"Consider your answer unchanged," I said.
Let a disturbance once set going travel along unchanged in form from A to B with velocity U.
It is a pleasantsmelling liquid which boils at 233° C. It is practically unchanged when boiled with aniline.
Rhyn stood in the same place she'd left him, unchanged in any way.
- The value of a determinant is unchanged if we add to the elements of any row or column the corresponding elements of the other rows or other columns respectively each multiplied by an arbitrary magnitude, such magnitude remaining constant in respect of the elements in a particular row or a particular column.
In 1885 it was shown by Bidwell, in the first of a series of papers on the subject, that if the magnetizing force is pushed beyond the point at which Joule discontinued his experiments, the extension of the bar does not remain unchanged, but becomes gradually less and less, until the bar, after first returning to its original length, ultimately becomes actually shorter than when in the unmagnetized condition.
- Teeth of Upper Jaw of Opossum (Didelphys marsupialis), all of which are unchanged, except the third premolar, the place of which is occupied in the young animal by a molariform tooth, represented in the figure below the line of the other teeth.
For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.
We shall regard the external force as applied in the form of a pressure X per square centimetre parallel to the line of propagation and varied from point to point as required in order to make the disturbance travel on unchanged in form with the specified velocity U.
Throughout the operation of increasing the focal length, the resolving power of the instrument, which depends only upon the aperture, remains unchanged; and we thus arrive at the rather startling conclusion that a telescope of any degree of resolving power might be constructed without an object-glass, if only there were no limit to the admissible focal length.
The azines are mostly yellow in colour, distil unchanged and are stable to oxidants.
The number of institutes devoted to secondary education remained almost unchanged between 1880-1881 and 1895-1896.
The arrangements thus established by Augustus continued almost unchanged till the time of Constantine, and formed the basis of all subsequent administrative divisions until the fall of the Western empire.
Those who were unwilling to accept evolution, without better grounds than such as are offered by Lamarck, and who therefore preferred to suspend their judgment on the question, found in the principle of selective breeding, pursued in all its applications with marvellous knowledge and skill by Darwin, a valid explanation of the occurrence of varieties and races; and they saw clearly that, if the explanation would apply to species, it would not only solve the problem of their evolution, but that it would account for the facts of teleology, as well as for those of morphology; and for the persistence of some forms of life unchanged through long epochs of time, while others undergo comparatively rapid metamorphosis.
This is the typical river of which there are infinite varieties, yet every variety would, if time were given, and the land remained unchanged in level relatively to the sea, ultimately approach to the type.
- It will be seen that apologetics by no means reissued unchanged from the long period of authority.
In three days, has a strong ammoniacal odour, which rapidly disappears, and in consequence of the loss of ammonia the latex will not keep for longer than a day unchanged; hence when it has to be carried to a distance from the place of collection, 3% of ammonia solution is added.
Undue stress is often laid on the fact that Lingula has come down to us apparently unchanged since Cambrian times, whilst Crania, and forms very closely resembling Discina and Rhynchonella, are found from the Ordovician strata onwards.
We can see that (abc)a x b x c x is not a covariant, because it vanishes identically, the interchange of a and b changing its sign instead of leaving it unchanged; but (abc) 2 is an invariant.
It consists of a chancel, nave and porch, in such unchanged condition that E.
Other conditions remaining unchanged, the force between two poles is proportional to the product of their strengths; it is repulsive or attractive according as the signs of the poles are like or unlike.
The small magnet may be a sphere rigidly magnetized in the direction of Ho; if this is replaced by an isotropic sphere inductively magnetized by the field, then, for a displacement so small that the magnetization of the sphere may be regarded as unchanged, we shall have dW = - vIdHo = v I+-, whence W = - 2 I + H2 ° (37) The mechanical force acting on the sphere in the direction of displacement x is 1 Hopkinson specified the retentiveness by the numerical value of the " residual induction " (=47rI).
The statements in ancient authorities as to the changes in the number of the equites during the regal period are very confusing; but it is regarded as certain that Servius Tullius found six centuries in existence, to which he added twelve, making,' eighteen in all, a number which remained unchanged throughout the republican ' period.
Their names also remain unchanged, except that of the federalized district in which the national capital is located, which is called the " districto federal."
This government, formed of gentiluomini or nobles, did not remain unchanged throughout the whole period, but was gradually forced to accept the participation of the popolani or lower classes, whose efforts to rise to power were continuous and determined.
If the wave-length remains unchanged, similar effects are produced by an increase in the scale of the aperture.
They remained essentially unchanged for centuries, and the Locrians subsequently enjoyed a high reputation as upholders of the law.
The filter presses remain substantially unchanged, although many ingenious but slight alterations have been made in their details.
After the decay of the roots some of the unchanged bacteria are left in the soil, where they remain ready to infect a new leguminous crop.
Apparatus can also be constructed in which the unchanged vapours are continually circulated through the tube.
They have remained unchanged ever since, though the terms of subscription have been modified.
Whatever the form of a wave, we could always force it to travel on with that form unchanged, and with any velocity we chose, if we could apply any " external " force we liked to each particle, in addition to the " internal " force called into play by the compressions or extensions.
We shall investigate the external force needed to make a train of plane waves travel on unchanged in form with velocity U.
If the velocity U is so chosen that E - poU 2 = o, then X = o, or the wave travels on through the action of the internal forces only, unchanged in form and with velocity U = (E/p).
(6) The pressure X is introduced in order to show that a wave can be propagated unchanged in form.
But a priori we are hardly justified in assuming that waves can be propagated at all, and certainly not justified in assuming that they go on unchanged by the action of the internal forces alone.
This investigation is obviously not exact, for it assumes that the form is unchanged, i.e.
As we obtained the result on the supposition of unchanged form, we can of course only apply it for such short lengths and such short times that the part dealt with does not appreciably alter.
If now the curve moves along unchanged in form in the direction ABC with uniform velocity U, the epoch e =OA at any time t will be Ut, so that the value of y may be represented as 2 y=a sin T (x - Ut).
In order that the velocity shall remain unchanged the tension T must remain the same.
Suppose that a disturbance is travelling with velocity U unchanged in form along a rod from left to right.
(33) But the condition of unchanged form requires that the matter shall twist through (dB/dx)dx while it is travelling over dx, i.e.
Though the woodchoppers have laid bare first this shore and then that, and the Irish have built their sties by it, and the railroad has infringed on its border, and the ice-men have skimmed it once, it is itself unchanged, the same water which my youthful eyes fell on; all the change is in me.
Dron was one of those physically and mentally vigorous peasants who grow big beards as soon as they are of age and go on unchanged till they are sixty or seventy, without a gray hair or the loss of a tooth, as straight and strong at sixty as at thirty.
If 127 parts of iodine, which is an almost black solid, and loo parts of mercury, which is a white liquid metal, be intimately mixed by rubbing them together in a mortar, the two substances wholly disappear, and we obtain instead a brilliant red powder quite unlike the iodine or the mercury; almost the only property that is unchanged is the weight.
Sulphur in some part escapes unchanged in the faeces.
Brewers' wort remains unchanged for years, milk keeps permanently sweet, and these and other complex liquids remain unaltered when freely exposed to air from which all these minute organisms are removed.
Keeping the electoral machinery almost unchanged (save that the lists of notables were to be permanent) Bonaparte entirely altered the upper parts of the constitutional pyramid reared by the philosopher.
We may take it then (and the fact is not disputed even by those who, like Dorpfeld, believe in one thorough racial change, at least, during the Bronze Age) that the Aegean civilization was indigenous, firmly rooted and strong enough to persist essentially unchanged and dominant in its own geographical area throughout the Neolithic and Bronze Ages.
Until after the War of Independence the primitive topography remained unchanged, but it was afterwards subjected to changes greater than those effected on the site of any other American city.
Sodium salicylate circulates in the blood unchanged, decomposition occurring in the kidney, and probably in tissues suffering from the Diplococcus rheumaticus of Poynton and Paine.
Government was maintained under the Cuban flag, - the diplomatic and consular relations with even the United States remaining in outward forms unchanged; and the regular forms of the constitution were scrupulously maintained so far as possible.
Apart from unimportant modifications, the form of the budget must have remained unchanged until the organic reforms of Selim III., while its complete transformation into European shape dates only from the year 1278 (1862), when Fuad Pasha attached a regular budget to his report on the financial situation of the empire.
Was the organizer of the fabric of Ottoman administration in the form which it retained practically unchanged until the reforms of Mahmud II.
Barreswil found that a strongly alkaline solution of copper sulphate and potassium sodium tartrate (Rochelle salt) remained unchanged on boiling, but yielded an immediate precipitate of red cuprous oxide when a solution of glucose was added.
Every symmetric function denoted by partitions, not involving the figure unity (say a non-unitary symmetric function), which remains unchanged by any increase of n, is also a seminvariant, and we may take if we please another fundamental system, viz.
And, other conditions remaining unchanged, the " sense " of any effect depends upon the nature of the metal under test, and (sometimes) upon the intensity of its magnetization.
In the recent methods the cotton remains in contact with the acids for two to four hours at the ordinary air temperature (15° C.), in which time it is almost fully nitrated, the main portion, say 90%, having a composition represented by the formula e C6H702(N03)3, the remainder consisting of lower nitrated products, some oxidation products and traces of unchanged cellulose and cellulose sulphates.
The ritual of the mass remained unchanged until the death of Henry VIII.
Generally, if any condition in the wave is carried forward unchanged with velocity U, the change of 4 at a given point in time dt is equal to the change of as we go back along the curve a distance dx = Udt at the beginning of dt.
Let the disturbance be supposed to travel unchanged in form from left to right with velocity U.
A Serpent was the Egyptian equivalent of Scorpio; the Arrow only of Sagittarius was retained; Capricornus became " Life," or a Mirror as an image of life; Aquarius survived as Water; Taurus, Virgo and Pisces remained unchanged.'
The unaccustomed coarse food, the vodka he drank during those days, the absence of wine and cigars, his dirty unchanged linen, two almost sleepless nights passed on a short sofa without bedding--all this kept him in a state of excitement bordering on insanity.