抄録
The ship's position is fixed by the intersection of two position lines found by observing the horizontal sextant angles subtended by two chords fixed with three objects. A three armed protractor is used for fixing the ship's position on the chart. The fixing point is intersection of two circles which contains angles subtended by two chord. This instrument is designed as follows. Every circle passing through two fixed points is changed into a straight line which passes through the other fixed point by inversion, well known mathematical transformation. There are three fixed objects A, B and C on the chart. Select arbitrary constant number "a", and plot point B' and C'respectively on the straight line AB and AC, so that AB・AB'=AC・AC'=a^2. Set a protractor around the point B' and C'. Two protractors are set as follows ; zero degree of one protractor is in heaps on the straight line B'A and the other on C'A. Sextant angles subtended by two chords AB, AC are α and β. Point X'is intersection of two straight lines B'P and C'Q so that ∠AB'P=α and ∠AC'Q=β. The point X, position of the ship, is the corresponding point of the point X'so that AX・AX'=a^2. To fix points B', C' and X easily from points B, C and X', it is convenient to use a particular rule. The rule is designed as follows, points E and F such as DE・DF=a^2 are represented by the same number.
