of the vertical angle, as if it were taken in vacuo at the station of observation.

Now the contained arc is equal to the sum of the two vertical angles in vacuo, when they are both depressions, or to the difference between them when one is an elevation, which relation gives the following simple precepts for computing the vertical angle in vacuo, at the object station. When the vertical angle in vacuo at the eye station is a depression, take the difference between it and the contained arc: when it is an elevation take their sum, the resulting element in either case, is the vertical angle in vacuo at the object station.

To determine whether the last deduced vertical angle is an elevation or a depression, the considerations which will require to be attended to, are three in number and they are as follows:

First, when the vertical angle in vacuo at the eye station is a depression, and less than the contained arc; second, when it is a depression and greater than the contained arc; and third, when it is an elevation.

In the first and third cases, the resulting vertical angle at the object station is a depression, and in the second, it is an elevation.

Having obtained the two vertical angles in vacuo, treat them as if they were apparent vertical arcs, and deduce therefrom the subtended angle, and the difference of height, as in Case 1st. To exemplify this computation, take the deduction of Himalaya snowy peak a from Amsot Hill station:

Observed vertical angle at Amsot,
Eye correction,

Object correction is evanescent, the top of the peak being
observed,

Refraction taken at of contained arc,

Vertical angle in vacuo at Amsot, .

Which being an elevation, will require to be augmented

CHAPTER XX.

ON MINOR TRIANGULATION, AND THE SAME AS APPLIED TO THE RAY TRACE SYSTEM, FOR CARRYING ON TOPOGRAPHICAL SURVEYS.

AFTER having explained the approved principles of observation and computation, as generally practised in a Trigonometrical Survey, we will now proceed to shew their application to the detail survey of a district.

The primary triangles of a Topographical Survey may be thrown into the form of a network as shewn in Fig. 1, or into that of a gridiron exhibited in Fig. 2. Plate 7 B. Of these two forms the gridiron is preferable to the network, in the first place, because it contains a smaller number of triangles and is more scientific; and secondly, because it is susceptible of a more systematic deduction than the other. This mode of distribution however, will be found more difficult in most hilly countries than the common network, and occupy a longer time than is generally allotted to Topographical Surveyors, but whatever form may be given to the primary triangles of a Topographical Survey, there is one condition, namely, that of symmetry, which ought to be strictly adhered to in their selection. In no case should a triangle of a primary character be admitted, any of whose angles falls short of 30° or exceeds 90° as before stated at page 393.

The sides of these primary triangles should average between two and five miles, and the best instrument for executing this description of work is a 12-inch Theodolite. The