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.s RHUMB LINES AND TRUE COURSES. In the Record of April 2. we commented briefly at the end of a communication from Capt. H. C. Pearsons, some of whose claims the RECORD did not wish to ap- pear asendorsing. Spaceand time were then too limited to admit of more than a briefreply. Further comment on his article is now submitted: In the beginning of Captain Pearsons’ letter he states: ‘It is generally supposed that when a vessel is correctly started on her course, and is kept strictly to that course as indicated by the ship’s compass, she makes a track that crosses the meridian in its run or voyage at the same angle.’”’ ‘‘Such a track is called a “rhumb-track.”’ This statement implies that mariners are generally ignorant of some of the first principles of navigation, such as the change in direction of the needle of the mariner’s compass with change of locality; for how can the writer of this article assume that it is generally sup- posed that a ship, steering an invariable compass course, passes over a track that crosses the meridians at the same angle, when all know, from the common knowl- edge of centuries, that, in a region of changing varia- tion, if the compass course remains the same, the true - course at successive meridians, or the angle at which the track crosses them, cannot also remain the same From Captain Pearsons’ definition of the rhuimb- track in the above quotation and his reference to a “true rhumb-line.’’ in paragraph 5 of his letter, it is difficult to interpret what his conception of a rhumb- line is, and whether he thinks there is more than one kind. For the benefit of those who have read his letter it is necessary to state that there is only one kind of rhumb-line and that it may be defined as the curveon the earth’s surface which cuts, at the same angle, the dif- ferent meridians over which it passes. This constant angle which it makes with the meridians is the course, and is called the true course to distinguish it from the compass. course. The principles of construction of the aew lake charts are such that any rhumb-line will be projected upon them as a straight line. In rhumb-sailing, the ship keeps on ‘he rhumb-line passing through the place of departure and the place of destination. This is the or- dinary sailing used in navigation, for when out of sight of land, the compass determines the ship’s track, and hence the selection of that track which makes a con- stant angle with the meridian. Strictly speaking, in order that a navigator may follow a rhumb-line, he must change his course at the same rate as the varia- tion of the compass changes in going from one port to another. ‘To accomplish this is, of course, impractica- ble, but he can approximate very closely to a rhumb- track by altering the course at frequent intervals along the track to compensate for the accumulated change in the variation of the compass during these intervals. This Captain Pearsons has very clearly and acceptably pointed out; but it has been the common practice of sea- men for centuries, only they have employed an interval between the changes of compass-course more in keeping POLYCONIC PROJECTION FIG. 1. with an appreciation of the uncertainties in the heading of a ship which is subject to the leeway due to winds and to currents of uncertain strength and set. Captain Pearsons writes: ‘The conditions necessary that a ship may sail on a true rhumb-line, when steered to a constant course, are that “The change of variation between the initial and ter- minal points of the voyage must be just equal to the THE MARINE RECORD. change in the inclination of the meridian for the voy- age: i. e., to the convergency of the meridian passing through the two points.”’ This statement has no scientific foundation. Let us investigate the example which he states, as follows: “Thus, if the change of the inclination or the conver- gency of the meridians passing through the points, is say,5°,and the change of the variation between those two points and the change of the variation between those FIG. 3. The two diagrams give a full view of the lines of actual direction of the compass needle when out of reach of | all magnetic influences except the earth’s. two points be also 5°, then the track of a ship sailed on a-constant course between those two points, would be a true rhumb-line, and on a Mercator chart would be represented by.a right line.”’ We assume that Captain Pearsons means by inclina- tion of the meridians the angle of convergence of these lines on a pglyconic projection, as employes in the U. S. Engineers’ lake charts. With this understanding, we turn to the annexed dia- grams on which the rhumb-line of, say 45°, appears as the curved line AB on the polyconic projection. This would be a straight line on the Mercator projection. Now, keeping in mind the correct definition of a rhumb-line, we know that it must make a constant angle with the successive meridians, other-wise it is not a rhumb-line as defined in connection with the Mercator charts. Evidently, the compass courses, if we neglect, for the sake of simplicity, the deviation and other in- fluences except the variation, would be as follows: At station 1, true course N. 45°E., var. 10° Ww. Comp. Course N 55°E. . 3B “ 2 N, 45°E., raed Uh oe N 56°F, be “ 3) “ N. 45°R.. “490 rr “ NBIOE. “ be a “ N. 45°E., 430. « “ “NE 5ROK. ae ae 5, a N. 45°R,, a ose is “N 59°E. We see from this that, ifa ship sailed on a constant compass course between two points A and B, she would not describe a rhumb-line on a Mercator chart in spite of the conditions stated by Captain Pearsons, viz.: that the variation and the inclination of the meridians are equal to each other. Captain Pearsons then proceeds to state that ‘‘this lamentable mistake that a ship’s track when steered to a constant compass course may be represented by a right lineon the Mercator chart is an outgrowth from another mistake equally untenable, and that is the idea that ‘there is one individual point, that, asa center, con- trots and gives direction to the compass needle in the entire inagnetic hemisphere.’ There is no such thing. “Krom well-known laws of navigation it is easy to show that the near portions of a magnetic field will con- trol and give direction to the compass needle, in spite of a larger and stronger position of the field that may be more remote. So that by changing the place of the com- pass, we bring it within the influence of other portions of the magnetic field ,when we find that we have a new pole, and so we may continue to do indefinitely, i. e., to say, instead of having merely one magnetic pole, we may have as many as there are possible positions for a compass in the magnetic hemisphere.”’ ‘This curious illustration has no connection with the preceding one concerning the rhumb-line and the infiu- ence of the convergence of the meridians in compensat- ing changes in the value of the variation of the compass. The magnetic poles of the earth are defined to be the points where there is no horizontal magneti where the dipping needle points vertically - The magnetic poles are the points where ee val ary. At any point where the potential is a minim the earth end of the dipping needle points verticall The magnetic lines relate to the year 1895. downwards, and, if a compass needie be placed any where near such point, the north end will be directe toward it. At points where the potential is a maximum, the sou end of the dipping needle points vertically downwards and the south end of the compass needle is attracted The theory of terrestrial magnetism, as given yj Maxwell, shows clearly that if there are n pointson th earth’s surface where the potential is a minimum, ther must be (n-1) other points where the north end of th dipping needle points downwards, but where the com FIG. 2. pass needle, when carried in a circle around the point instead of revolving so that its north points constantly towards the center, revolves in the opposite direction so as to turn sometimes its north and sometimes it south end towards the point. If we call the poles where : the potential is a minimum true north poles, then these outer points may be called false north poles, because the compass needle is not true tothem. If there aren true north poles, there must be (n-1) false north poles, and likewise, if there are m true south poles, there must be (n-1) false south poles. The number of poles of the same name must be odd, so that the opinion, at one time prevalent, that there are two north poles and two south poles, is erroneous. Observations carried on for centuries in all parts of the world, and the exhaust- ive theoretical investigations by Gause have proved that there is in fact only one true north pole ard one true south pole on the earth’s surface, and there fore, there are no false poles. In the accompanying diagram, the points toward which the heavy lines converge in the northera and southern hemispheres are the magnetic poles. ‘The