note the number of degrees on the horizontal circle at e; and which are measured by the chain, are called chain then the difference between this and the former num-lines, or station lines. ber is the required horizontal angle. To measure a vertical angle: Direct the telescope to the object whose angle of elevation is required; then the arc, intercepted between Q and o, is the required angle. An angle of depression is similarly measured. The plane table is frequently used in surveying. This instrument consists of a plane and smooth rectangular board fitted in a moveable frame of wood, which fixes the paper on the table PT, in the adjoining figure. The cen- P tre of the table below is fixed to a tripod, having at the top a ball-and-socket joint, so that the table may be fixed in any required position. The table is fixed R T in a horizontal position by means of two spirit-levels lying in different directions, or by placing a ball on the table, and observing the position of it in which the ball remains at rest. The edges of one side of the frame are divided into equal parts, for the purpose of drawing on the paper lines parallel or perpendicular to the edges of the frame; and the edges of the other side are divided into degrees corresponding to a central point on the board for the purpose of measuring angles. A magnetic compass box C, is fixed to one side of the table for determining the bearings of stations and other objects, and for the purpose of fixing the table in the same relative position in different stations. There is also an index-rule of brass IR, fitted with a telescope or sights, one edge of which, called the fiducial edge, is in the same plane with the sights, and by which lines are drawn on the paper to represent the direction of any object observed through the sights. This rule is graduated to serve as a scale of equal parts. A principle of measuring by triangles, which is alike common to land-surveying and the trigonometrical surveys of engineers, may be comprehended from the following figure. We wish to find the distance between two objects that are either invisible from each other, or inaccessible in a straight line from each other. B Let A and C be the two objects inaccessible in a straight line from each other, on account of a marsh. Measure two lines AB, BC, to the objects and the contained angle B. In the triangle ABC, two sides AB, BC, and the contained angle B, are known; hence AC may be found. I Divide the field into triangles, or into triangles and quadrilaterals, the principal triangles or quadrilaterals occupying the great body of the field, and the rest of it containing secondary triangles and trapezoids formed by offsets from the chain lines. Measure the base and height, or else the three sides of each of the principal triangles, then calculate their areas by the rules in Mensuration of Surfaces, and also the offset spaces, and the sum of all the areas will be that of the entire field. I Example 1.-Find the contents of the adjoining field from these measurements, A being the first and B the second station :— B gC = 141 to left. hE = 180 to right. iD = 167 to left. kF 172 to right. = triangle AgC= Ag gC= 150 × 141 BiiD 172 x 167 = = 323 x 180 = 21150 = = 137676 = 28724 = 58140 =105952 145 x 172 = 24940 Twice area = 376582 And area = 188291 = 1 acre, 3 roods, 21-26 poles. These admeasurements, instead of being written out as above, are generally registered in a tabular form. A field-book, which is used to enter these measurements, is divided into three columns. The different I distances on the chain line are written down in the middle column, and in the right and left-hand columns the offsets are inserted, with any remarks that may be made. The measurements on the chain lines are written in order upwards in the middle column, the first being written at the foot of the column, as the surveyor can thus more conveniently compare the measurements with the imaginary lines in the field. measurement, or in engineering plans for canals, railIn surveying a whole country by trigonometrical ways, and roads, it is necessary to make allowance for the earth's convexity in all the calculations of levels. Such a problem as the above is common in measur- The degree of convexity, or departure from a true ing heights and distances; and it will be understood, level, is reckoned to be about 7 inches and 9-10ths in that the principle of throwing the area of any given the space of a mile. (See article HYDROSTATICS.) In field or set of fields into triangular spaces, is that pur-land-measuring, the scale of operations is ordinarily too sued in all processes of land-measurement. In most limited to require any such allowance for difference of instances, fields are irregular in form; their outlines levels. being often bent, with a greater width at one place than another. In such cases, after measuring the areas of the triangles, the odd pieces at the sides require to be measured, and their aggregate area added to the whole. We may illustrate the process of surveying as follows: The angular points of the large triangles or polygons, into which a field is to be divided for the purpose of taking its dimensions, are called stations, and are denoted by the marko; thus, o, is the first station; o, the second; and so on. The lines joining the stations, We have now, as far as our limits would admit, presented an outline of the methods pursued in land-surveying; and to those who design following out the study of this, as well as other branches of theoretic and prac tical mathematics, we recommend a regular course of instruction from Mr Bell's excellent treatises in Chambers's Educational Course-works so cheap as to be within every one's reach. Printed and published by W. and R. CHAMBERS, Edinburgh jects where many causes are presumedly involved, and which are so extensive that it is difficult to command a general view of them. As an example, we have only to remind the reader of the various notions which are usually entertained as to the causes of any distress which may take place throughout the country. The higher class of statisticians usually, however, are cautious in drawing inferences and tracing causes, believing it to be their best course, in all doubtful cases, to restrict themselves to the collection of facts. BIRTHS. Proportion of the Sexes. Many millions of observations have been made upon births in the various countries of Europe, from which one uniform result appears, that about 21 boys are born for 20 girls. The proportion in different states is here stated: Russia, STATES AND PROVINCES. The province of Milan, Mecklenburg, France, Belgium and Holland, Brandenburg and Pomerania, Kingdom of the Two Sicilies, Austrian Monarchy, Silesia and Saxony, Prussian States (en masse), Westphalia and Grand Dutchy of the Rhine, Kingdom of Wurtemburg, Eastern Prussia and Dutchy of Posen, Kingdom of Bohemia, Great Britain, Average for Europe, 100 Females. 1C8-91 107.61 107.07 106-55 The proportion of dead-born to live-born children is found in European cities to be about 1 in 20, but in the country not above half that amount; showing apparently that rural life is most favourable to the health of women during pregnancy and to successful parturition. It is worthy of remark, that more male than female children are still-born; the proportion in Western Flanders has been found as 14 to 10, and the same result appears in some other countries. At Gottingen, in 100 births, 3 were of legitimate and 15 of illegitimate children. Effects of Scarcity. Times of scarcity and privation tend to reduce the number of marriages, and also of births, though geneMales to rally not immediately. The great scarcity which oc curred in England at the commencement of the present century, occasioned a diminution in the number of marriages to the extent of about 18 per cent., as compared with the previous years of abundance. In the Netherlands, wheat was at 9.56 florins per hectolitre in 1816, and the births in the year 1818 had sunk, from a previous higher number (195,362 in 1815), to 183,706: in 1819, wheat had fallen to 3·72 florins per hectolitre, and the births, two years thereafter, rose to 210,359. 106:44 106.27 106-18 106-10 106-05 Further inquiries have shown some curious modifications of the law which seems to preside over this part of the natural economy of the world. In illegitimate births, the over proportion of boys is somewhat less, nearly approximating in some countries to a par with the number of girls. There is also a less over-proportion of boys from marriages in which the husband is the younger party, and where both are extremely young.* The average fruitfulness of marriages is not clearly ascertained, in consequence of imperfect registrations; but it is considered by Mr M'Culloch to be in England in the ratio of 4-2 children to each marriage. Legitimate and Illegitimate Births. The proportion of illegitimate to legitimate births is a point of great importance in political economy as well as morality, for illegitimate children are generally a burden to the state, and have an inferior chance of growing up useful citizens. It is also a fact ascertained by statistics, in opposition to common ideas, that such children have generally less of the elements of health and vitality than other children. The proportion of illegitimate to other births is-for France, 1 to 12:5; Prussia, 1 to 131; England, 1 to 14; Sweden, 1 to 146; the preponderance of morality thus appearing in favour of the two latter countries. In cities the proportions are strikingly different. In Paris, for 28 legitimate there are 10 illegitimate births; in other and stricter terms, the latter are in proportion to the former as 1 to 2:84. In Stockholm, from the report of a recent traveller, the proportion is 1 to 2:3; that is, nearly a third of the "In France, it was observed a few years ago, that out of 6,705,778 persons born, legitimate and illegitimate, there are 3,458,965 males and 3,246,813 females, or nearly 16 males to every 15 females. Out of 460,391 illegitimate children, there are 235,951 males, 224,440 females. From these data it follows that, in France, for every 100,000 legitimate female children, there will be 106,534 legitimate males; but for every 100,000 illegitimate females, there will be born only 105,128 illegitimate males; so that the probability of a child about to be born being a female is greater if it is illegitimate than if it is legitimate."-Babbage. MARRIAGES. The number of marriages per annum, in proportion to the population, and the ages at which marriages take place in both sexes, form interesting subjects of inquiry. In England and Wales, the number of marriages registered was 111,481 in 1837-8; 121,083 in 1838-9; and 124,329 in 1839-40. The number is believed to have been less in the first of these years than it otherwise would have been, in consequence of a popular error which induced parties to hurry on their nuptials before the commencement of the operation of the registration act. Taking the two latter years against each other, we find an increase of 3246 marriages upon the latter; but this is liable to a reduction of 1700 on account of the increase of population; so that, on the same number of people in 1838-9 and 1839-40, there was an increase of marriages, strictly, of about 1500. While there was thus an increase upon the whole country, the greater portion of the manufacturing districts in the west of England, where at this time commercial difficulties existed, showed a decrease, amounting in some districts to 6 per cent.; in Manchester and Salford to no less than 12 per cent. In England and Wales, the proportion of marriages to the whole population seems to have been diminished during the last fifty years. It is calculated that, in the period 1796-1800, there was 1 marriage annually to every 123 persons; in the period 1816-20, 1 for every 127 persons; in the period 1826-30, 1 for every 128 persons. This seems to be nearly its present propor tion. Some years ago, Mr Finlaison made a calculation of the ages of women at the time of their marriage from an assemblage of 878 cases, which was too small for very satisfactory results. Enlarging the number to 1000 for the sake of arithmetical distinctness, he found the following to be the various ages at marriage :— According to this table, the average age of marriage in England is for men, 27-4 years; for women, 25.5 years. It presents, upon the whole, a favourable view of the prudence of the English people as to marriage. Only 2-3 per cent. men, and 13 per cent. women, are wedded under the age of 20. About one-half of both sexes are married between 20 and 26. Only about three-fourths of a per cent. of first marriages are contracted by either men or women after the age of 44. It seems to be clearly ascertained, that the tendency of the sexes to marriage is liable to be modified by a number of conditions. Above a certain point in education, comfort of circumstances, and respectability of position, the tendency diminishes, and we see men and women of the middle and upper classes living contentedly in celibacy, from a dread of the increased expenses of matrimonial life. Below that point, the tendency increases, from opposite causes. It is observably more powerful amidst a dense operative population than amongst a scattered one, and it reaches its extreme in the half-destitute class, however otherwise circumstanced. Statistics affords us some information respecting two widely separated parts of the earth, one of which is remarkable for early and numerous, and the other for rare and long-delayed marriages-Glasgow and the parish of Montreux in Switzerland. In Glasgow, the marriages were, in 1839, in the proportion of I to 112 of the population; and this ratio rises much higher in unusually prosperous years, as, for instance, in 1825, when it was 1 in 84. Montreux is too small a district to afford basis for a calculation of this kind; but the people, who are all small labouring proprietors, are remarkable for postponing marriage to a late age, the average ages of men and women being 30 and 26.75 respectively. In Montreux, the births are as 1 to 46 of the population, and the deaths as 1 in 75, both uncommonly low proportions. Those of Glasgow will be found very different. It seems incontestible, indeed, that a multiplication of marriages in most situations is attended by an increase of mortality, and particularly an increase in the mortality of the young. We trust we may here venture upon a few general remarks with respect to marriage amongst the industrious orders. It is a familiar saying among the industrious orders, that the mouth never comes without the meat for it; by which they encourage themselves to marry, or console themselves when, having married, they find their family increasing upon them more rapidly than they can well see how they are to provide for it. This fallacy has been in some measure brought to the test of figures. Dr James Philips Kay, an assistant Poor-Law Commissioner, instituted in the year 1838 an inquiry into the actual income of agricultural labourers in the counties of Norfolk and Suffolk. Returns to the circulars which he issued for this purpose enabled him to make the following abstract of the annual earnings of 539 families: The first question suggested by this table is—how much of the increased income of the men with families was owing to their working more steadily, from a sense of their families being dependent upon them? and how much to the earnings of their wives and children flowing into the common stock? This does not directly appear, but the returns afford means of arriving pretty near the truth by calculation. Out of the 539 male heads of families, 475 earned annually by day-work £7382, 5s. 2d., which gives the average annual earnings of each man by this means at £15, 10s. 10d., or within a fraction of 6s. a-week. The earnings by task-work are specified in 350 cases, and amount in all to £5018, 17s. 7d., which gives the average earnings of each man by this means at £14, 6s. 10d. annually, or 5s. 6d. a-week. There are enumerated at least 286 cases in which the labourer obtained earnings in both ways; but it would give too high an average to add the two sums together. We are enabled to approach to the truth in another direction, by deducting the amount of earnings said to be made by women and children from the average incomes of the families. The sum of all the annual earnings of all the families (counting each single man as a family), in the table given above, is £19,129, 16s. 5d. ; and this gives an average annual income of £35, 10s. The men are stated to have earned on an average £5, 8s. by harvest work, in addition to their regular wages: the average earnings of wives are about £2, 12s. 7d.; of children able to work, £8, 1s. 11d.; and the value of gleanings by the younger children is £1, 1s. 10d. Deducting these sums from the average family income, leaves £17, 4s. 4d. for the average annual earnings of the man by ordinary task and day work; and this, when we take into consideration the number of men, and the amount earned in the year by these routine kinds of labour, seems not an improbable estimate. This £17, 4s. 4d. added to the £5, 8s. of harvest wages, gives £25, 12s. 4d. as the average annual earnings of a man (7s. 3d. per week), or only 13s. more than the average earnings of the unmarried men; from which we infer, that the additional income of the married men is derived from the labour of their wives and children. Deducting the earnings of the unmarried men from the whole amount, and dividing the remainder by |