Chap. VIII.

GEOMETRY.

831

Fig. 1042.

compass, bone its position through the sights of alhidade, and remarkingthat the needle indicated 45° \V., write this against the visual ray.

Draw out the map, tracing a line A B, on the paper, and set outupon it 1600 feet, the distance measured from A to B; against theline A B, used as the base, place the side of the alhidade of the com-pass, and turn the sheet of paper, keeping the compass againstthe side A B, until the needle points at the same degree as whenboning to A : without removing the paper, observe what is the degreeof the ray to C, and having found it to be 22° \V., place the side ofthe alhidade against the side A, and turning the compass, with theside of the alhidade always against the point A, and the paper un-moved until the needle makes 22° W., as found from the point A to C,draw a right line along the side of the alhidade of the compass,which must also be done for the other positions as 7° W., for thepoint D : then observe, where the station B is marked, what is thedegree on the line which goes towards C, and having found it 45° W.,place the side of the alhidade on the sheet of paper at the point B,the extremity of the line A B; and doing the same at the point B,we shall have second rays which will cut the first in several points,and give the positions of the places to be set down on the map.

The compass is also used to mark the meridian on maps;this is done by placing against the line drawn from one planeto another, as from A to B, one of the sides of the compass,and then observing the place where the needle points, andmarking its direction, as K L ; this is afterwards again provedby placing the box against this second line, and finallydrawing E F parallel to it.

The compass should be extremely susceptible and possess-ing an intensity of directive force; the first of these is ob-tained by constructing the needle of the material and formbest suited to receive and retain the magnetic power. Shearsteel has been found best adapted to receive the greatestamount of magnetic force, and the best form is that of alozenge or rhomboid cut out in the middle, so as to diminishthe extent of surface in proportion to the mass, it being as-certained that the directive force of the needle when mag-netised to saturation depends not on the extent of surface,but on the mass.

To measure Angles with a Compass , attach a long ruleto its north side, and present it against one of the sidesof the angles to be measured, and observe how many degreesthe north point of the needle declines from the north point ofthe compass, beginning to count these degrees from thesmallest arc there is from the north point of the card, to thedegree where the north point of the needle stops, in order tofigure on one side the degree of declination, supposing that the north point of the needledoes not coincide with the north point of the compass: then present the same side of thecompass to the other side of the angle, and countfrom the smallest arc how much the north pointof the needle is distant from the north pointof the card; subtract the degrees from each other,and the remainder from 180°, and this remainderwill be the angle required. As in the salientangle B A C , apply the long side marked northof the compass to the side A B, and observehow many degrees the north point of the needledeclines from the north point of the card; andsince they coincide, it is a proof there is nodeclination; write therefore, north to the sideA B : then apply the same side of the compass tothe other side A C, to count how much the northpoint of the needle declines from the north point of the card, as 90°, write down A C 90°;above mark north, in order to subtract this from 90°, which being subtracted from 180° stillleaves 90° for the angle B AC. But if the angle required was CD A, when the northpoint of the needle is 36° from the north point of the card, having placed the north sideof the compass against the other side I) B, it will be seen that the declination of theneedle would be 92°; subtract the 36° from 92°, there will remain 56°, which being sub-tracted from 180° leaves 124° for the angle CDB.

n

Fig. 1043.

Fig. 1044.