水路測量に於ける円座標法に反転法を利用すること(日本航海学会第22回講演会)

抄録

In Hydrographic survey there are three fixed points X, Y and Z on the earth. Projection of points X, Y and Z are points A, B and C on the paper. The ship's position is fixed by the intersection of two position lines found by observing the horizontal sextant angles subtended by two chords XY and XZ. In hydrographic survey sometimes points A, B and C are not on the surveyor paper (Cf. fig 1). Then there must be drawn two systems of many circles, one pass through two fixed points A and B. and the other pass through two fixed points A and C. To draw many circles as explained above is complicated. This subject is to transform circles into straight lines passing through the point D and E, such as AB・AD=AC・AE=a^2, (a is arbitrarily constant). Every straight line is determined by any two points on the line, so that it is shown for example as 50° and 50°, 60° and 60°, 70° and 70°, etc. In fig.1, it is shown to make surveyor paper by the indoor work. The surveyor paper is almost as big as the rectangular frame. In fig.2, the point A is the center of inversion. It transforms circles into straight lines. An inversion rule (a particular rule) has a scale, the scale point H, I such as EH・EI=a^2 are same numbered. In fig.3, it is shown how to make the rule. Fig.4 is the surveyor paper, used up to the present. Fig.5 is the new surveyor paper, devised by me. The dotted line is prepared to illustrate the directions for use. Fig.6 and 7 are tools for plotting the ship's position. Fig.8 shows a section for surveying.