649 



MAUVE. 



MEADOWS. 



60 



Corinthian. We may also mention those at Cobham in Kent, and 

 Brocklesby in Lincolnshire, by the late James Wyatt. 



MAUVE. A new lilac colour or dye, obtained from aniline by Mr. 

 Perkin. [COLOURING MATTERS.] 



MAXIMA and MINIMA. These Latin words, which simply 

 mean " greatest " and " least," are used to imply, not the absolute 

 greatest and least values of a varying quantity, but the values which it 

 has at the moment when it ceases to increase and begins to decrease, 

 or rice versa. Thus, if it be said that the height of the barometer was 

 a maximum at ten o'clock, it means that up to that hour the barometer 

 rose, and then began to fall ; in which case it would still be said to 

 have been a maximum, even though it should afterwards rise, and 

 stand at a greater height than that at ten o'clock. Thus it is possible 

 that there should be several maxima and minima in one day, and even 

 that one of the minima should be greater than one of the maxima : 

 that is, at one moment when the fall ceases and a rise begins, the 

 barometer may then be higher than it was at another time when a rise 

 had ceased and a fall began. 



The theory of maxima and minima is, mathematically speaking, 

 very simple. It is obvious, from the definition of a differential 

 coefficient, that if y be a function of x, and if x be increasing, then 



dy dy 



when y also increases, -r- is positive; and when y diminishes, -T- is 



negative 1 . If the words increase and diminution have their full alge- 

 braical sense, this proposition is true whatever the sign of y may be. 



d// 

 It follows that when increase ceases and diminution begins, -77 changes 



from positive to negative, and when diminution ceases and increase 

 begins, it changes from negative to positive. But as a quantity cannot 

 change its sign without becoming either nothing or infinite, it follows, 

 first, that y can only be a maximum when x has such a value that 



fly 



jjj u nothing or infinite ; secondly, that there is not then a maximum 



unless the latter change from positive to negative, when x increases 

 through that value ; nor a minimum unless the same differential 

 coefficient change from negative to positive, in the same case. 



Thus when y = a + x x-, the differential coefficient of which is 

 1 2x, we see that the latter changes sign when x changes from less 

 than 4 to greater than ^ ; and the change of sign is from positive to 

 negative. There is therefore a maximum when ar=i, and this 

 maximum is o + 4 i, or a + ^. 

 dy 



When jj = (which is by far the most common case), and there is 



a maximum, it changes sign from + to , or diminishes, algebraically 



d*y dy 



speaking : therefore ^3 i negative. "Similarly, when -JJT = 0, and 



d*y dy 



there is a minimum, y* is positive. But when r- is infinite, and 



there is a maximum or minimum, this additional rule does not apply. 



Works on the differential calculus give the development of this 

 theory and examples. We shall here only add one of the rules for 

 determining the maximum or minimum when there are two distinct 

 variables. 



When 2 is a function both of x and y, two variables independent of 



dz <h I 

 one another, there may be a maximum or minimum when ^ and ^- 



are both nothing, both infinite, or one nothing and the other infinite, I 

 When they are both nothing, which is the only case in which this 

 theory i of any practical application, it must be determined as follows 

 whether there be any maximum or minimum, and which it is. Find 



dz dz 



the values of x and y which make ^ = 0, T- = 0, and with any pair 



of these values find the value of the expression 

 / iFi 

 \tl.c dy 



If thi be negative, or nothing, there is a maximum or minimum ; 

 if it be positive, there is a mixture of the two which can only be satis- 

 factorily explained by illustrations drawn from the theory of curved 

 surfaces. When the expression is negative or nothing, there is a 



maximum if -7-5 and -7-3 be both negative, and a minimum if they be 



both positive. 



Tim usual method of establishing all the preceding formula, 

 namely, by the application of Taylor's theorem, applies only to the 

 cases in which the differential coefficients become nothing, and not to 

 that in which they become infinite. It is also frequently stated that 

 there U always a maximum or minimum when a differential coefficient 

 vanishes, which is not true. 



MAXIMUM IN MACHINES. [MACHINE.] 



MAY, the fifth month of our present year, was the second in the old 

 Alban calendar, the third in that of Komulua, and the fifth in the 

 calendar of Numa Pompilius. In the Alban calendar it consisted of 

 twenty-two days ; of thirty-one in the calendar of Komulus ; and of 

 thirty in that of Numa. Julius Cwsar restored to it the odd day of 



which Numa had deprived it, and of which it still keeps possession; 

 Its etymology is doubtful. Ovid, in the fifth book of his 'Fasti,' 

 proposes three derivations : one from majestai ; another from majores, 

 a term which signified the patres, or governing body of the city of 

 Romulus ; and the third from Mam. The Roman month was under 

 the protection of Apollo ; and on account of the celebration of the 

 Lemuria, marriages undertaken during its course were considered ill- 

 omened. (Ovid, Fasti, v. 483-490.) 



Our Saxon ancestors, after the Romans, called it Maiusmontk; and, 

 in their native language, threo-meolce, three-milk month, when cows 

 were milked three times a day. 



MAY-DAY and MAYING. It was anciently the custom, observes 

 Brand, for all ranks of people to go out a-maying early on the 1st of 

 May. Bourne (' Antiq. Vulg.', ch. xxv.) tells us that, in his time, in 

 the villages in the north of England, the juvenile part of both sexes 

 were wont to rise a little after midnight on the morning of that day, 

 and walk to some neighbouring wood, accompanied with music and 

 the blowing of horns, where they broke down branches from the trees, 

 and adorned them with nosegays and crowns of flowers. This done, 

 they returned homeward with their booty about the time of sunrise, 

 and made their doors and windows triumph in the flowery spoil. 



There was a time when this custom was observed by noble and royal 

 personages as well as the vulgar. Chaucer, Shakspere, Browne 

 (' Britannia's Pastorals'), and other writers in verse and prose, have 

 described or alluded to the popular celebration of the day. The may- 

 pole was raised in every town and village, and milk-maids and morris, 

 dancers danced round it. These customs gradually fell into disuse ; 

 and in London the celebration of the day was left to the chimney- 

 sweepers/whose representatives still in London and its suburbs struggle 

 for an existence with their Jack-in-the-green and their tawdry finery. 

 In many country villages, however, the observance of May-day is kept 

 up on a small scale, by children carrying from door to door garlands 

 of paiglcs (or cowslips), blue-bells, and other field flowers ; and in 

 some places there is a feeble imitation of "going a-maying." (See 

 Notes and Queries, 1st series, passim.) 



In the Highlands of Scotland the 1st of May was celebrated as 

 Bel-tein day, on which they made a fire, and performed certain puerile 

 ceremonies, which are supposed to have had reference to the worship 

 of Baal, or the sun. The Irish celebrated it by having a peculiar dish 

 of food, the partaking of which they imagined secured them against 

 want for the year. The Germans imagined that on the night of this 

 day the witches had an assemblage on the Brockeu iu the Harz 

 mountains. In France and Italy the youth of both sexes gathered 

 branches in the night, which they placed before the doors of those to 

 whom they wished to show good-will. There were many other super- 

 stitious observances connected with this day, nearly all of which are 

 now obsolete, or about to become so. 



The celebration of this day probably owed its origin to the heathen 

 observances practised at this season of the year in honour of Flora, the 

 deity who presided over fruits and flowers. (Hospinian, De Festis 

 Judceorum et Ethnicorum, fol. 100 ; Brand's Popular Antiquities; Strutt's 

 Sports and Pas/imes; Hone's Every Day Book.) 



MAYOR. [MUNICIPAL CORPORATIONS.] 



MEADOWS are properly low grounds ou the banks of rivers, which, 

 being kept moist by their situation, and also occasionally flooded by 

 the rise of the waters, are best adapted for the growth of grass, and 

 are generally mown for hay. Some meadows of great extent, 

 belonging to a community or district, in which every inhabitant has a 

 right to send his cattle to graze, under certain regulations, are never 

 mown. 



When the number of those who have a right of common pasture is 

 not very great, they frequently agree among themselves to abstain from 

 depasturing the meadows in spring, and, dividing them into portions, 

 each makes hay of his share ; after which the cattle are admitted in 

 common for the remainder of the season. Thus a common meadow is 

 converted into a Lammat meadow, that is, a meadow which becomes a 

 common pasture after the 1st of August, this being the time when it 

 is supposed that all the hay has been made and secured. 



When meadows are private property they become much more 

 valuable. The flooding is encouraged or prevented, according to 

 circumstances, and in many cases artificial irrigation is adopted. 

 [IRRIGATION.] If they are exposed to be too often inundated, they are 

 protected by dams and sluices. 



The herbage of low wet meadows is generally coarser and less 

 nutritious than that of those which lie higher : hence upland hay, as 

 it is called, is preferred for the better sort of cattle. Good grass land, 

 to which the floods never rise, is often called meadow laud when the 

 natural herbage is permanent, and frequently made into hay. 



Upland meadows are very valuable wherever there is a demand for 

 good hay. A considerable degree of attention is required to make 

 them most productive. Not being annually recruited by flooding, 

 they would soon degenerate if some pains were not taken to keep up 

 their natural fertility. This may be done in various ways : the most 

 obvious is to recruit them frequently with the richest animal and 

 vegetable manure, which, being spread over the surface at a time when 

 showers are abundant, that is, either early in spring or immediately 

 after midsummer, is washed down to the roots of the grass. A rapid 

 growth is thus produced, which is soon perceived by comparing the 



