About the time of the maxima there must be a longer tidal range (that is, a greater rise and fall than the average); the difference between neap tides and spring tides will also be increased, and as results of these conditions there must be great tidal floods breaking over lowlying coasts and producing extensive denudation.
In most cases two distinct maxima and minima occur in the 24 hours.
And intended to eliminate irregular changes, but they also to some extent eliminate regular changes if the hours of maxima and minima or the character of the diurnal variation alter throughout the year.
The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes.
Aepyornis maxima, which laid enormous eggs, and not unnaturally recalls the mythical " roc " that figures so largely in Arabian tales.
For maxima, and between - 40° and - 70° Fahr.
Inhabited by the Rauraci and the Sequani, it formed part of ancient Gaul, and was therefore included in the Roman empire in the provinces of Germania Superior and Maxima Sequanorum.
But the average of two presi dential votes was 85.37%; and the maxima, minima and means for mayors and governors were respectively 83.86, 74.99, 78.36 and 8 4.73, 61.7 8, 75.7 2.
He also gave in his Fluxions, for the first time, the correct theory for distinguishing between maxima and minima in general, and pointed out the importance of the distinction in the theory of the multiple points of curves.
Newlands in England, that if they are arranged in the order of their atomic weights they fall into groups in which similar chemical and physical properties are repeated at periodic intervals; and in particular he showed that if the atomic weights are plotted as ordinates and the atomic volumes as abscissae, the curve obtained presents a series of maxima and minima, the most electro-positive elements appearing at the peaks of the curve in the order of their atomic weights.
For the subjects of this heading see the articles DIFFERENTIAL EQUATIONS; FOURIER'S SERIES; CONTINUED FRACTIONS; FUNCTION; FUNCTION OF REAL VARIABLES; FUNCTION COMPLEX; GROUPS, THEORY OF; INFINITESIMAL CALCULUS; MAXIMA AND MINIMA; SERIES; SPHERICAL HARMONICS; TRIGONOMETRY; VARIATIONS, CALCULUS OF.
There are therefore maxima and minima in the value of the tide-generating force, depending on the relative positions of the sun, earth and moon.
In addition to these there are subsidiary maxima at intervals of 41, 9 and 84-93 years.
Given, then, that the variations in tide-generating force are big enough, the periods when the maxima occur will be critical with regard to oceanographical and meteorological phenomena.
The theory of inequalities is closely connected with that of maxima and minima, and therefore seems to come properly under this head.
The maxima occur when u=tan u, (4), and then sin 2 u/u 2 = cos 2 u (5).
Since the maxima occur when u = (m +1)7r it nearly, the successive values are not very different from 4 4 4 &c The application of these results to (3) shows that the field is brightest at the centre =o, =0, viz.
Within the rectangle formed by pairs of consecutive dark lines, and not far from its centre, the brightness rises to a maximum; but these subsequent maxima are in all cases much inferior to the brightness at the centre of the entire pattern (=o, n =o).
When z is great, the descending series (io) gives i 2J 1 (z) = 2 sin (z1 7r) 22; (2) z so that the places of maxima and minima occur at equal intervals.
The intensity may be expressed by 12= (2+Cv) 2 +(2+Sv) 2 and the maxima and minima occur when dC dS (z+Cv)a`j+(2+Sv)dV=0, whence sin rV 2 +cos27rV 2 =G..
Rich annual displays of meteors have often been remarked on about the 10th of August, directed from Perseus, but they do not appear to have exhibited periodical maxima of great strength.
In each of the three oceans there are two maxima of salinity-one in the north, the other in the south tropical belt, separated by a zone of minimum salinity in the equatorial region, and giving place poleward to regions of still lower salinity.
Buchanan pointed out in 1876, that the great contrasts in surface salinity between the tropical maxima and the equatorial minima give place at the moderate depth of 200 fathoms to a practically uniform salinity in all parts of the ocean.
The tropical maxima of salinity on the poleward side of the trade-winds coincide with the regions of minimum rainfall, high temperature, strong winds and consequently of maximum evaporation.
The range between the mean of the maxima of the summer months (June, July and August) and the mean of the minima of the winter months (December, January and February) is only from 88° to 50° at Galveston, but at Mount Blanco, Crosby county, on the eastern border of the Llano Estacado, it is from 90° to 26°.
To this victory was assigned the founding of the Ara maxima by Evander.
Thus, an interval of one-third of a second elapses between two successive maxima or beats, and there are produced three beats per second.
To Zenodorus (c. 200100 B.C.) is due the important problem in maxima and minima that for a given surface the sphere is the solid of maximum volume.
The absolute minima at these two places are respectively-46° and -29°; the absolute maxima, III ° and 1066°, and the mean annual temperatures, 42° and 46°.
The strong changes of temperature with the seasons are indicated also by the distribution of summer maxima and winter minima; summer temperatures above 112 are known in the south-western deserts, and temperatures of 100 are sometimes carried far northward on the Great Plains by the hot winds nearly to the Canadian boundary; while in winter, temperatures of 40 occur along the mid-northern boundary and freezing winds sometimes sweep down to the border of the Gulf of Mexico.
Imhof, Beitrdge zur Anatomie von Perla maxima (Aarau, 1881); K.
Diocletian added Helvetia, and part of Germania Superior to Sequania, which was now called Provincia maxima Sequanorum, Vesontio receiving the title of Metropolis civitas Vesontiensium.
We may say therefore that if the difference between the frequencies n 1 and n, of the two waves is such that in the combined image of the slit the intensity at the minimum between -the two maxima falls to 0.81, the lines are just resolved and n l /(n l n 2) may then be called the resolving power.
2 Basing the investigation on the same criterion of resolution as in the case of narrow slits, we postulate for both narrow and wide slits that two lines are resolved when the intensity of the combined image falls to a value of o 8ro in the centre between the lines, the intensity at the maxima being unity.
In the 5th century there were five provinces, Britannia Prima and Secunda, Flavia and Maxima Caesariensis and (for a while) Valentia, ruled by praesides and consulares under a vicarius, but the only thing known of them is that Britannia Prima included Cirencester.
The summer maxima on the mountains are usually 8° to 10° less than in the valleys directly below them; Saegerstown, Crawford county, is nearly 30 m.
As we have seen, the maxima of the various curve-branches at C, E, G, and J correspond with the melting points of the various hydrates at 37°, 32.5°, 56° and 73.5° respectively; and at these points melting or solidification of the whole mass can occur at constant temperature.
Of the "Bibliotheca Patrum Maxima" (Lyons, 1677).
To the south of this in Europe the single maximum at mid-winter is replaced by two maxima, somewhere about the equinoxes.
The Scandinavian data, from the wealth of observations, are probably the most representative, and even in the most northern district of Scandinavia the smallness of the excess of the frequencies in December and January over those in March and October suggests that some influence tending to create maxima at the equinoxes has largely counterbalanced the influence of sunlight and twilight in reducing the frequency at these seasons.
The 6-month term has the earliest of its two equal maxima about the 26th of March.
All are observed frequencies, derived after Wolf's method; maxima and minima are in heavy type.
The maxima and minima in the two phenomena in a good many cases are not found in the same years.
Schuster, who has considered the matter very fully, has found evidence of the existence of other periods-notably 8.4 and 4.8 years-in addition to the recognized period of 11.125 years, and he regards the difference between the maxima in successive II-year periods as due at least partly to an overlapping of maxima from the several periodic terms. This cannot, however, account for all the fluctuations observed in sun-spot frequencies, unless other considerably longer periods exist.
Fawsitt (The Education of the Examiner, Royal Philosophical Society of Glasgow, 1905) shows that frequency-curves deduced from actual investigation of class-marks are not symmetrical, but have two maxima corresponding to the performance of " non-workers " and of " workers."
The different maxima differ considerably in brightness; thus in 1906 (the brightest maximum since 1779) the second magnitude was reached, but in other years (as in 1868) it has failed to reach the fifth magnitude.
Also, the period varies somewhat; the maxima occur sometimes early and sometimes late as compared with the mean period, but the difference is never more than forty days.
A large eccentricity also produces an unsymmetrical light variation, the minimum occurring at a time not midway between two maxima; stars of this character are called Cepheid variables, after the typical star S Cephei.
And the mean summer temperature (June, July and August) 75°; the mean of the winter minima was 27°, and the mean of the summer maxima 85°.
In favour of this may be mentioned: the similarity of the Greek Oeo Evta, in which, however, the gods played the part of hosts; the gods associated with it were either previously unknown to Roman religion, though often concealed under Roman names, or were provided with a new cult (thus Hercules was not worshipped as at the Ara Maxima, where, according to Servius on Aeneid, viii.
The fifth book contains properties of normals and their envelopes, thus embracing the germs of the theory of evolutes, and also maxima and minima problems, such as to draw the longest and shortest lines from a given point to a conic; the sixth book is concerned with the similarity of conics; the seventh with complementary chords and conjugate diameters; the eighth book, according to the restoration of Edmund Halley, continues the subject of the preceding book.
All details of the object so resolved are perceived, if two diffraction maxima can be passed through the objective, so that the character of the object is seen in the image, even if an exact resemblance has not yet been attained.
13, we suppose that a diffracting particle of such fineness is placed at 0 that the diffracted pencils of the 1st order make an angle w with the axis; the principal maximum of the Fraunhofer diffraction phenomena lies in F' 1; and the two diffraction maxima of the 1st order in P' and P' 1.
Abbe showed that for the production of an image the diffraction maxima must lie within the exit pupil of the objective.
At least two successive diffraction maxima must be admitted through the objective for there to be any image of the objects.
These diffracting details become especially distinct if the direct lighting cone of rays, the spectrum of zero:order or the chief maximum, is not allowed to enter the objective and instead only two or more diffraction maxima are taken up; the details then appear bright on a dark background.
In the subdivision of Gaul in the 4th century, Helvetia, with the territory of the Sequani and Rauraci, formed the Provincia Maxima Sequanorum, the chief town of which was Vesontio (Besancon).