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Of the Surveying Cross, or Cross-staff. The surveying cross, fig. 1, consists of two pair of sights at right angles to each other : these sights are sometimes pierced out in the circumference of a thick tube of brass ; and sometimes the cross-staff consists of four sights strongly fixed upon a brass cross, and, when used, is screwed on a staff, having a sharp point to stick in the ground. The accuracy of the cross-staff depends on the sights being exactly at right angles to each other. A cross-staff may be easily inade by a carpenter, thus : take a picce of beech or box, ADBC, of four or five inches in breadth, and three or four inches in depth, and upon ADBC draw two lines, AB and CD, crossing each other at right angles. Then, with a fine saw, make two slits, ABG and CDH, of about two inches in depth ; fix this piece of wood upon a staff S, of about four and a half, or five feet in length, pointed at one end, so that it may easily stick into the ground.
Prob. 1. To nieasure off-sets with a chain and cross-staff.
Let Abcdefg, fig. 2, be a crooked hedge, river, or brook, &c. and AG a base line. First, begin at the point A, and measure towards G; when you come to B, where you judge a perpendicular must be erected, place the cross staff in the line ÅG in such a position that both G and A may be seen through two of the sights, looking for. ward towards G, and backward towards A. Then look along one of the cross sights, and if it point directly to the corner, or bend at b, the cross-staff is placed right; otherwise move backward or forward along AG till the cross sights do point to b, and measure Bl, which set down in links: proceed thus till you have taken all the off-sets, as in the following field-book. *
To lay down the Plan. Draw the line AG of an indefinite length : then, by a diagonal scale,
A field-book is usually divided into three columns. The middle columu contains the different distances on the chain line, and in the right and lefthand colurans, the off-sets and remarks are entered. The best method of entering field-notes, tho gh perhaps not the most conveniect, is to begin at the buttom of the page, and write towards the top.
set off AB equal to 45 links, draw Bb perpendicular to AG, and equal to 62 links. Next set off AC equal to 220 links, or 2 chains 20 links; draw Cc perpendicular to AG, and equal to 84 links : then set off AD equal to 340 links, or 3 chains 40 links, and make Dd equal to 70 links : proceed thus till you have completed the figure.
To cast up the Content. ABb must be measured as a triangle ; BCcb, CDdc, DEed, &c. must be measured as trapezoids. Some authors direct you to add all the perpendiculars Bl, Cc, &c. together, and divide their sum by the number of them, then multiply the quotient by the length AG ; but this method is always erroneous except the off-sets Bb, Cc, &c. be equally distant from each other.
AB = 45 AC=220 AD=340|AE=510'AE=634/AG=784
90 BC=175 CD=120 DE=170 EF =124 GF=151 270
B6 = 62Cc = 84 Dd = 70 Ee = 98 Ff = 57 2790 Cc = 84 Dd = = 70'Ee 98 Ff = 57 Gg 91
Sum 146 Sum 154 Sum 168 Sum 155 Sun 148
2)116948 = double area of the who.e in square links.
58474 = area in
58474 = area in acres = 0 A. 2 R. 13.5584 P
2. Required the plan and content of part of a field, from the follow. ing field.book.
The figure must be laid down, and the content calculated as in the first example. Thus, in fig. 3, you will find the area of the part EdcöaA to be 1 R. 13.4 P. and of the part FfgG to be 30 perches; so that the whole is 2 roods 3:4 perches.
Prob. 2. To measure a field in the form of a trapezium.
Set up station-staves, or long poles, at the corners A, B, C, fig. 4. Then begin at D, and neasure along the diagonal DB, in a straight line, till you come to the place of the perpendicular AF, which will be known by looking backward and forward through the sights of the cross-staff, as before directed. Make a mark at F, and measure the perpendicular AF; then proceed from F towards B, and when you come to E, the place where the second perpendicular will fall, make a mark, and measure the perpendicular EC: lastly, continue your measure from E to B. You may either draw a rough plan of the field by the eye, and write the length of the diagonal and perpendiulars on it, which some writers recommend as the best method, or set them down in a field-book, thus :
To lay down the Plan. Draw the station-line DB equal to 1360 links, or 13.60 ènains, from D set off DF equal to 600 links, or 6 chains ; draw AP perpendicular to DB, and equal to 342 links, or 3 chains 42 links: make
DE equal to 1190 links, and at E erect the perpendicular EC equal to 625 links. Join DA, AB, BC, and DC, and the field is constructed.
Calculation. This field being a trapezium, its content must be found as directed in Prob. 7.
680 half the diagonal DB
6:57560 area in acres=6 acres, 2 roods, 12.096 perches." 2. Required the plan and content of a field fron the following fieldbook.
Ans. The content is 1 acre, 2 roods, 4.3776 perches.
Note.-In either of the two figures, 4 aud 5, if the sides DC, CB, BA, AD, and the diagonal DB, had been measured with the chain, the figures might have been planned, and their contents found, by Prob. 5, without using a crossstaff, or measuring the perpendiculars AF and CE.
Unskilful measurers fregnently measure round a four-sided field, and find the content by adding each two opposite sides together, and taking half their sum; then they inultiply these half sums together for the area. It may be necessary to inform the learner, that this method is, generally, very erroneous, and ought necer to be practised.
Prol. 3. To measure a four-sided field with crooked hedges.
Set up staves, or poles, at the corners D, C, B, fig. 6, as before directed. Then begin at A, and measure from A to B, noting all the necessary off-sets, and in this manner go round the field, then measuro the diagonal AC.
Acres. The sides of the triangle ABC are 750, 1500, and 1294 links, and its content
4.85239 The sides of the triangle ACD are 1000, 800, and 1294 links, and its content.....
3.99907 Content of the off-sets along AB= 0 50250 Ditto
along BC= 1.67500 :
along CD= 1.07500
Sum=12'10396 Content of the off-sets along DA, deduct 1'00000
Remains the content of the field=11•10396
Prob. 4. To measure an irregular field.
Set up station-staves at every angle, and divide the field into trapeziums and triangles ;