and vice versa.
This equation is generally true for any series of transformations, provided that we regard H and W as representing the algebraic sums of all the quantities of heat supplied to, and of work done by the body, heat taken from the body or work done on the body being reckoned negative in the summation.
If after any series or cycle of transformations the body is restored to its initial state, we must have E=E 0, whence it follows that H= W.
Of special interest are the transformations of Platygaster, belonging to this family, discovered by M.
The discovery of definite laws in this region might at first sight seem hopeless; but the argument rests on an implied postulate of stability and continuity of constitution of material substances, so that after a cycle of transformations we expect to recover them again as they were originally - on the postulate, in fact, that we do not expect them to melt out of organized existence in our hands.
For the distinguishing marks of all these, the number of their genera and species, their habits and transformations and dwellings, the reader must be referred to the writings of specialists.
In the middle ages the story of Caesar did not undergo such extraordinary transformations as befell the history of Alexander the Great and the Theban legend.
In the most important of his writings, De la religion consideree dans sa source, ses formes, et ses developpements (5 vols., 1825-1831), he traces the successive transformations of the religious sentiment imperishable under its varying forms. Besides Adolphe, in its way as important as Chateaubriand's Rene, he left two other sketches of novels in MS., which are apparently lost.
Next, Anaximenes, preferring air, resolved its transformations into processes of thinning and thickening.
GHSa gives the temperature at which, for any given percentage of carbon, these transformations begin, and PSP' that at which they end.
But, far below the freezing-point, transformations may take place in the solid metal, and follow a course quite parallel with that of freezing, though with no suggestion of liquidity.
1), let us follow by means of the ordinate QUw the undisturbed slow cooling of molten hyper-eutectiod steel containing 1% of carbon, for simplicity assuming that no graphite forms and that the several transformations occur promptly as they fall due.
The corresponding critical points which occur during rise of temperature, with the reverse transformations, are called Ac1, Ace, Ac 3, &c. A (Tschernoff) is the generic name, r refers to falling temperature (refroidissant) and c to rising temperature (chauffant, Osmond).
The degree of hardening which the steel undergoes increases with its carbon-content, chiefly because, during sudden cooling, the presence of carbon acts like a brake to impede the transformations, and thus to increase the quantity of 0-iron caught in transit, but probably also in part because the hardness of this 0-iron increases with its carbon-content.
Nevertheless, the theoretical possibility, and its realization in many cases, has brought considerations to the front which have recently become of predominant interest; consequently the possible transformations of isomers and polymers will be considered later under the denomination of reversible or dynamical isomerisms.
These laws have the advantage of being applicable to the mutual transformations of isomers, whatever be the nature of the deeper origin, and so bring polymerism, metamerism and polymorphism together.
A second law for these mutual transformations is that when they take place without loss of homogeneity, for example, in the liquid state, the definite transition point disappears and the change is gradual.
Longago Kiitzing went so far as to express the belief that the lower algae were all capable of transformations into higher forms, even into moss-protonemata.
Later writers have also thought that in all four groups of algae transformations of a most farreaching character occur.
We can only sketch in outline the transformations of certain typical university systems of examinations.
On the other hand, the " rattlesnake " men of the Moqui are merely transformations and expect to return at death to their original reptile form (Maclennan, 357).
In fact, Christianity has been widely accepted by varied races in very different stages of culture, and it has maintained itself through a long succession of centuries in lands where the transformations in political structure, the revolutions in social conditions, and the changes in science and philosophy, have been numerous and extreme.
Siace E2 + if + ~1, or ef, is necessarily an absolute invariant for all transformations of the (rectangular) co-ordinate axes, we infer that XE + un + v~ is also an absolute invariant.
This expression gives the work done by a given wrench when the body receives a given infinitely small twist; it must of course be an absolute invariant for all transformations of rectangular axe~.
By these and the similar transformations relating to y and z the equation (6) takes the form d IOT\ aT
Empedocles took an important step in the direction of modern conceptions of physical evolution by teaching that all things arise, not by transformations of some primitive form of matter, but by various combinations of a number of permanent elements.
The details of the further transformations have not yet been completely followed.
The first and third transformations (reckoned in order with increasing temperature of the transition point) are attended by an increase in volume, the second with a contraction; the solubility follows the same direction, increasing up to 82.8°, then diminishing up to 125.6°, and then increasing from this temperature upwards.