On the other hand, let both the reference points “a” and “b” (fig. 6) be situated short of the objective O, “a” being nearer the objective and “b” nearer to the balloon. An error aa′ in spotting “a” leads to an error OO′ in the objective greater than aa′. Notice that this error diminishes as “A” approaches O, thus “a” being as a₁, the error a₁a′₁ equal to aa′ leads to an error OO′₁, in the objective, less than OO′. We would thus obtain an analogous result if we would move the point “b” farther away. Therefore, =when you are obliged to take the two reference points between you and the objective, choose one as near the objective as possible and the other as near as possible to the balloon=. 3. _Investigation of range._ Identify details of the terrain situated over and short of the objective on the alignment. Narrow this bracket down step by step; situate the objective on the map according to its relative distance from the two nearest identifiable reference points, taking into account the deformations due to the laws of perspective and the relief of the ground. If you have a vertical photograph of the region, trace the alignment on this photograph and make the investigation in range by the same means. The dangers against which I warned you before in connection with the investigation of range apply in this case also, so it is unnecessary to repeat them. When the two last identifiable reference points are some distance from each other, the situation of the objective has a possible error, of which you know the size according to the distance between the two reference points; it might be interesting to remember this in case different information is obtained on this objective from that obtained in the balloon. This error can be considerably diminished if you use a vertical photograph; the investigation can then be carried on by the same method as on the map, with greater precision. In the case of a battery, particularly, it is for the observer to find the position of each piece. In case, on account of dead ground or of a mask before the battery, the observer sees the flashes or the smoke without seeing the battery itself, he should mark the exact alignment in which the flashes or smoke are seen, and determine the bracket in range--that is, the reference points nearest the objective which are clearly over and short. This document compared with other information can facilitate the identification of the battery. CHAPTER III. OBSERVATION OF FIRE. The observation of fire is essentially the following operation, repeated for each shot or salvo: Locating on the ground the position of one point, which is the point of burst, and announcing its situation in reference to another point, which is the target. But it has been demonstrated that it is impossible, without using the map, to determine the error in range of one point relatively to another point not on the same alignment. The operation must consist in: