In the preceding observations we have supposed that the binocular centre D″, &c., is between the eye and the lines AC, BC; but the points A, C, and all the other points of these lines, may be united by fixing the binocular centre beyond AB. Let the eyes, for example, be at E″; then if we unite A, B when the eyes converge to a point, Δ″, (not seen in the Figure) beyond G, we shall have GE × AB GΔ″ = ———————; RL - AB and if we join the point Δ″ thus found and C, the line Δ′C will be the united image of AC and BC, the binocular centre ranging from Δ″ to C, in order to see it as one line. In like manner, we may find the position and length of the image Δ‴C, Δ′C, and ΔC, corresponding to the position of the eyes at E‴E and E. Hence all the united images of AC, BC, viz., CΔ‴, CΔ″, &c., will lie below the plane of ABC, and extend beyond a vertical line NG continued; and they will grow larger and larger, and approximate in direction to CG as the eyes descend from E‴ to M. When the eyes are near to M, and a little above the plane of ABC, the line, when not carefully observed, will have the appearance of coinciding with CG, but stretching a great way beyond G. This extreme case represents the celebrated experiment with the compasses, described by Dr. Smith, and referred to by Professor Wheatstone. He took a pair of compasses, which may be represented by ACB, AB being their points, AC, BC their legs, and C their joint; and having placed his eyes about E, above their plane, he made the following experiment:—“Having opened the points of a pair of compasses somewhat wider than the interval of your eyes, with your arm extended, hold the head or joint in the ball of your hand, with the points outwards, and equidistant from your eyes, and somewhat higher than the joint. Then _fixing your eyes upon any remote object_ lying in the plane that bisects the interval of the points, you will first perceive two pair of compasses, (each by being doubled with their inner legs crossing each other, not unlike the old shape of the letter W). But by compressing the legs with your hand the two inner points will come nearer to each other; and when they unite (having stopped the compression) the two inner legs will also entirely coincide and bisect the angle under the outward ones, and will appear more vivid, thicker, and larger, than they do, so as to reach from your hand to the remotest object in view even in the horizon itself, if the points be exactly coincident.”[38] Owing to his imperfect apprehension of the nature of this phenomenon, Dr. Smith has omitted to notice that the united legs of the compasses lie below the plane of ABC, and that they never can extend further than the binocular centre at which their points A and B are united.