In publishing the explanation of this short and simple method of finding the longitude at sea, no claim is made of originality nor of having discovered anything new. The method has been in existence a number of years. It is simply intended to bring to the attention of the navigators of the navy a short, easy and accurate method which will lighten and simplify their work. This method, although used to some extent in the merchant marine, is, so far as I know, practically unknown in the navy.
It is G. F. Martelli’s method for finding the apparent time, and was brought to my attention by the former captain of a merchant ship converted into a naval transport, which I recently commanded.
I have tested the method carefully and exhaustively in comparison with the Marcq Saint-Hilaire method, working innumerable sights by both methods, and have found it absolutely accurate and to be depended upon, the results of the two methods invariably checking to within a mile of each other.
In working longitude sights by the two methods, the advantages of the Martelli method in brevity, simplicity and the lesser likelihood of making mistakes are readily apparent. The entire operation consists in looking up five logs, making two simple additions and looking up the answer in a table. No books other than Martelli’s Tables are required, except the Nautical Almanac.
There are five tables essential to the method, bound in a thin book of convenient size of 50 odd pages, which also contains a page of explanation of the method with examples worked out, and additional tables for the correction of the altitudes of the sun and stars. The five tables are arranged consecutively in the order in which they are used, which tends to prevent mistakes in picking the logs out of wrong tables.
Main Tables
Table I contains the logs to four places of the latitude and declination.
Table II contains numbers expressed in minutes and seconds corresponding to the sum or difference of the latitude and declination.
Table III contains numbers also expressed in minutes and seconds corresponding to the angle of altitude.
Table IV contains auxiliary logs to four places used in the computation.
Table V contains the logs of the hour angle from which the L. A. T. is found.
Additional Tables
Table VI contains the corrections of the apparent altitudes of the sun and stars.
Table VII contains the dip of the horizon for heights of eye up to 100 feet.
Table VIII contains the correction to be added to the observed altitude of the sun’s lower limb to find the true altitude.
Table IX contains the correction to be subtracted from the observed altitude of a fixed star to find the true altitude.
The explanation of the method given below is taken directly from the book, and the examples arc actual sights worked out in the course of navigating my ship.
Explanation of the Method.
The data required are the assumed latitude, the corrected declination and the true altitude of a heavenly body. Nothing else is required except the chronometer time of sight, chronometer correction on G. M. T. and the equation of time. From these latter is obtained the G. A. T. in the usual manner.
Put down the assumed latitude and corrected declination and opposite to them their logs taken from Table I.
It the latitude and declination are of the same name, both north or both south, subtract one from the other. If they are of different names, one north and the other south, add them together.
From Table II take out the minutes, seconds and tenths of a second corresponding to the sum or difference of the latitude and declination.
From table III take out the minutes, seconds and tenths of a second corresponding to the true altitude.
Add these last two quantities together. With their sum enter Table IV and take out the auxiliary log.
Add the auxiliary log to the logs of the latitude and declination. With their sum enter Table V and take out the L. A. T.; from the top of the page, if the sight was taken in the forenoon, or from the bottom of the page, if taken in the afternoon.
The longitude is of course obtained by subtracting the L. A. T. from the G. A. T. as in all other methods.
Example I.—At Sea, September 16, 1919, in latitude 430 25' N., at 4.50 p. m., ship’s time; the sun’s true altitude was 150 51' 44" ; chronometer time, 6" 10m 54’; C. C., 49”' 54. Find the longitude.
The principle involved is the same as in all problems of determining the position from the altitude of a heavenly body measured above the horizon; that is, to find a line of position, which is a small arc of the circle of equal altitudes. But the computation employed to arrive at the solution is entirely different from that of the time sight, the Marcq Saint-Hilaire, or the Aquino methods, and is much shorter and simpler.
The columns to be added in one case comprise three figures, and in the other case only two. The logs are only to four places and there are no characteristics. The tables are concise and follow each other in the order in which they are to be used. There are no tedious interpolations to be made. What little interpolation there is to be done is readily accomplished at a glance. Finally, the cumbersome tables of logarithmic functions are done away with, and everything is found in one small thin volume.
This method possesses the same advantage as the Marcq Saint- Hilaire method over the old time sight, of being available at any hour of the day, and can be used near noon to obtain a fix by crossing its line of position with the meridian altitude or ex-meridian. The nearness to noon at which it can be employed for this purpose of course depends upon the relative magnitudes of the latitude and declination. If the declination is equal to the latitude, the path of the sun of course follows the prime vertical, and it can theoretically be used to within a few seconds of noon, the sun in this case bearing due east or west and the line of position cutting the meridian altitude at right angles. Naturally the nearer the sun bears North or South, the sharper the angle between the line of position found and the meridian altitude line and a small error in the sight produces a large error in longitude.
For the benefit of those who may be interested in giving this method a trial, the following information is given: Martelli’s Tables are contained in a book entitled “Short, Easy, and Improved Method of Finding the Apparent Time at Ship,” published by D. M’Gregor & Co., of Glasgow, for four shillings. It can also be obtained from Negus, 140 Water St., New York.