How to use Variation in a sentence
There is a good deal of variation in the colour of the fur, the prevailing tint being grey.
The greatest variation, however, is seen in the tentacles.
One variation is illustrated in fig.
In some cases a pair of animals pro- ‘ duce ten million offspring, and in such a number a large range of congenital variation is possible.
This variation, however, is not always linear.Advertisement
The system of canals shows great variation even in the same species.
The method is again that of the variation of elements.
He pointed to the admitted fact of congenital variation, and he showed that congehital variations are arbitrary and, so to speak, non-significant.
The details of the structure of the flower show a wide variation; the flowers are often extremely simple, sometimes as in Arum, reduced to a single stamen or pistil.
In some cases there is a very sudden drop at or below a certain temperature to a much lower value, and above and below the point the temperature variation is small.Advertisement
Though all yield fur of serviceable quality, the commercial value varies immensely, not only according to the species from which it is obtained, but according to individual variation, depending upon age, sex, season, and other circumstances.
A similar expression for the variation of the specific heat S at constant pressure is obtained from the second expression in (8), by taking p and 0 as independent variables; but it follows more directly from a consideration of the variation of the function (E+pv).
The cause of the variation in the signature still remains unexplained, but ceases to have therefore any great historical importance.
This indicates that less attention has been paid to the straw than to the grain, for it is certain that, were it desirable, a great range of variation might be induced in the foliage and straw.
Apart from the botanical interest of these diversities, as indications of the faculty of variation in plants, and possibly as clues to the genealogy and origin of the cultivated plant, their practical importance is very great.Advertisement
If seeds of tio of these "sporting" plants be taken and grown in another season, they may (or may not) reproduce the particular variation.
If they do, and the same process of selection be continued, the variation becomes in time "fixed," though it is always more or less liable to revert to its original condition.
In the progeny of these crossed wheats, especially in the second generation, much variation and difference of character is observable - a phenomenon commonly noticed in the descendants from crosses and hybrids, and styled by Naudin "irregular variation."
The originality of Epicurus lay in his theory that the highest point of pleasure, whether in body or mind, is to be attained by the mere removal of pain or disturbance, after which pleasure admits of variation only and not of augmentation; that therefore the utmost gratification of which the body is capable may be provided by the simplest means, and that " natural wealth " is no more than any man can earn.
A luminous idea of the nature of these two classes of variation may be gained by conceiving of the, motion of a ship, floating on an ocean affected by a long ground swell.Advertisement
This newly discovered inheritance of " variation in the tendency to react " has a wide application and has led the present writer to coin the word " educability."
To make this apparatus more perfectly automatic, an arrangement for continually adding to and mixing with the juice the proper proportion of milk of lime has been adapted to it; and although it may be objected that once the proportion has been determined no allowance is made for the variation in the quality of the juice coming from the mill owing to the variations that may occur in the canes fed into the mills, it is obviously as easy to vary the proportion with the automatic arrangement from time to time as it is to vary in each separate direction, if the man in charge will take the trouble to do so, which he very seldom does with the ordinary defecators, satisfying himself with testing the juice once or twice in a watch.
It is not yet experimentally proved that variation as the inverse square is absolutely true at all distances.
The above theory, coupled with such facts as the variation of the composition of the constant boiling-point fraction with the pressure under which the mixture is distilled, the proportionality of the density of all mixtures to their composition, &c., shows this to be erroneous.
This, which has long been recognized as a class-reaction, is obviously capable of endless variation.Advertisement
Among his happy conjectures may be mentioned that of the sun's axial rotation, postulated by him as the physical cause of the revolutions of the planets, and soon after confirmed by the discovery of sun-spots; the suggestion of a periodical variation in the obliquity of the ecliptic; and the explanation as a solar atmospheric effect of the radiance observed to surround the totally eclipsed sun.
This is especially the case in the lower and moister regions, such as the west coast, where malarial fever is very prevalent and deadly; the most unfavourable factors being humidity with absence of climatic variation (daily or seasonal).
The variation of type among the Bantu is due probably to a varying admixture of alien blood,which is more apparent as the east coast is approached.
Arago in 1811 found that in the case of white light and with moderately thin plates the transmitted light is no longer white but coloured, a variation of brightness but not of tint being produced when the polarizer and analyser being crossed are rotated together, while the rotation of the analyser alone produces a change of colour, which passes through white into the complementary tint.
This involves no assumptions as to the law of variation of E.M.F.
In many cases the deviations do not appear to favour any simple hypothesis as to the mode of variation of s with temperature, but as a rule the indication is that s is nearly constant, or even diminishes with rise of temperature.
A comparison of the results of different observers would also suggest that the law of variation may be different in different metals, although the differences in the values of d 2 E/dP may be due in part to differences of purity or errors of observation.
An attempt has been made to explain the Volta effect as due to the affinity of the metals for each other, but that would not account for the variation of the effect with the state of the surface, except as affecting the actual surface of contact.
Amid the different climatic conditions of so vast a continent as America, variation in size, and in the capacity of frames used, is in some measure accounted for.
Up to 1890 the most careful observations and researches failed to establish the periodicity of such a rotation, though there was strong evidence of a variation of latitude.
C. Chandler, from an elaborate discussion of a great number of observations, showed that there was really a variation of the latitude of the points of observation; but, instead of the period being 305 days, it was about 428 days.
Near one phase of this combined period the two component motions nearly annul each other, so that the variation is then small, while at the opposite phase, 3 to 4 years later, the two motions are in the same direction and the range of variation is at its maximum.
But, as a matter of fact, they are subject to an annual variation.
Hence the motion of the pole of rotation is also subject to a similar variation.
When the ovules are very numerous (indefinite), while at the same time the placenta is not much developed, their position exhibits great variation, some being directed upwards, others downwards, others transversely; and their form is altered by pressure into various polyhedral shapes.
Thomson, on the other hand, set to work to overcome the difficulty by improvement in the manufacture of cables, and first of all in the production of copper of high conductivity and the construction of apparatus which would readily respond to the slightest variation of the current in the cable.
A few Coal Measure and Permian stems (Cycadoxylon and Ptychoxylon) resemble Lyginodendron in the general character of their tissues, but show a marked reduction of the primary wood, together with an extensive development of anomalous wood and bast around the pith, a peculiarity which appears as an individual variation in some specimens of Lyginodendron oldhamium.
The considerable variation in the size of the pinnae of Podozamites, as represented by species from the Jurassic rocks in the Arctic regions and various European localities, recalls the variation in length and breadth of the leaves of Agathis.
Starting from simple elementary propositions, Steiner advances to the solution of problems which analytically require the calculus of variation, but which at the time altogether surpassed the powers of that calculus.
A ray of light is reflected from this mirror and from another mirror which is rocked by a small motor driven off the same circuit, so that the ray has two vibratory motions imparted to it at right angles, one a simple harmonic motion and the other a motion imitating the variation of the current or electromotive force under test.
The vertical section, on the other hand, is subject to considerable variation according to the work to which the furnace is applied.
Your confession is a tad different variation; is it your wife or mommy?
Care to explain why there are six unused Christmas cards, six Birthday cards..." she began counting, "â€¦and seven Valentine cards, all 'To My Loving Wife,' or some variation thereof?
There is dialect variation across the UK.
Variation of districts 2. (1) The districts specified in Schedule 1 to this Order are hereby abolished.
Diagram to illustrate parathyroid anatomy (posterior view) - click to enlarge There is variation in the number and location of glands.
Relatively minor variation from perfect symmetry is called fluctuating asymmetry.
Magnetic variation occurs and must be added to - or subtracted from - the actual compass reading to give the true azimuth.
Data from the survey have been used to study biogeography, biodiversity, seasonal and inter-annual variation, long-term trends, and exceptional events.
This recipe, with very little variation, also makes an excellent blue cheese.
Hundreds of victims have recently fallen for a variation that plays upon people's misunderstanding about how bank cashier 's checks work.
Today the standard is methyl cellulose or some variation thereof.
Variation ground chili can be substituted for the fresh chili.
Another variation uses coagulant to form a sludge blanket part way up the tanks.
Since dE=dH - pdv, we have evidently for the variation of the total heat from the second expression (8), dF=d(E + pv) =dH+vdp=Sde - (Odv/de - v)dp .
Observing that F is a function of the co-ordinates expressing the state of the substance, we obtain for the variation of S with pressure at constant temperature, dS/dp (0 const) '=' 2 F/dedp =-0d 2 v/d0 2 (p const) (12) If the heat supplied to a substance which is expanding reversibly and doing external work, pdv, is equal to the external work done, the intrinsic energy, E, remains constant.
This coefficient is sometimes called the " angular coefficient," and may be regarded as a measure of the deviations from Boyle's law, 'which may be most simply expressed at moderate pressures by formulating the variation of the angular coefficient with temperature.
The values of the corresponding functions for the liquid or solid cannot be accurately expressed, as the theoretical variation of the specific heat is unknown, but if we take the specific heat at constant pressure s to be approximately constant, and observe the small residual variation dh of the total heat, we may write F'=s'D+dh+B'.
With regard to the degree in which this armature is developed, not only do the species differ from each other, but almost every species shows an extraordinary amount of variation.
There is a wide variation of climate for so small a territory, the higher elevations of the Sierra de Ajusco being cold and humid (the Mexican Central crosses the range at an elevation of 9974 ft.); the lower spurs mild, temperate and healthy, the lower valleys subtropical, hot and unhealthy.
No better example could be found of the almost limitless variation in so-called species.
Precision, which was at first unattainable for want of an epoch, was afterwards no less unattainable from the multiplicity, and sometimes the variation, of epochs.
The general characters of the jaws have been mentioned above, and in detail there is great variation in these organs among the different families.
The chief errors to which the stereometer is liable are (I) variation of temperature and atmospheric pressure during the experiment, and (2) the presence of moisture which disturbs Boyle's law.
The adventures of Blanchefleur, wife of Charlemagne, form a variation of the common tale of the innocent wife falsely accused, and are told in Macaire and in the extant fragments of La Reine Sibille (14th century).
The composition of the ashes of different coals is subject to considerable variation, as will be seen by Table II.
As the former are only active in the air while the latter are anaerobic, the activity of either agent is conditioned by variation in the water level of the bog.
The variation in the composition of coal seams in different parts of the same basin is a difficult matter to explain.
To maintain e µe constant, compensation for variation of µ is made by inversely varying 0.
In this way the brake may be arranged to maintain a constant torque, notwithstanding variation of the speed.
They are both reddish yellow and brownish black (according to individual variation) in skin colour, with head hair often tending to russet, and body hair of two kinds - black and bristly on the upper lip, chin, chest, axillae and pubes; and yellowish and fleecy on the cheeks, back and limbs.
The approximate theory of pipes due to Bernoulli assumes a loop at the open end, but the condition for a loop at the open end, that of no pressure variation, cannot be exactly fulfilled.
It may be noted that in practice there is another reason for pressure variation at the end of the pipe.
Formerly it was generally supposed that the Tartini tone was due to the beats themselves, that the mere variation in the amplitude was equivalent, as far as the ear is concerned, to a superposition on the two original tones of a smooth sine displacement of the same periodicity as that variation.
This want of proportionality will have a periodicity, that of the impinging waves, and so will produce vibrations just as does the variation of pressure in the case last investigated.
Baker and others, show that the breaking stress of a bar is not a fixed quantity, but depends on the range of variation of stress to which it is subjected, if that variation is repeated a very large number of times.
The real nature of the action is not well understood, but the word fatigue may be used, if it is not considered to imply more than that the breaking stress under repetition of loading diminishes as the range of variation increases.
An idea as to the advance made by this method is recorded in the variation in the price of calcium.
Later still he engaged in the study of the relations between chemical constitution and rotation of the plane of polarization in a magnetic field, and enunciated a law expressing the variation of such rotation in bodies belonging to homologous series.
This innate power of variation has enabled the florist to obtain, and ultimately to "fix," so many remarkable varieties.
The principal causes of variation in the individual are age, period of lactation, nature and amount of food, state of health, and treatment, such as frequency of milking, &c. The following table indicates the The average quantity of milk yielded by variable, both in individuals and breeds.
In the Weston standard cell cadmium and cadmium sulphate are substituted for zinc and zinc sulphate; it has the advantage of a much smaller coefficient of temperature variation than the Clark cell.
When so made, the cell has an electromotive force of 1.072 volts and no sensible temperature variation.
More important are those passages in which the Massoretes have definitely adopted a variation from the consonantal text.
The first missionary journey may have begun in 47 or 48; the arrival of Festus may have taken place in the summer of 58 or of 59; the two years of the Roman imprisonment recorded in the last chapter of Acts may have ended in the spring of 61 or 62; and the dates which fall in between these extremes are liable to the same variation.
But the limbs show with regard to development great variation, and an uninterrupted transition from the most perfect condition of two pairs with five separate clawed toes to their total disappearance; yet even limbless lizards retain bony vestiges beneath the skin.
In the verification of a precise standard of length there may be taken into account the influence of the variation of atmospheric pressure.
Covering a longer time, we find an average variation of 1/200 in the Attic foot (25), 1/150 in the English foot (25), 1/170 in the English itinerary foot (25).
So we may say that an average variation of 1/400 by toleration, extending to double that by change of place and time, is usual in ancient measures.
In weights of the same place and age there is a far wider range; at Defenneh (29), within a century probably, the average variation of different units is 1/36, 1/60, and 1/67, the range being just the same as in all times and places taken together.
Even in a set of weights all found together, the average variation is only reduced to 1/60 in place of 1/36 (29).
Taking a wider range of place and time, the Roman libra has an average variation of 1/50 in the examples of better period (43), and in those of Byzantine age 1/35 (44).
Average variation may be said to range from 1/40 to 1/70 in different units, doubtless greatly due to defective balances.
Hence we see that if one unit is derived from another it may be possible, by the similarity or difference of the forms of the curves, to discern whether it was derived by general consent and recognition from a standard in the same condition of distribution as that in which we know it, or whether it was derived from it in earlier times before it became so varied, or by some one action forming it from an individual example of the other standard without any variation being transmitted.
In Greece it is the most usual unit, occurring in the Propylaea at Athens 12.44, temple at Aegina 12.40, Miletus 12.51, the Olympic course 12.62, &c. (18); thirteen buildings giving an average of 12.45, mean variation .06 (25), = (3/5)ths of 20.75, m.
A variation on the main system was made by forming a mina of 50 shekels.
The same circumstances detertnine the variation of profits, but in an opposite direction; the increase of stock, which raises wages, tending to lower profit through the mutual competition of capitalists.
Towards the head and on the limbs the spots tend to become solid, but there is great local variation in regard to their form and arrangement.
The rapid variation of certain groups of animals or the acceleration of certain organs is also not evidence of the sudden appearance of new adaptive characters.
Little proof is afforded among the mammals of extinction through arrested evolution or through the limiting of variation, although such laws undoubtedly exist.
They also exhibit a variation from the characteristic dualism of Gnosticism into monism, in their conception of the fall of Sophia and their derivation of matter from the passions of the fallen Sophia.
The sodium vapour in the middle is very dense on the heated side, the density diminishing rapidly towards the upper part of the tube, so that, although not prismatic in form, it refracts like a prism owing to the variation in density.
Trypanosomes vary greatly with regard to size; even in one and the same species this variation is often noticeable, especially under.
There is, however, considerable local variation both in the matter of size and of colour from the typical coyote of Iowa, which measures about 50 in.
A further variation consists in the development of additional shelly plates upon the dorsal line between the two large valves (Pholadidae).
This Long Period, However, May Be Reduced To Four Hundred Years; For Since The Dominical Letter Goes Back Five Places Every Four Years, Its Variation In Four Hundred Years, In The Julian Calendar, Was Five Hundred Places, Which Is Equivalent To Only Three Places (For Five Hundred Divided By Seven Leaves Three); But The Gregorian Calendar Suppresses Exactly Three Intercalations In Four Hundred Years, So That After Four Hundred Years The Dominical Letters Must Again Return In The Same Order.
Both vertically and transversely it measures about an inch and a quarter, while antero-posteriorly it is only about three-quarters of an inch, though its size is liable to great variation.
But it is clear that if we increase A, the sectional area of the stem, we shall diminish 1, the length of a scale-division corresponding to a given variation of density, and thereby proportionately diminish the sensibility of the instrument, while diminishing the section A will increase land proportionately increase the sensibility, but will diminish the range over which the instrument can be employed.
The genus which is common to the northern parts of both hemispheres is distinguished by the large cheek-pouches and by the absence or rudimentary condition of the claw of the first hind-toe, resembles Tamias in the slender form of the body, but displays great variation in the length of the tail, which may be a mere stump, or comparatively long.
The rapid variation in the intensity of the magnetic field causes a brilliant electrodeless discharge which is seen in the form of a ring passing near the inner walls of the bulb when the pressure is properly adjusted.
The Litany, for example, in the Prayer Book is based upon the medieval Latin Litany, but great variation both in substance and language and by way of addition and omission, are made in it.
Lutheran influence can likewise be traced in way of variation introduced into the baptismal and other sacramental or occasional offices.
As a result of their isolation, the proportion of endemic plants is greater here than in any other region, and the great elevation of the mountains, with the consequent variation in temperature, moisture and barometric pressure, has multiplied the number of species.
By thus supposing a psychical basis to evolution, Fechner, anticipating Wundt, substituted a psychical development of organs for Darwinian accidental variation.
Examples are subject to much variation in colour and shade, and in some the lower parts are deeply tinged with yellow.
Following the first chart of lines of equal variation compiled by Edmund Halley in 1700, charts of similar type have been published from time to time embodying recent observations and corrected for the secular change, thus providing seamen with values of the variation accurate to about 30' of arc. Possessing these data, it is easy to ascertain by observation the effects of the iron in a ship in disturbing the compass, and it will be found for the most part in every vessel that the needle is deflected from the magnetic meridian by a horizontal angle called the deviation of the compass; in some directions of the ship's head adding to the known variation of the place, in other directions subtracting from it.
It is also provided with an azimuth circle or mirror and a shadow pin or style placed in the centre of the glass cover, by either of which the variable angle between the compass north and true north, called the "total error," or variation and deviation combined, can be observed.
In the Leiden MS. of this work, which for long was erroneously ascribed to one Peter Adsiger, is a spurious passage, long believed to mention the variation of the compass.
It has since been discovered, however, that the magnitude of the acceleration in question is not exactly the same at different places on the earth, the range of variation amounting to about 2%.
He attained correct views as to the character of centrifugal force in connexion with Galileo's theory; and, when the fact of the variation of gravity (Galileo's acceleration) in different latitudes first became known from the results of pendulum experiments, he at once perceived the possibility of connecting such a variation with the fact of the earth's diurnal rotation relatively to the stars.
This represents about two-thirds of the total variation of Galileo's acceleration between the equator and the poles, the balance being due to the ellipticity of the figure of the earth.
In all the cases hitherto considered, the liquid phase alone has been capable of continuous variation in composition.
The reasoning given above is independent of the temperature, so that the variation with temperature of the osmotic pressure of a dilute solution must be the same as that of a gas, while Boyle's law must equally apply to both systems. Experimental evidence confirms these results, and extends them to the cases of non-volatile solutes - as is, indeed, to be expected, since volatility is merely a matter of degree.
Callendar has shown that the variation of vapour pressure of a solution with pressure is given by the expression V'dP = vdp, where V' is the change in volume of the solution when unit mass of solvent is mixed with it.
The probable error in neglecting any variation of specific heat is small, and we may calculate L from the values of Lo - (s - s') (To - T), where s - s' is about 0.5 calories.
The variation of L with pressure is probably small.
The variation of gases from Boyle's law is represented in the equation of Van der Waals by subtracting a constant b from the total volume to represent the effect of the volume of the molecules themselves.
The above arrangements are found with scarcely any variation in all the charter-houses of western Europe.
The condition of albinism thus assumed as a seasonal variation is never complete, for the eyes at least retain their pigmented state.
The variegated plumage of the Snipe is subject to no inconsiderable variation, especially in the extent of dark markings on the belly, flanks, and axillaries, while examples are occasionally seen in which no trace of white, and hardly any of buff or grey, is visible, the place of these tints being taken by several shades of chocolate-brown.
This unusual variation probably arises from early differences of opinion as to whether there was one Mark or more than one.
The combination of the two, however, shows clearly that, without much variation of heat or loss of light, any extent of space may be covered, and houses of any altitude constructed.
The colour of the fruit varies from green to deep purple, the size from that of a small cherry to that of a hen's egg; the form is oblong acute or obtuse at both ends, or globular; the stones or kernels vary in like manner; and the flavour, season of ripening and duration are all subject to variation.
All commercial iron and steel contain more or less of both these impurities, the influence of which is so strong that a variation of o o, %, i.e.
On its way from the blast furnace to the converter or open hearth furnace the pig iron is often passed through a great reservoir called a " mixer," which acts also as an equalizer, to lessen the variation in composition of the cast iron, and as a purifier, removing part of the sulphur and silicon.
The vowel i could become e as de = di, &c. Consonantal variation is most common.
Fox, Common.-The variation of size and quality is considerable, and the colour is anything from grey to red.
The underwool in all sorts is generally of a bluish-grey tone, but the top hair in the depth of winter is usually full enough in quantity to, hide any such variation.
Pelton wheels are very sensitive to variation of load, and considerable trouble was experienced at first in securing adequate A s has now become one of 5.
The emigration of Belgians from their country is small and reveals little variation.
From certain differences in the striping of the legs, as well as from variation in skull-characters, the existence of more than a single species has been suggested; but further evidence is required before such a view can be definitely accepted.
The true name of the book appears in the authorities in a variety of forms, the variation affecting both the author's name and the description of his book.
The effect of the rising tide is in the nature of a secular variation, while the pitching is periodic.
But when these changes are averaged through years and centuries it is found that the average orbit has a secular variation which, for a number of centuries, may appear as a very slow progressive change in one direction only.
In this case the variation will be simply periodic, The value of any element of the planet's motion will generally be represented by the sum of an infinite series of such periodic quantities, having different periods.
Actually the curve in which it moves is nearly a circle; but the distance varies slightly owing to the minute secular variation in the position of the ecliptic, caused by the action of the planets.
The chief differences between Burnet's original draft as represented by the Bodleian MS. and the printed history consist in a more lenient view generally of individuals, a modification of the censure levelled at the Anglican clergy, changes obviously dictated by a general variation in his point of view, and a more cautious account of personal matters such as his early relations with Lauderdale.
This recipe is a variation of the wiener dog cake.
His first contribution 3 was a variation of the method of Archimedes.
The oscillation of the earth's axis may arise in two distinct ways; distinguished as " nutation of the axis " and " variation of latitude.
The variation of c is uncertain.
Since both k and c are generally variable with the temperature, and the mode of variation of either is often unknown, the results of these methods are generally less certain with regard to the actual Carves showing Cie farzalaon of Temperature wilki FIG.
This can be measured graphically without any knowledge of the law of variation of the surface temperature, or of the laws of propagation of heat waves.
To illustrate the main features of the calculation, we may suppose that the surface is subject to a simple-harmonic cycle of temperature variation, so that the temperature at any time t is given by an equation of the form 0 - 0 0 = Asin 27rnt= A sin 27rt/T, (5) where 0 0 is the mean temperature of the surface, A the amplitude of the cycle, n the frequency, and T the period.
Angstrom endeavoured to find the variation of conductivity by this method, but he assumed c to be the same for two different bars, and made no allowance for its variation with temperature.
He thus found nearly the same rate of variation for the thermal as for the electric conductivity.
Ang3trom's value for iron, when corrected for obvious numerical errors, and for the probable variation of c, becomes Iron, k =0.164 (1-0.0013 0), but this is very doubtful as c was not measured.
The variation of c was determined by a special series of experiments.
No allowance was made for the variation of density with temperature, or for the variation of the distance between the thermometers, owing to the expansion of the bar.
Neglecting the external heat-loss, and the variation of the thermal and electric conductivities k and k', we obtain, as before, for the difference of temperature between the centre and ends, the equation O, Tho z Go = C 2 R1/8qk = ECl/8qk = E 2 k'/8k, (11) where E is the difference of electric potential between the ends.
Moreover, the variation of thermal conductivity with temperature is small and uncertain, whereas the variation of electrical conductivity is large and can be accurately determined, and may therefore be legitimately utilized for eliminating the external heat-loss.
This, at first sight, paradoxical result is explained by the fact that the mean free path of each molecule increases in the same proportion as the density is diminished, so that as the number of molecules crossing each square centimetre decreases, the distance to which each carries its momentum increases, and the total transfer of momentum is unaffected by variation of density.
The question of the variation of conductivity with temperature is more difficult.
In some cases this variation is comparatively little.
Amongst causes of variation in the quantity of water needed will be its quality and temperature and rate of flow, the climate, the season, the soil, the subsoil, the artificial drainage, the slope, the aspect and the crop. In actual practice the amount of water varies from 300 gallons per acre in the hour to no less than 28,000 gallons.
If sunlight and twilight were the sole cause of the apparent annual variation, the frequency would have a simple period, with a maximum at midwinter and a minimum at midsummer.
It is only during winter and in high latitudes that we can hope to ascertain anything directly as to the real diurnal variation of the causes whose influence is visible at night as aurora.
The preceding remarks relate to auroras as a whole; the different forms differ considerably in their diurnal variation.
At most places the variation in the frequency has shown a general similarity to that of sun-spots.
Between the two extremes there was variation not only between city and city, but, no doubt, in one and the same city at different times.
There is evidence that the amount of stress on syllables, and the consequent length of vowels, varied greatly in spoken Coptic, and that the variation gave much trouble to the scribes; the early Christian writers must have taken as a model for each dialect the deliberate speech of grave elders or preachers, and so secured a uniform system of accentuation.
The base of the pyramid of Snefru had an average variation of 6 in.
But, immediately after, Cheops improved on this with a variation of less than 6 in.
Apart from the omissions the most striking difference between the two sections is the variation in order, the different sections of ch.
For this version exhibits numerous cases of variation, both as regards order and contents, from the Hebrew text; moreover the translation, more particularly of many technical terms, differs from that of ch.
In colour different specimens present a considerable range of variation, but the animal is ordinarily of a rich dark brown, scarcely or not paler below than on the general upper parts; but the back xviii.
It may be considered as arising from a semi-annual variation in the eccentricity of the moon's orbit and the position of its perigee.
The species is subject to great racial variation.
On extending his inquiry to other aelotropic crystals he observed a similar variation, and was thus led, in 1825, to the discovery that aelotropic crystals, when heated, expand unequally in the direction of dissimilar axes.
There is, however, considerable variation in the nature of the membrane in different species; thus the cell-wall of Oedogonium, treated with sulphuric acid and iodine, turns a bright blue, while the colour is very faint in the case of Spirogyra, the wall of which is said to consist for the most part of pectose.
The two were to perform a new variation upon the theme of Abelard and HeloIse.
In the progress of this erosion full scope has been afforded for the modification of form by variation in geological structure.
Treviranus, in the beginning of the 10th century, laid stress on the indefiniteness of variation, but assumed that some of it was adaptive response to the environment, and some due to sexual crossing.
Variation was in fact a purposive response.
St Hilaire and afterwards his son Isodore regarded variation as not indefinite but directly evoked by the demands of the environment.
Schleiden regarded variation and the production of new or improved structures as an unfolding of possibilities latent in the stock.
Robert Chambers, in the once famous Vestiges of Creation, interested and shocked his contemporaries by his denial of the fixity of species and his insistence on creation by progressive evolution, but had no better theory of the cause of variation than to suppose that organisms - "from the simplest and oldest to the highest and most recent" were possessed of "an inherent impulse, imparted by the Almighty both to advance them from the several grades and modify their structure as circumstances required."
Although the pre-Darwinian writers amongst them invoked nearly every principle that Darwin or his successors have suggested, they failed to carry conviction with regard to evolution, and they neither propounded a coherent philosophy of variation nor suggested a mechanism by which variations that appeared might give rise to new species.
He did not suggest that every variation and every character must have a "selection value," although he pointed out that, because of our ignorance of animal physiology, it was extremely rash to set down any characters as valueless to their owners.
It is even more important to notice that he did not suggest that every individual with a favourable variation must be selected, or that the selected or favoured animals were better or higher, but merely that they were more adapted to their surroundings.
He laid much stress on the unity of the organism in every stage of its existence, with the resulting correlation of variations, so that the favouring of one particular variation entailed modifications of correlated structures.
He showed how different varieties in a species, or species in a genus, tended to display parallel variation, clearly indicating that the range and direction of variation were limited or determined by the nature of the organism.
It now remains to examine in closer detail the further knowledge that has been gained with regard to variation and the bearing of that on the Darwinian position.
Darwin was well aware that variation ranged from differences so minute as to become apparent only on careful measurement to those large departures from the normal which may be called abnormalities, malformations or monstrosities.
Wallace, whilst insisting that the range of observed and measured variation was much larger in proportion to the size of the organisms or parts of organism affected than was generally believed, leaned to the Darwinian view in excluding from the normal factors in the origin of species variations of the extremer ranges of magnitude.
Darwin was careful to insist that we did not know the laws of variation, and that when variation was attributed to "chance" no more should be read into the statement than an expression of our ignorance of the causation.
It cannot now be doubted that a very large amount of observed variation, and especially of the indefinite variation which is sometimes spoken of as fluctuating variation, and which is usually distributed indefinitely round a mean, is directly associated with or induced by the environment.
On various grounds attempts have been made to exclude such variation from the material for the making of species.
These attempts to reject environmental variation rest on several grounds.
In the second place, it has been urged, particularly by de Vries, that experiment and observation have shown that the possible range of fluctuating variation is strictly limited.
Something will be said later in this article as to the limitation of variation; here it is necessary only to say that de Vries is introducing no new idea.
Vernon have adduced experimental evidence as to the induction of variation by such causes as difference in the ages of the parents, in the maturity or freshness of the conjugating germ cells, and in the condition of nutrition for the embryos.
With our present knowledge it is impossible to discriminate between variation that may or that may not be the material for the differentiation of species by scrutinizing either magnitude or probable causation.
It is equally impossible to draw an exact line between variation induced by the environment and variation that may be termed intrinsic. Extrinsic and intrinsic factors are involved in every case, although there is a range from instances in which the external factor appears to be extreme to instances where the intrinsic factor is dominant.
A difference in calibre, elasticity or branching of a blood vessel, the smallest variation in a nerve or group of vessel-cells, any anatomical or physiological divergence, is reflected throughout the organism.
Here, again, a variation in the order, nature and number of the divisions, in itself simple, may result in symmetrical or correlated changes in all the progeny of the affected embryonic part.
The theory of chance was applied to the study of human variation by Quetelet; but the most important applications of this theory to biological problems are due in the first instance to Francis Galton, who used the theory of correlation in describing the relation between the deviation of one character in an animal body from the mean proper to its race and that of a second character in the same body (correlation as commonly understood), or between deviation of a parent from the mean of its generation and deviation of offspring from the mean of the following generation (inheritance).
Bateson is pre-eminent, would appear to simplify the problem of variation, especially on its mechanical and physiological sides.
A similar kind of segregation may take place in the formation of the repeated parts of an organism, so that symmetrical repetition may be compared with normal heredity, and be due to the presence of similar factors in the divisions of the embryonic cells, whilst the differentiation of repeated parts may be due to the unequal distribution of such factors and be comparable with variation.
On such an interpretation, variation would result from asymmetrical division and normal inheritance from symmetrical division.
It is to be noticed, however, that the Mendelian conceptions are in no sense an alternative to Darwinism; at the most they would serve to assist in explaining the mechanism of variation, and by enlarging our idea of the factors, increase the rate at which we may suppose selection to work.
Darwin certainly was impressed with the view that natural selection and variation together formed a mechanism, the central product of which was adaptation.
On the other hand, dislike of mystical interpretations of natural facts has driven many capable naturalists to another extreme and has led them to insist on the "all-powerfulness of natural selection" and on the complete indefiniteness of variation.
Both sides concur in the position assumed by Darwin, that the word "chance" in such a phrase as "chance variation" does not mean that the occurrences are independent of natural causation and so far undetermined, but covers in the first place our ignorance of the exact causation.
The implication of the phrase may go farther, suggesting that there is no connexion between the appearance of the variation and the use to which it may be put.
No doubt a large amount of variation is truly indefinite, so that many meaningless or useless variations arise, and in one sense it is a mere coincidence if a particular variation turn out to be useful.
But there are several directions in which the field of variation appears to be not only limited but defined in a certain direction.
When beetles, or medusae, or cats vary, the range of possible variation is limited and determined by the beetle, medusa or cat constitution, and any possible further differentiation or specialization must be in a sense at least orthogenetic - that is to say, a continuation of the line along which the ancestors of the individual in question have been forced.
Variation, again, as has been shown in this article, is limited by correlation; as any change involves other changes, the possibilities are limited by the organic whole.
A continuous environment both from the point of view of production of variation and selection of variation would appear necessarily to result in a series with the appearance of orthogenesis.
The past history of the organic world displays many successful series and these, as they have survived, must inevitably display orthogenesis to some extent; but it also displays many failures which indeed may be regarded as showing that the limitation of variation has been such that the organisms have lost the possibility of successful response to a new environment.
Although knowledge of variation has become much wider and more definite, the estimation in which natural selection is held has changed very little since Darwin and Wallace first expounded their theories.
Variation provides the material for selection, and although opinions may differ as to the nature of that material, the modes by which it comes into existence and their relative values and permanences, there is an increasingly wide consensus of opinion that all such material has to pass through the sieve of natural selection and that the sifted products form new varieties and species, and new adaptations.
The decision as to whether it is the course of variation or the course of selection that has been different in different localities can be made only by the field naturalist and the experimental breeder.
There remains open a wide field for inquiry as to the precise relations between selection and variation on the one hand, and their products, specific differences and adaptive structures, but the advance of knowledge has supplied no alternative to the Darwinian principles.
In the broadest way variation in organisms is primarily the necessary result of the absence of uniformity in the distribution of physical forces on the globe, in fact is a mere necessary response to the variation of inorganic conditions.
So, also, in the broadest way, the result of the existence of variation is equally inevitable.
It is plain that whilst the existence of variation can be demon strated and the occurrence of evolution established by induction and deduction, the part played by selection must remain largely theoretical.
From the time of Humboldt's visit to this remarkable region down to the present time there have been many diverse calculations of the height of these peaks, but with a considerable variation.
There is little difference between the quality of the two woods, the variation being in the foliage and fruit.
This construction assumes that the sun describes daily a small circle about the pole of the celestial sphere, and ignores any diurnal variation in the declination.
This variation is, however, so small that it can be neglected for most purposes.
In 1883 he was chosen to succeed Henry Smith in the Savilian chair of geometry at Oxford, and there he produced his theory of reciprocants, largely by the aid of his "method of infinitesimal variation."
The flora of Palestine has a considerable range and variety, owing to the variation in local climatic conditions.
The daily variation of temperature is also considerable.
It was found impossible, after many interviews, to obtain from Habibullah his consent to any addition to or variation of the terms of the assurance given by the British government in 1880, with which he professed himself entirely satisfied, so that the treaty finally settled in March 1905 went no further than a formal confirmation of all engagements previously concluded with the amir's predecessor.
The results were published in a General Chart of the Variation of the Compass in 1701; and immediately afterwards he executed by royal command a careful survey of the tides and coasts of the British Channel, an elaborate map of which he produced in 1702.
The lowest Gondwanas are very constant in character, wherever they are found; the upper members of the lower division show more variation, and this divergence of character in different districts becomes more marked in the Upper Gondwana series.
The temperature is nearly constant in southern India the whole year round, but in northern India, where the extremes of both heat and cold are greatest, the variation is very large.
The difficulty is that the automatic motion of a single mirror capable of reflecting the rays of any star continuously along the axis of a fixed horizontal telescope, requires a rather complex mechanism owing to the variation of the angle of reflexion with the diurnal motion.
The variation of precipitation is as great as 30 in.
The effects of a season of drought on the dry portions of the state need not be adverted to; and as there is no rain or snow of any consequence on the mountains during summer, a succession of dry seasons may almost bare the ranges of the accumulated stock 1 During the interval from 1850 to 1872 the yearly rainfall at San Francisco ranged from 11.37 to 49.27 in.; from 1850 to 1904 the average was 22.74, and the probable annual variation 4 in.
The variation is from dwarf mountain pine to giant cactus and dates.
But the mode of exercise of a power and its intensity are subject to variation, while the power remains essentially the.
Individuals reproduce unexpectedly the traits of earlier ancestors, and ethnologists and criminologists frequently explain by "atavism" the occurrence of degenerate species of man; but the whole subject is complicated by other possible explanations of such phenomena, included in the scientific study of normal "variation."
In each case the magnetograph only records the variation of the element, the absolute values being determined by making observations in the neighbourhood with the unifilar magnetometer and inclinometer.
The variation of the horizontal force is obtained by the motion of a magnet which is carried either by a bifilar suspension or by a fairly stiff metal wire or quartz fibre.
The apparatus was first used to investigate the variation in the volume of air with pressure, and the conclusion was that up to twenty-seven atmospheres, the highest pressure attained in the experiments, Boyle's law holds good.
We learn also that on account of the variation of g with the locality a gravitational system of force-measurement is inapplicable when more than a moderate degree of accuracy is desired.
The deviation of the earths figure from sphericity, and the variation of g with latitude, are here ignored.
This would cause a periodic variation in the latitude of any place on the earths surface, as determined by astronomical methods.
There appears to be evidence of a slight periodic variation of latitude, but the period would seem to be about fourteen months.
Further, on examining the small variation in i/i, it appears that in a slightly disturbed slow precession the motion of any point of the axis consists of a rapid circular vibration superposed on the steady precession, so that the resultant path has a trochoidal character.
These variables represent the whole assemblage of generalized co-ordinates qr; they are continuous functions of the independent variables x, y, 1 whose range of variation corresponds to that of the index r, and of 1.
Then the variation of the cubic contents of the vessel in a unit of time by reason of the motion of one piston is Va.
Although this method balances the pistons in the horizontal plane, and thus allows the pull of the engine on the train to be exerted without the variation due to the reciprocation of the pistons, yet the force balanced horizontally is introduced vertically and appears as a variation of pressure on the rail.
In practice about two-thirds of the reciprocating weight is balanced in order to keep this variation of rail pressure within safe limits.
Let da be the deviation of angular velocity to be produced in the interval dt, and I the moment of the inertia of the body about an axis through its centre of gravity; then 1/8Id(&) = Iada is the variation of the bodys actual energy.
Let M be the moment of the unbalanced couple required to produce the deviation; ther by equation 57, 104, the energy exerted by this couple in tht interval dt is Macit, which, being equated to the variation of energy gives da R2W da -
Romer 1 this is exactly the variation which a poet would introduce to relieve the primitive ballad-like sameness of question and answer; and moreover it forms the transition to the lines about the Dioscuri by which the scene is so touchingly brought to a close.
The present purpose being merely to illustrate the variation of distribution amongst a few representative countries, it is unnecessary to enter into more detail than such as will serve to distinguish the proportions of the population in main divisions of life.
At the same time, where the range is very wide, as between the rates in Scandinavia and Australia, and those in southern and eastern Europe, the variation, to a great extent, cannot be accounted for otherwise than by difference in hygienic conditions, more especially in the light thrown by the figures of infantile mortality in the second part of the table.
The variation from year to year in the quantity of wine produced in individual countries is, of course, far greater than that observed in the case of beer or spirits.
In that year he described a new eudiometer to the Royal Society and detailed observations he had made to determine whether or not the atmosphere is constant in composition; after testing the air on nearly 60 different days in 1781 he could find in the proportion of oxygen no difference of which he could be sure, nor could he detect any sensible variation at different places.
The sandy soil quickly absorbs the sun's heat and also quickly radiates it, so that there is great daily variation in the temperature.
In ten days of brilliant investigation, guided by clear insight from the very first into the meaning of the phenomena concerned, he established experimentally the fact that a current may be induced in a conducting circuit simply by the variation in a magnetic field, the lines of force of which are linked with that circuit.
The whole of Faraday's investigations on this subject can be summed up in the single statement that if a conducting circuit is placed in a magnetic field, and if either by variation of the field or by movement or variation of the form of the circuit the total magnetic flux linked with the circuit is varied, an electromotive force is set up in that circuit which at any instant is measured by the rate at which the total flux linked with the circuit is changing.
It will, of course, be understood that the base mark is subject to variation, the ruling factors being the amount of crop, quality and demand.
We have here, therefore, a perfect example of acclimatization by means of a spontaneous constitutional variation.
Wallace has recorded cases of simultaneous variation among insects, apparently due to climate or other strictly local causes.
The general laws of heredity and variation have been proved to apply to man as well as to animals and plants.
The variation may have been one of local use, either in Judea or in Babylonia; or the author may have had some fanciful reason for the transposition, such as, for example, that Pe following Samech (mo) might suggest the word nmo, " Wail ye!
Finally, these observers traced the variation to the fact that the wire supporting the aluminium needle as well as the wire which connects the needle with the sulphuric acid in the Leyden jar in the White pattern of Leyden jar is enclosed in a metallic guard tube to screen the wire from external action.
Fraunhofer, who defined the colours by means of the dark lines in the solar spectrum; and showed that the ratio of the dispersion of two glasses varied about 20% from the red to the violet (the variation for glass and water is about 50%).
The wound may simply have set up that variation in the buds the occasional existence of which has been already noted.
Their analysis of sensation supposes it to react, by a variation in tension, against the current from the sense-organ; and this is the mind's assent or dissent, which is inseparable from the sense presentation.
He maintained that there is a rapid variation of density near the surface of a liquid, and he gave very strong reasons, which have been only strengthened by subsequent discoveries, for believing that this is the case.
In more recent times the method of Gauss has been modified so as to take account of the variation of density near the surface, and its language has been translated in terms of the modern doctrine of the conservation of energy.'
In fact, the quantity 41rp 2 K, which we may call with van der Waals the molecular pressure, is so great for most liquids (5000 atmospheres for water), that in the parts near the surface, where the molecular pressure varies rapidly, we may expect considerable variation of density, even when we take into account the smallness of the compressibility of liquids.
He has also ccnstructed an apparatus in which this variation in the surface-tension is made to do work and drive a machine.
The groups which ornamented, as acroteria, the two gables of the temple have been in part recovered, and may now be seen in the national museum at Athens; at the one end was Boreas carrying off Oreithyia, at the other Eos and Cephalus, the centre in each case being occupied by the winged figure that stood out against the sky - a variation on the winged Victories that often occupy the same position on temples.
The insignia of an oriental bishop, with considerable variation in form, are essentially the same as those of the Catholic West.
Anciently it was called Twittenham or Twicanham, and the first form, or a variation of it, is used by both Pope and Walpole.
This work, which embodied the results of many years' research, was distinguished by its strict adherence to the scientific method of investigation by experiment, and by the originality of its matter, containing, as it does, an account of the author's experiments on magnets and magnetical bodies and on electrical attractions, and also his great conception that the earth is nothing but a large magnet, and that it is this which explains, not only the direction of the magnetic needle north and south, but also the variation and dipping or inclination of the needle.
Situated in the equatorial zone, Belgian Congo shows, over the greater part of its area, only a slight variation of temperature all the year round.
Owing to the action of the planets, the position of the ecliptic is subject to a slow secular variation amounting, during our time, to nearly 47" per century.
The motion of the ecliptic produces a secular variation in the obliquity which is now diminishing by an amount nearly equal to the entire motion of the ecliptic itself.
Several of them consist of a singing-match, conducted according to the rules of amoebean poetry, in which the second singer takes the subject chosen by the first and contributes a variation in the same air.
This state of things, due partly to mixture and crossing of races, and partly to independent variation of types, makes the attempt to arrange the whole human species within exactly bounded divisions an apparently hopeless task.
The great problem of the monogenist theory is to explain by what course of variation the so different races of man have arisen from a single stock.
The slightness and slowness of variation in human races having become known, a great difficulty of the monogenist theory was seen to lie in the apparent shortness of the Biblical chronology.
Inasmuch as several well-marked races of mankind, such as the Egyptian, Phoenician, Ethiopian, &c., were much the same three or four thousand years ago as now, their variation from a single stock in the course of any like period could hardly be accounted for without a miracle.
The general tendency of the development theory, however, is against constituting separate species where the differences are moderate enough to be 'accounted for as due to variation from a single type.
In addition to the variation in climate dependent on elevation, the year may be divided into three seasons.
In these cases the variation may have been due to altitude.
The second (or temperature) variation gives rise to phenomena which we proceed to discuss.
It increases as we ascend and reaches a maximum at a certain height, and then decreases according to the normal variation.
If a mare or other female animal is liable to be "infected" by her first or by subsequent mates, telegony will rank as a cause of variation, and breeders will be justified in believing (1) that pure-bred females are liable to be "corrupted" when mated with sires of a different breed; and (2) that inferior or cross-bred females, if first mated with a high-class sire, will thereafter produce superior offspring, however inferior or cross-bred her subsequent mates.
If, on the other hand, "infection of the germ" is impossible, telegony will not count as a factor in variation, and breeders will no longer be either justified in regarding mares and other female animals as liable to be "corrupted" by ill-assorted unions, or benefited by first having offspring to a high-class, or it may be more vigorous, mate.
Even now we know surprisingly little about the causes of variation, and not many years ago it was frequently asserted that there was no such thing as reversion or throwing back to an ancestor.
But even were the laws of heredity and variation better understood, the fact remains that we know little of the origin of the majority of our domestic animals.
The better we understand the laws of heredity and variation, and the more we learn of the history of the germ cells, the less need will there be to seek for explanations from telegony and other like doctrines.
The variation in leaf-form and the tendency of leaves to arrange themselves in various ways on different branches of the same plant are features which it is important to bear in mind in the identification of fossil conifers.
An examination of the wood of branches, stems and roots of the same species or individual usually reveals a fairly wide variation in some of the characters, such as the abundance and size of the medullary rays, the size and arrangement of pits, the presence of wood-parenchyma - characters to which undue importance has often been attached in systematic anatomical work.
The observance or variation of the discipline belongs to the Congregation of Rites; in pontifical processions, which are regulated by the masters of the ceremonies (magistri ceremoniarum pontificalium), these points are decided by the chief cardinal deacon.
The first essential is an elevated observatory; the next is a long series of bolographs taken at different times of the year and of the day, to examine the effect of interposing different thicknesses of air and its variation in transparency (chiefly due to water vapour).
The results vary between 1.89 and 2.22, and the variation appears to be solar, not terrestrial.
The isolation of these distant inland settlements has served to preserve the language, manners and physical characteristics of these early colonists with less variation than in any other Spanish-American state.
It may be taken as an axiom that the variation of minimum discharges from their mean values increases as the separate areas diminish.
Even neglecting the isolated and local discharges due to excessive and generally unrecorded rainfall, the variation in the discharge of all streams, and especially of mountain streams, is very great.
The particular drought shown on the diagram is the result of an exceptionally early deficiency of rainfall which, in conjunction with the variation of demand shown by the dotted line b b, is the most trying condition.
To avoid this loss the II% is in this case to be increased by the small quantity b e determined by examination of the variation of the actual from a constant demand.
After the reservoir begins to fall - in this case at the end of February - no ordinary change in the variation of demand can affect the question, subject of course to the cumulative demand not exceeding the reservoir yield for the assumed year of minimum rainfall.
The winds may also be the cause of the daily variation of level, which on Speke Gulf has been found to reach 20 in.; but this may also partake of the character of a "seiche."
No other state, except perhaps Washington, has such a great variation in the amount of its rainfall.
Motion in either direction is thereby obtained, and a considerable variation in the speed of rotation can be obtained by providing a cone pulley on the countershaft, which drives the cone pulley secured to the lathe E FIG.
The thecae in the earliest family - Dichograptidae - are so similar in form to the sicula itself that the polypary has been compared to a colony of siculae; there is the greatest variation in shape in those of the latest family - Monograptidae--in some species of which the terminal portion of each theca becomes isolated (Rastrites) and in some coiled into a rounded lobe.
The long-legged hairy sheep, which stands a good deal taller than a Southdown, ranges, with a certain amount of local variation, from Lower Guinea to the Cape.
To complete Pliicker's theory it is necessary to take account of compound singularities; it might be possible, but it is at any rate difficult, to effect this by considering the curve as in course of description by the point moving along the rotating line; and it seems easier to consider the compound singularity as arising from the variation of an actually described curve with ordinary singularities.
In point of bodily size mammals present a greater range of variation than is exhibited by any other living terrestrial animals, the extremes in this respect being displayed by the African elephant on the one hand and certain species of shrewmice (whose head and body scarcely exceed an inch and a half in length) on the other.
In regard to sense-organs, ophthalmoscopic observations on the eyes of living mammals (other than man) have revealed the existence of great variation in the arrangement of the bloodvessels, as well as in the colour of the retina; blue and violet seem to be unknown, while red, yellow and green form the predominating shades.
As a rule, the teeth of the two sides of the jaws are alike in number and character, except in cases of accidental or abnormal variation, and in the tusks of the narwhal, in which the left is of immense size, and the right rudimentary.
His grandfather was said to be Helias, knight of the Swan, one of the brothers whose adventures are well known, though with some variation, in the familiar fairy tale of "The Seven Swans."
There is no doubt that Callisto is identical with Artemis; her name is an obvious variation of KaXMiaTrt, a frequent epithet of the goddess, to whom a temple was erected on the hill where Callisto was supposed to be buried.
The Hexapoda are all provided with a highly developed tracheal system, which presents considerable variation in regard to its stigmata or orifices of communication with the exterior.
The modern methods of celestial mechanics may be considered to begin with Joseph Louis Lagrange, whose theory of the variation of elements is developed in his Mecanique analytique.