BOOK DEPARTMENT
The Institute Book Department will supply any obtainable naval, professional, or scientific book at retail price, postage prepaid. The trouble saved the purchaser through having one source of supply of all books should be considered. The cost will not be greater and sometimes less than when obtained direct from dealers.
Address all communications to: Secretary-Treasurer, U. S. Naval Institute, Annapolis, Md.
NEW METHODS IN EXTERIOR BALLISTICS. By Forest Ray Moulton, Ph.D., Sc.D., Professor of Astronomy in the University of Chicago, Research Associate of the Carnegie Institution of Washington (1908-22), formerly Lieutenant Colonel Ordnance Reserve Corps, U. S. Army. The University of Chicago Press. $4.00.
Interest in exterior ballistics dates back to Galileo and Newton and includes throughout the time up to the present, names prominent in mathematical and physical research. Galileo demonstrated the parabolic shape of the trajectory in vacuo, and Newton was the first to take into account the resistance of the air on a basis of experiments with falling spheres. From time to time the art of gunnery has made greater and greater demands upon the science of ballistics and many and strenuous efforts have been put forth to meet these increasing demands. Siacci’s methods as improved by Colonel Ingalls were considered adequate in this country up to the time of the World War. Then, however, the increased ranges of heavy artillery, the stringent requirements of barrage fire without observation, and the introduction of anti-aircraft guns showed that these methods were inadequate. New methods were accordingly developed by the ballistic section of the Army Ordnance Department under Professor Moulton who was personally responsible for the greater part of the revision.
Professor Moulton enjoys international preeminence for his fundamental research in celestial mechanics and mathematics and is one of those exceedingly rare individuals who, while capable of reaching the greatest heights of intellectual achievement, are yet able to keep their feet firmly planted on the solid ground of practice and experience. His interest in exterior ballistics thus commenced has been continued up to the present time in connection with the instruction of army and naval officers sent to study under him at Chicago. Many of the results contained in the book have, of course, been published previously, having in fact been used during the World War. There are, however, many new important results given.
The book is not of an elementary character and, in many places, would be extremely difficult reading for one who has not been sufficiently grounded in the methods and notations of higher analysis. The results obtained are of a fundamental character and give a rigorous justification of the methods advanced. Throughout, it is characterized by elegance of treatment and of choice of notation. Of necessity, assumptions as to physical laws are made due to our ignorance of the true relations. However, the theory is constantly checked against such experience as is available. The assumptions made are set forth explicitly and the consequences of their possible inadequacy are discussed. No tables for use in actual computation are given but numerical illustrations are frequent and the needs of the computer have been kept well in mind.
The typography and the illustrations are excellent. Only a few misprints have been observed and these few are quite obvious and unimportant.
There are six chapters. In Chapter I are deduced the differential equations for the motion of the projectile considered as a material particle. It is shown that contrary to what has been often supposed the effects of the moon and sun on even the longest trajectories of the present day are negligible.
In Chapter II are treated the attraction of gravity and the nature of the resistance function. It is shown that a conical-headed projectile will probably experience less resistance by the air than one with the classical ogival head. This conclusion seems to be borne out by experiment. In this chapter there is also developed a new and more rigorous analysis of resistance function firings. It has recently been adopted at the naval proving ground. This method not only avoids the theoretical errors committed heretofore but furnishes more data from each firing.
In Chapter III is expounded the numerical solution of differential equations, which is illustrated by its use in solving a two body problem. Its application to computation of trajectories is briefly outlined.
In Chapter IV is taken up the theory of differential variations, or in other words, the effects on “normal” trajectories of relatively small abnormalities. The method here developed is characterized by its generality. Unlike Bliss’s system of adjoint equations (which is also described) Moulton’s method gives the coordinates and components of velocity throughout the perturbed trajectory. The chapter includes a discussion of weighting factors which although used in the Army have not as yet been introduced into naval practice. A method is developed for the construction of general ballistic tables with a minimum bulk which will yet give not only the coordinates and components of velocity for primary trajectories but also for secondary ones, and weighting factors as well.
Chapter V is devoted to establishing the validity of the method of numerical integration. It includes the proof of Picard’s process, the extension of Picard’s interval, and a new proof of the validity of the Cauchy-Lipschitz process by showing its relations to the former proof. The effects of approximate quadratures are considered and it is shown that the method may be made as precise as desirable. The solution is shown to have properties of continuity and differentiability with respect to the independent variable and the initial conditions.
The last chapter of the book, Chapter VI, includes what will probably be of greatest interest to those who are already familiar with the subject. It treats the dynamics of the projectile as a rotating rigid body of finite dimensions. The equations of motion are derived by a direct method, thus avoiding any possibility of erroneous definition. The problem treated in this chapter is of extraordinary difficulty, a fact which may not be fully appreciated even by experienced mathematicians who have not encountered the subtle possibilities of error latent in its final development. The method of attack adopted is to treat first a simplified case and then on this as a basis to build the additional complications necessary to secure harmony with observed results. The experimental difficulties involved in the attack on this problem have been so great that it was unavoidable to make assumptions as to the physical relations involved. The justification of these assumptions rests on the double ground of making the problem mathematically tractable and of conforming closely to experimental results. Undamped motion is first treated and the resulting types of motion classified and discussed. So far the treatment is similar to that of the classical top problem. Expressions are obtained for the period of the yaw and the precession during this period. A criterion of stability is deduced and there is enunciated the important principle of dynamic similarity between projectiles of different sizes but the same shape. Based on the criterion of stability, a discussion is made of the effects of various modifications of projectiles and the conditions under which they are fired. The effects of damping are next considered. The damping of the spin is treated first, and then the effects of a damping force opposing the oscillations of the projectile. Both types of damping are treated in terms of the effects on the maximum and minimum yaw. Here, as always, close harmony with physical observations is obtained. Finally the differential equations for motion on a curved trajectory are developed and the effects of damping forces, when the projectile moves in a curved trajectory, are considered. This discussion leads to an explanation of the reasons for a projectile maintaining its axis of spin nearly in the line of the tangent to its trajectory. Professor Moulton has demonstrated the existence of a steady- state solution which gives the first adequate analytic explanation of drift. In other words it is shown that the projectile may attain and retain a position in which its nose is a little below and a little to the right of the tangent to the trajectory, thus giving rise to a transverse component of force tending to cause drift. In conclusion Professor Moulton outlines the ways in which his theory can be modified to take account of advancing knowledge of the physical relations as it may be acquired from time to time by experiment.
L. W.
SHIP MODEL MAKING. By Captain E. Armitage McCann. Norman W. Henley Publishing Company, New York. $2.50.
Reviewed by Rear Admiral Elliot Snow (CC), U. S. Navy
Ship Model Making, which has recently made its appearance, has for its object the interest of beginners in the fascinating pastime of making ship models. To this end the author describes and gives the details of two models which are “a happy medium between purely decorative craft and exact scale models.” The craft with which the book deals have, according to the author, been designed from original matter instead of being copied from other models “of vessels that one time were in service.” Because of the author’s object which has been realized in an interesting way the models are “rather different from most of those now seen.” Captain McCann calls them “sketch-models” a term which is fairly descriptive.
Two models only have been dealt with in the book—A Barbary pirate felucca which is based largely upon information obtained from models collected by Peter the Great of Russia, and a Spanish galleon. The description and plans of these two vessels were originally written for the Popular Science Monthly and appeared m recent issues of that magazine.
Throughout the text are some eighty-three drawings and sketches of details. For instance, quarter lanterns, oars, cannons und their carriages, fittings for spars, gun port shutters and a good deal of what is termed “ginger bread” work—decorative features. In addition, working plans for the larger parts of both vessels are contained, on separate sheets, in a pocket inside the back cover. Nearly every sketch is drawn to full size; for parts not so drawn, or if the model maker desires to change the scale, the author shows how the drawings and sketches may be proportionately enlarged or reduced. The felucca, if built to a scale of about one eighth of an inch to the foot, will be about twenty inches long, three inches in width (of beam) and seventeen inches from keel to top of masthead. The galleon on approximately the same scale will be thirty inches long, five inches beam and thirty inches in height. The plans and descriptions are easy for an amateur to follow.
For each craft there is included a list of the tools needed to make them, and complete bills of all materials required in their make-up. The method of building or assembling the parts and numerous details of accessories and rigging all of which are so necessary, even in “sketch-models,” are given.
The chapters on painting, and decorating and the colored frontispiece, will enable anyone who makes the model of these two curious looking vessels—one a treasurer carrier, the other a marauder, to color their hulls, sails and sail devices, flags and banners in the brilliant and variegated hues used on real similar craft in their heyday.
With some instructions as to finishing touches, the book ends appropriately thus “Just a bit of this and a bit of that, a little patience and perseverance, handy fingers and good taste and a [tiny] ship is built which will give lasting joy and be the admiration of your friends.”
Though the models with which the book deals, do not represent any particular craft which centuries ago sailed the Mediterranean or other seas, this book for beginners makes a very acceptable addition to the growing literature of its kind.
THE DARDANELLES EXPEDITION. By Captain W. D. Puleston, U. S. Navy. U. S. Naval Institute. $2.50.
(See Secretary’s Notes, page 2408, this issue.)