HI MEAN. 



appearance of meadow which ha* been manured with that of one left 

 in iU natural slate. It ha* been inserted by many agricultural author* 

 that the produce of hay is greater when the meadows are mown every 

 year, provided they be occasionally manured, than when mows and 

 depastured alternately. But the productiveness of a meadow depends 

 entirely on the circumstances of soil and situation. A meadow, the 

 oil of which is naturally of a rich nature, and adapted to produce fine 

 iisssn. may be mown year after year without any perceptible change 

 in the quality of the hay ; while another of inferior quality requires 

 to be occasionally cropped close, to check the growth of the coarser 

 ftiinmi. and to allow tie finer to rise. As to the effect of taking otf 

 the hay by mowing it, compared with that of the bite of cattle, there 

 is little difference, except that in pasturing the grass is repeatedly 

 cropped close to the ground as soon as it rises to such a height that 

 the teeth of the cattle can sever it. It consequently spreads by the 

 roots, and the pile becomes closer. The urine of the cattle greatly 

 promotes luxuriant vegetation in rainy weather, but in hot dry 

 weather it does more harm than good. The dung, when dropped on 

 the grass, is of little or no value compared with what it would be if 

 mixed up with straw, earth, or peat, or diffused through water in a 

 tank. It is therefore an excellent practice to employ women and 

 children to collect the fresh dung in the pastures, and to carry it to a 

 heap of earth where it may be covered up, or to a tank where it may be 

 diluted with water. 



Of late years the practice of tolling has been extensively adopted ; 

 that is, all the grass is mown and carried every day, in a green state, 

 to cows or hones tied up in a stable. By this means all the advantage 

 of mowing for hay is obtained, besides an abundant supply of rich 

 manure, which con be applied to the land in a liquid and diluted state, 

 when its effect is powerful and certain. So much more fodder is pro- 

 duced from the land by the system of soiling, that arable fields are 

 converted into artificial and temporary meadows, in which the different 

 species of grasses are sown, in order to be cut green or made into hay ; 

 and when, from the nature of the soil, the herbage degenerates, the 

 field being ploughed up again is greatly improved by this change of 

 cultivation. [GRASS-LAND.] 



When a natural meadow has been neglected, and the grass is of an 

 inferior quality, ami mixed with rank weeds and moss, it requires 

 much care to restore it to its original fertility. In most cases the 

 shortest method and the best is to plough it up, clean and manure it 

 during a course nf tillage, without taking very exhausting crops from 

 it, and then to lay it down again in a clean and enriched state, by 

 sowing the best sort of grass seeds; or, which is preferable, by 

 inoculating, or planting in it small tufts of gross from some rich 

 meadow, which will soon increase, and produce a new and improved 

 sward. But where the soil is a very stiff clay, with only a small depth 

 of good mould over it, there is some danger in breaking the old sward, 

 for it will take a long time and much manure to reproduce a proper 

 covering of gnus. In this case it is a preferable practice to scarify the 

 meadow, by means of instruments which do not go deep, but only tear 

 up the surface. If this is done early in spring, when the ground is 

 moist, and the whole surface is brought to resemble a fallow field, good 

 grass seeds may be immediately sown. If rich manure, mixed with 

 lime or chalk, be then spread over the land, and the whole well 

 harrowed and rolled, the old and young grass will spring up together, 

 and show a wonderful improvement in a very few months. It is 

 prudent to mow this renovated meadow before the seeds of the grasses 

 are formed, contrary to a common notion that in a thin meadow the 

 eed should be allowed to shed, in order to increase the number of 

 plant*. The notion is good, but it should be done by sowing seed 

 produced on other ground : for the ripening of the seed tends to 

 exhaust the soil. If the grass be cut before the flower is faded, the 

 root* will soon spread, and produce a new and improved sward. 



It must be observed that it is not indifferent what cattle are turned 

 into the meadow after hay making. Horses invariably produce coarse 

 weeds by their dung and urine ; cows may be depastured in autumn, 

 a* long as the surface is dry ; but sheep are far more advantageous, 

 and may be kept in the meadows at all times, if they are not too wet 

 for the health of the sheep, and if there is no danger of their having 

 the rot. 



MKAN. By the mean of two or more quantities is meant an inter- 

 mediate quantity determined by mathematical rules. There are more 

 way* than one of finding a mean, but the two principal results of thin 

 kind an called the arilAmelieal and the geometrical means. The names 

 are not properly expressive of the distinction between them, but they 

 are established by use. 



An arithmetical mean is the simple AVERAGE, formed by adding the 

 '{tiautitics together, and dividing by the number of quantities. A 

 geometrical moo is the square root of the product of the quantities. 

 Generally, let there be a number of quantities, r t , r t , t v Ac., and let 

 ., .-., 4c.) be a function of them which is symmetrical, that in, 

 whkh is nut altered when any two of them are interchanged ; then if 

 5 be found from the equation 



* (y, V, y, *c.)= * (* * * &c.), 



;/ may be called t ipecies of mean. 



The arithmetical mean, or average (which is always to be understood 

 when the word meau U mentioned, unless the contrary be specified), is 



MEAK. ui 



taken to be the most probable result of a number of discordant 

 quantities, which would have been the lame but for errors of obser- 

 vation or experiment. Thus if three measures of the same length give 

 122, 123, and 123-4, the mean of which is 122'8, it is presumed that 

 1 22*8 is more likely to be the real length which was attempted to be 

 measured than any other. We confine ourselves in the present article 

 to pointing out how it may be ascertained what degree of prol 

 belong* to such result*. 



In assuming the average as the most probable result, it is presumed 

 that any one measurement is as likely to err one way as the other ; 

 that is, a* likely to be too small as too great. If nothing but results 

 be known, this presumption is justifiable ; but if it be known that there 

 is more tendency to error of one sort than the other, the most pro- 

 bable result cannot be ascertained until it is found out by how much 

 the average of a very large number of observations would be affected 

 by this tendency. Say it is known that in the long run the average 

 will be increased -8 above the truth by a greater tendency to measure 

 too much than too little; then 122-8 -3, or 122'5, is the most pro- 

 bable result of the preceding three observations. 



It is obvious that when observations nearly agree with each other, 

 the average must be nearly the truth required, and the nearer the 

 agreement of the observations, the more nearly. If the observation* 

 do not agree well, the average is still more likely than anything else, 

 but not so likely as before. 



We now show how, having a number of observations, to determine 

 the probability that the truth lies within a given degree of nearness to 

 the average. A table must be used, which we here give to a greater 

 extent than we should otherwise do, on account of succeeding articles. 

 Let M be the average of a number of observations, and let u + m and 

 M m be the limits of which it is required to know what is the chance 

 of the truth being between them. Take the difference between M and 

 each of the results of observation, and add the squares of these dif- 

 ferences. Multiply 100 times the number of observations by m, and 

 divide by the square root of twice the sum just found : take the number 

 nearest to the result in the column marked A, and opposite to it, in the 

 column marked B, will be found the number of chances out of 10,000 

 for the degree of nearness required. 



Suppose, for example, that seven observations give 10-03, l<i-7I, 

 10-98, 10-26, 10-30, 1072, 10-81, the average of which is 10'54,difr, rin- 

 from the respective observations by -51, -17, '44, -28, -24, -18, and -27, 

 the sum of the squares of which is '7239, twice which JM 1 -.1478, the 

 square root of which is 1-203. Let it be required to tind the chance of 

 the truth lying between 10-54 + '06 and 10'54 -06, we have then to 

 multiply 700 by -06, which gives 42, and to divide by 1-203, whi.-li 

 gives 34-9. Opposite to 35 m the column A in found 37t>4, so that 

 3794 out of 10,000, or 3794 to 6206 is the chance of the result lj in- 

 between the limits given : that is, nearly 31 to 19 against it. If the 

 limits proposed had been 10-54 + -1 and 10-54 !, 700 multiplied by -1 

 and divided by 1'203 would have given 68'2. Opposite to 58 in the 

 table we find 6879, so that it is GS79 to 4121, or about 59 to 41, in 

 favour of the result lying between 10T>4 and 1 o 1 1. 



In the preceding rule it is supposed that all the observation* are 



