Online Encyclopedia

Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.

S4X

Online Encyclopedia

Originally appearing in Volume V26, Page 145 of the 1911 Encyclopedia Britannica.

» Make a correction to this article.
» Add information or comments to this article.

Encyclopedia Home :: RON-SAC

Spread the word:

del.icio.us it!

S4X = -63A. X . See also:

TANA

tanA S4L = +54A. Y.tanA S,A = +S4L .Z The calculations described so far suffice to make the angles of the several trigonometrical figures consistent inter se, and to give preliminary values of the lengths and azimuths of the sides and the latitudes and longitudes of the stations. Reduction The results are amply sufficient for the requirements of See also:

PRINCIPAL

Principal of the topographer and See also:

LAND

land surveyor, and they are published in preliminary charts, which give full numerical tion. details of See also:

LATITUDE (Lat. latitudo, latus, broad)

latitude, See also:

LONGITUDE (from Lat. longitudo, " length ")

longitude, See also:

AZIMUTH (from the Arabic)

azimuth and See also:

side-length, and of height also, for each portion of the triangulation—secondary as well as principal—as executed See also:

YEAR

year by year. But on the completion of the several chains of triangles further reductions became necessary, to make the triangulation everywhere consistent inter se and with the verificatory See also:

BASE

base-lines, so that the lengths and azimuths of See also:

COMMON

common sides and the latitudes and longitudes of common stations should be identical at the junctions of chains and that the measured and computed lengths of the base-lines should also be identical. As an See also:

ILLUSTRATION

illustration of the problem for treatment, suppose a See also:

COMBINATION (Lat. combinare, to combine)

combination of three meridional and two See also:

LONGITUDINAL

longitudinal chains comprising seventy-two single triangles with a base-See also:

LINE

line at each corner as shown in the accompanying c e See also:

DIAGRAM

diagram (fig. 2) ; suppose the three angles of every triangle to have been measured and made consistent. Let A be the origin, with its latitude and longitude given, and also the length and azimuth of the adjoining base-line. With these data processes of calculation are carried through p the triangulation to obtain the lengths and azimuths of the FIG. 2. sides and the latitudes and longitudes of the stations, say in the following See also:

order: from A through B to E, through F to E, through F to D, through F and E to C, and through F and D to C.

Then there are two values of side, azimuth, latitude and longitude at E—one from the right-See also:

hand chains via B, the other from the See also:

LEFT

left-hand chains via F; similarly there are two sets of values at C; and each of the base-lines at B, C and D has a calculated as well as a measured value. Thus eleven See also:

ABSOLUTE (Lat. absolvere, to loose, set free)

absolute errors are presented for See also:

dispersion over the triangulation by the application of the most appropriate correction to each See also:

ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

angle, and, as a preliminary to the determination of these corrections, equations must be constructed between each of the absolute errors and the unknown errors of the angles from which they originated. For this purpose assume X to be the angle opposite the flank side of any triangle, and Y and Z the angles opposite the sides of continuation; also let x, y and z be the most probable values of the errors of the angles which will satisfy the given equations of See also:

CONDITION (Lat. condicio, from condicere, to agree upon, arrange; not connected with conditio, from condere, conditum, to put together)

condition. Then each See also:

EQUATION (from Lat. aequatio, aequare, to equalize)

equation may be expressed in the See also:

FORM (Lat. forma)

form [ax+by+cz] =E, the brackets indicating a summation for all the triangles involved. We have first to ascertain the values of the coefficients a, b and c of the unknown quantities. They are readily found for the side equations on the circuits and between the base-lines, for x does not enter them, but only y and z, with coefficients which are the cotangents of Y and Z, so that these equations aresimply[cot Y.y—cot 'Z.z] E. But three out of four of the See also:

CIRCUIT (Lat. circuitus, from circum, round, and ire, to go)

circuit equations are See also:

GEODETIC

geodetic, corresponding to the closing errors in latitude, longitude and azimuth, and in them the coefficients are very complicated. They are obtained as follows.

End of Article: S4X

Additional information and Comments

There are no comments yet for this article.

» Add information or comments to this article.

Please link directly to this article:
Highlight the code below, right click, and select "copy." Then paste it into your website, email, or other HTML.

Site content, images, and layout Copyright © 2006 - Net Industries, worldwide.
Do not copy, download, transfer, or otherwise replicate the site content in whole or in part.

Links to articles and home page are always encouraged.

[back]
S2A

[next]
SAALE