is evaluated for its effect during each time-interval, and for the the particular position of the shell. The following list gives the yariations from standard conditions which are normally corrected for:

1. Difference in angle of departure and muzzle velocity. 2. Rotation of the earth (only in extreme cases).

3. Variations in range and deflection, caused by the ballistic wind.

4. Variations in range due to density, or change in the ballistic coefficient.

5. Variation in the G (v) function with air-temperature changes. These variations are applied by means of weighting-factor curves, which are so constructed as to give the proportion between the effect of a unit disturbance acting throughout the entire trajectory, and the same effect acting throughout any given part of the trajectory. Their construction is not very difficult and their use quite simple.

The data from which the effects of the two components of the wind are computed, are collected by observing and plotting the path of a small balloon, released from a known point on the earth. This balloon has certain pre-determined characteristics which make the record reasonably accurate. The plotting enables one to determine the force and direction of the wind in the upper air, and to allow for the changes which take place with altitude. The density at present is determined by observations taken by an airplane and is used in the same way as the ballistic wind.

Thus it will be seen that this new method of computation is more exact; free from mean values of constants; capable of applying more accurate corrections for variations from standard conditions; and able to compensate for more variables. It should be said that this paper merely aims to sketch the briefest outlines of the new method with its recent developments, and to indicate the lines in which the science is now progressing. It is to be understood that rapid advances may be made in our knowledge of the velocity-function, in our density tables, and in many other directions, without introducing any error in the fundamental principles involved as exterior ballistics must still be considered an experimental science. With improved types of shell, higher muzzle velocities, and greater angles of departure it is important that naval officers be cognizant of the elementary principles involved in the computation of the resultant trajectories.

[COPYRIGHTED]

U. S. NAVAL INSTITUTE, ANNAPOLIS, MD.

USING AN OLD WRINKLE

By COMMANDER C. N. HINKAMP, U. S. Navy

While engaged in mine sweeping on the French coast, in waters where the currents are strong it became necessary to use more than ordinary care in keeping the track of the areas covered, and the following method of navigating these waters when sweeping was frequently used. Never having seen it described in the PROCEEDINGS of the Naval Institute, I submit it for the information of the service after extensive use in the World War, on the mine fields off the entrances to St. Nazaire.

The idea is the application of the old principle of passing a danger by the use of the danger angle, which is based on the fact that a chord of a circle subtends the same angle from any point in the circumference of that circle. Sketch No. 1 shows all the work necessary for the execution of the idea, while Sketch No. 2 shows the geometric proof and the actual paths traversed by the vessels.

Taking Sketch No. 1, suppose the dangerous mined area to be included in the space PQRS. Select two prominent landmarks on shore, lighthouses, churches, or other forms of towers, preferably so located or selected as to be about equidistant from the center of the area. They need not be exactly equidistant from the center of the area, but this is desirable for simplicity, and easy execution. Suppose the points to be A and B. Join A and B and in the center of AB erect a perdendicular CD which will pass through the area PQRS if the points are well selected. On the line CD, and within the limits of the area, lay off to scale the width of the path which can be swept by the complement of sweepers, and call these points in succession, 1, 2, 3, 4, 5, 6, 7, etc. Next join A-1, A-2, A-3, A-4, A-5, A-6, A-7, and B-1, B-2, B-3,

R.

B-4, etc. Measure with a protractor the angles AIB, A2B, A3B, etc., marking them on the chart. Set the angle AIB on the sextant and maintain this angle between these landmarks, by maneuvering the ship to the right or left until the limiting bearings of the area are reached. After a bit of practice it is simple to tell which way

SKETCH NO.1.

S

to put the rudder to keep the angle, as the right object moves to the right or the left of the left object. A surveying or horizontal sextant is best adapted for this purpose, although we used an ordinary sextant fitted with a handle specially made on board ship. After passing the limits of the area and desiring to make the return trip on another angle, make the turn, set the sextant to the

-C.

next angle, A2B, and get on that angle by maneuvering the ship. When the lower limits of the area are reached, make the turn, set the sextant to the angle A3B, and get on that angle. Keep this up until the entire number of angles have been cruised over, and the area has been swept if the leading vessel kept the angles, and

the following vessels kept their position accurately on the leader. By this method no regard need be paid to the current as the only thing to remember is to keep on that angle no matter how oddly the ship may be heading.

For those who are skeptical, and I have seen many, I will submit a little proof construction to remove any doubts that may

remain. Take Sketch No. 2, and carry out the work started in Sketch No. 1, first, mark carefully points 1, 2, 3, 4, 5, 6, 7, etc., for identification purposes, and bisect A-1, A-2, A-3, A-4, and erect perpendiculars at these points intersecting the line CD in the points 1, 2, 3, 4, 5', etc. With point r', as a center, and with radius equal to 1'1, draw the arc of a circle, and it will pass through A and B. The arc 1-1-1 is the path traveled over if the angle A1B is held. For the second curve, take the point 2' as a center, and with radius 2'2 describe a circle and it will pass through the points A and B. The same may be done for all the points and the same results will be found to occur. This method is useful near shore, but there is no reason why it can't be used off shore using two ships or buoys of known position.