236 Mr J. Sang on a Systematic Method <)f 



data, for the sides and angles depend on one another in a very 

 complex manner. Yet if corrections be not made, the error in- 

 creases and accumulates in every new step of the operations, 

 until it becomes altogether unmanageable. By employing the 

 method I am going to describe, the errors are easily corrected, 

 and accumulation is rendered impossible. 



The chief features of the method are, that the interior sur- 

 face is not divided into trigons, but is considered solely as a po- 

 lygon, the number of its sides being of no consequence to the 

 accuracy of the result, and, that the field measurements are 

 made so that all the terminations of the surveying lines can be 

 readily co-ordinated to three assumed planes. To understand 

 the principles of the system no exertion is required. They are 

 developed by the collation of a few simple facts, resulting in a 

 simple and very beautiful law. 



Three perpendiculars falling from a point upon three planes 

 mutually intersecting one another at right angles, are called the 

 rectangular co-ordinates of that point, and their lengths deter- 

 mine its position with regard to the planes. And it is evident, 

 that the co-ordinates of a series of points to the same plane will 

 determine the positions of these points in relation to one ano- 

 ther. For the sake of convenience, I will designate the co-ordi- 

 nates severally by the names of Altitude, Latitude, and Longi- 

 tude. The altitude is defined as the distance of a point from 

 an assumed horizontal plane situated below it, as the continua- 

 tion of the surface of the sea ; the latitude as the distance north- 

 wards from a vertical plane stretching east and west ; and the 

 longitude as the distance eastward from another vertical plane 

 stretching north and south. And I shall suppose all the co- 

 ordinates to lie on these sides of the planes, in order to avoid 

 the contemplation of negative quantities. I shall designate by 

 the term Inclination, the angle which a line forms with its pro- 

 jection on the horizontal plane, and which may be either nega- 

 tive or positive, according as the line tends upwards or down- 

 wards ; and by the term bearing, the angle which the horizontal 

 projection of a line makes with the north line. The bearing 

 shall be read from left to right, and shall be conceived always 

 to increase in that direction. 



