HEIGHTS, MEASUREMENT OF. 



HEIGHTS, MEASUREMENT OF. 



The water which may fall on the bulk and run down the smooth side 

 b arrested by the Mgn and soak* into the root*. In the other case 

 the top of the bank is the proper place, and a small concavity may be 

 given to it to retain the water and keep the roots moist. 



In a dry soil which does not require draining, ditches are unneces- 

 sary, and it is much better to plant a hedge on a little bank formed by 

 few sods about eighteen inches wide, with a small water-furrow on 

 each side. The whole width need not be above two feet six inches, 

 whereas a bank and ditch take up at least six feet, and the plough 

 cannot go nearer than a foot from the edge of the ditch or the bank. 

 Thus eight feet are taken up by the fence. 



When a hedge has been left uncut for several years, it grows wide 

 and high. It requires to be cut down once in seven or eight years ; 

 in this case much care is required in the cutting that the shoots may 

 grow out again regularly. The common labourers often do this very 

 carelessly, by cutting the stems downwards with one or more cuts of 

 their bill-hook. The consequence is that the stem is split and shivered, 

 and the rain lodging in the ragged cut injures the wood and causes it 

 to die down farther than it otherwise would. Hence the general 

 maxim of " cutting up," so strongly recommended by all those who 

 give directions about cutting hedges. Portions of the stems are often 

 left of a greater length than the rest for the purpose of holding the 

 bushes, whieh are generally laid over the cut stumps to protect them 

 against cattle. But it is better to cut the hedge regularly, one row 

 close to the ground, and one a few inches longer ; this will .strengthen 

 the foot of the hedge, and prevent its being thin and hollow at 

 bottom. 



When a hedge has become old, and many of the plants are decayed, 

 it is very difficult to renew it If young quicks are planted on the 

 same spot, they will scarcely ever succeed, unless very great precau- 

 tions are taken. The soil is exhausted or deteriorated, and must be 

 renewed : but manuring is not sufficient ; fresh earth is required for 

 the new quick. The simplest process is to level the old bank, spread 

 the earth of which it was formed, which will be of great use to the 

 ground where it is spread, and form a new bank in the same place 

 from earth taken elsewhere ; or, where it can be done without incon- 

 venience, it is better to make an entirely new ditch and bank, and to 

 fill up the old. This is perhaps the surest as well as the soonest way of 

 having a new hedge which will be permanent. 



What has been said of renewing a hedge is equally applicable to 

 repairing gaps in an old one. It is of no use to put in young plants 

 in the old bank. The earth must be removed, and fresh earth put in 

 its place. The old hedge must be cut and trimmed, so that the young 

 quick may not be shaded, and in that case the gap will shortly be filled 

 up, and the hedge be restored as a continuous fence. Where the gaps 

 are very small, and the hedge is not cut down altogether, it may some- 

 times be advisable to plant hollies or other plants, which will grow 

 well and fill up the deficiency. 



Well managed hedges are the most effective fences, the cheapest, 

 and the most pleasing to the eye. It is to the hedge-rows that England 

 owes much of its garden-like appearance; but the trees, which are 

 their chief ornament, are very destructive of the hedge as a fence ; 

 and where trees are planted it would be much better if they stood 

 within the bank, without interfering with the hedge. Whether trees 

 can be allowed in hedge-rows, in a perfect system of agriculture, is a 

 question which we will not attempt to answer. 



There is a method of repairing hedges which is called " plashing" 

 (pleaching). It consuls in cutting half through some of the stems 

 near the ground, and then bending the upper parts down in a hori- 

 zontal or oblique position, keeping them so by means of hooked sticks 

 driven into the bank. Thus a live hedge is made, which fills tip tin- 

 gaps in the same manner as a dead hedge would have done, and the 

 bent stems soon throw out shoots. If the stems are young, and not 

 above the thickness of a finger, an excellent hedge may be thus formed, 

 which, when clipped, will be close and perfectly impervious. But the 

 work is generally done in a very injudicious manner. When a hedge 

 is plashed which has been long neglected, the thick stems, which are 

 hacked through, leaving only a small portion of the under bark uncut, 

 have an unsightly appearance, and seldom throw out shoots near the 

 bottom, where they are most wanted. To plash a young hedge by 

 merely bending the twigs is an excellent practice : but when the stems 

 are thick and old, the only remedy is to cut them down, or make an 

 entirely new bank well planted with quick. 



IIKIUHTS, MEASUREMENT OK. There are three very distinct 

 ways by which height* may be measured. The first is by observation 

 of the angles of elevation of objects, supposing their distances to be 

 known, which is explained roughly in works on trigonometry and men- 

 oration, and with more precision in those on geodesy. [MENSURATION.] 

 The second serves for the measurement of heights in cases where not 

 only the height of a summit is required, but also that of the slope 

 which leads to it, at different distances from the summit ; and this is 

 done by means of the level. [LEVELLING.] The third, which we 

 propose here to describe more particularly, is accomplished by means 

 of the barometer. [BAROMETER.] We may also refer to a fourth 

 method, depending on the diminished temperature at which liquids 

 boil under diminished pressures : for the experimental detail* of thin 

 method, see BOILIXU or LIQUIDS. 



If we ascend with a barometer through any height, the weight of 



the column of air which presses on the instrument is diminished, and 

 the counterpoise, namely, the column of mercury under the vacuum, 

 must diminish likewise ; that is, the mercury must fall. The amount 

 of this fall depends upon the height in question : and when the relation 

 between the two is perfectly well ascertained, may be made the means 

 of determining it. If the temperature at the higher and lower station 

 were the same in all places and at all limes, and if the force of gravity 

 were precisely the same at all heights, one formula would serve for all 

 times and for different places, if the height of the barometer remained 

 always the same at the some height above the sea. In such a case, one 

 observation made in London a hundred years ago, combined with one 

 made at Quito in the present time, would serve to determine the dif- 

 ference of level between those two places. And even as it is, the mean 

 height of the barometer at the two places, when known, could be made 

 to determine the point. But when only one or two observations can 

 be mode at each place, the differences of temperature, Ac., must be 

 noted and allowed for: and this necessity renders the numerical 

 operations connected with the solution of the problem more intricate 

 than they would otherwise be. 



If the temperature were unaltered during the ascent, and the force 

 of gravity also remained uniform, the logarithm* of the atmiwpli. i i.- 

 pressures corresponding to different altitudes would demote in arith- 

 metical proportion as the altitudes themselves increase in arithmetical 

 proportion ; that is, the density of the atmosphere d-frtaxt in a 

 geometric progression, as the heights increate in an arithmetic progres- 

 sion. Thus if at altitudes and A the logarithms of the pressures 

 were k and k I, at an altitude 2 A the logarithm of the pressure would 

 be i 2 /, and so on. And since the height of the barometer is pro- 

 portional to the pressure for the time being, this would lead to an 

 equation of the form 



r=c(log.A-log.A'); 



where z is the difference of altitudes at two stations, and A and A' the 

 heights of the mercury at the lower and upper stations. 



The constant c might be determined either from theery or actual 

 measurement ; for if A and A' were known in any one cose, and 

 also 2 by trigonometrical or other measurement, c might be deter- 

 mined, and being independent of z,h, and A', would then be known 

 in all cases. But in truth c is not to be thus determined, for 

 though independent of A and It', it varies with temperature, the force 

 of gravity, &c. 



1. If the temperature cither of the higher or lower stations be not 

 the same in different observations, the multiplier c will be of one value 

 or another, depending on the temperatures. 



2. If the mercury be not of the same temperature at all times, its 

 specific gravity will vary, so that a given column of it will not represent 

 the some atmospheric pressure at all times. 



3. If the force of gravity be taken into account, the pressure taken 

 off by the ascent will be a larger proportion of the whole pressure 

 than was supposed in the investigation of the preceding formula, since 

 it is taken from the part of the atmosphere where the force of gravity 

 is greatest. This is independent of its greater weight as being token 

 from the densest part of the atmosphere. The latter circumstance 

 has been already taken into account in the formula, and from it 

 comes the law that the logarithms of the pressures diminish in arith- 

 metical progression, since the pressures themselves would diminish 

 in arithmetical progression if the density of the air were the some at 

 all heights. 



4. Bessel lias recently shown that another correction must be 

 applied, owing to the modifications produced by the existence of a 

 humid atmosphere of peculiar habitudes, within the dry or permanently 

 elastic one. After applying all these corrections, the formula.' are 

 determined by the aid of subsidiary or Ay/uumt/riV tables, the best of 

 which are those by Delcroe, published in the ' Annuaire Meteorologique,' 

 for 1849. Those containing alto Bessel's correction ore given in the 

 same work by Plantamour, for 1852. 



We now proceed to describe two formula; mode on slight differences 

 of hypothesis as to the element of the problem about which we know 

 least, namely, the law of variation of the temperature of the atmosphere. 

 The first formula, which is nearly in the form given by Laplace, is 

 t.ikc-n from Poisson's Mechanics, and supposes that the air intermediate 

 between the higher and lower stations may be treated u ii it lia.l 

 throughout the mean between the temperature of the two stations. 

 The second, token from Lindenau's Barometric Tables, is on the sup- 

 position (which was also made by Eulcr and Orioni) that the tem- 

 perature of the air diminishes in harmonic progression through a series 

 of heights increasing in arithmetical progression. 



Let A and A' be tint heights of the barometer at the lower ami tippi T 

 stations; I and t' the temperatures of the air; T and T' those of tin- 

 mercury (ascertained by a thermometer whose bulb is in the cistern) ; 

 r the radius of the earth, .m.l \ tlio latitude of the place. All the 

 temperatures are in degrees of Fahrenheit. Let 



=A( I+ *=*\ 



\ 990/ 



CMIUS / 



c= 1- -00267 cos 2A V 1 + 

 t=c(log. A log. t). 



