NA rURE 



?6i 



THURSDAY, AUGUST 17, 1905. 



IHE MATHEMATICS OF iV.4r'.4L STRATEGY 

 AND TACTICS. 



Manuel Pratique de Cinematique nai'ale et maritime. 

 By Captain Leon Vidal. Pp. viii+171. (Paris: 

 Gauthier-\'illars, 1905.) Price 7.50 francs. 



THIS book was undertaken b}' the author in 

 accordance with instructions from the Minister 

 of Marine issued seven years ago. Captain Vidal 

 was directed to collect in a single volume the 

 numerous essays on mathematical naval tactics con- 

 tributed by various authors, French and foreign, and 

 scattered over many publications. Officers of the 

 French Navv were asked officially to give all possible 

 assistance to the compiler, and many of them have 

 done so. The laborious task has been admirably per- 

 formed, various problems dealt with have been clas- 

 sified, and those relating to similar subjects have been 

 grouped in distinct chapters. Captain Vidal has 

 drawn largely upon work done by other officers, and 

 acknowledges the fact. He is an enthusiast on the 

 subject and has supplemented theorems due to others 

 bv much original work, extending or completing his 

 scheme. Solutions alone are given and detailed 

 demonstrations are avoided, so that the volume is 

 compressed within narrow limits in proportion to the 

 range and variety of subjects dealt with. In order 

 to facilitate the practical use of his book by naval 

 officers, elaborate numerical tables have been cal- 

 culated by which readers can construct diagrams re- 

 presenting particular cases that may require to be 

 dealt with either during naval manoeuvres or in war- 

 like operations. Numerous illustrations are intro- 

 duced, and the descriptions are brief and clear 

 throughout. Captain Vidal had to examine and col- 

 late an enormous mass of material produced during 

 the last thirty years, and it is not surprising, there- 

 fore, that he has been so long engaged on the book. 

 French naval officers and professors have done most 

 in this field, but foreign authorities have also been 

 laid under contribution, and the volume will probably 

 long remain the chief book of reference on its special 

 subject. 



The science of naval cinematics, says the author, 

 " consists in the study of the movements of vessels 

 considered ordinarily as moving points, but in many 

 instances it also takes account of their length and 

 gyration, as well as their powers." For the most 

 part, in the strategical theorems dealt with it has 

 been assumed that ships may be treated as particles, 

 the influence of length and turning-power being neg- 

 lected. Further, it is generally assumed that move- 

 ments take place in a calm and tideless sea. Cer- 

 tain corrections are suggested subsequently in order 

 to make allowance for wind, wave, and current, but 

 these sections are very brief, besides being incomplete 

 in treatment, as is indeed unavoidable from the 

 nature of the case. The turning-powers of steam- 

 ships are but lightly touched, although they are most 

 important in tactical manceuvres either for single 

 ^hips or squadrons. 



NO. 1868, VOL. 72] 



It is well known that the mathematical training of 

 French naval officers is more extensive than that 

 given to officers in the Royal Navy, and Captain Vidal 

 is exceptionally well equipped in this respect, 

 even among French officers. The book is indeed 

 mainly a collection of geometrical theorems, in two 

 dimensions, bearing upon the movements of ships or 

 squadrons performed under certain assumed condi- 

 tions. Many of these theorems can have little prac- 

 tical value, but not a few have been made the basis 

 of modern French naval manoeuvres. The funda- 

 mental idea is that when the course of a ship de- 

 parts from a straight line it may be assumed to 

 follow a logarithmic spiral. Captain Vidal enumerates 

 the principal properties of that curve, and gives tables 

 for estimating the lengths of arcs and chords, the 

 values of tangents at different points, and other use- 

 ful items. He takes special cases for spirals described 

 about a fixed point, or about a point in the rectilineal 

 course of another moving body, so as to examine the 

 relative positions, from instant to instant, of two 

 vessels or two squadrons. Theorems attaching to the 

 well-known " curves of search " employed by ships 

 when scouting, or endeavouring to detect the posi- 

 tion of an enemy who attempts either to arrive at or 

 depart from some fixed point, are discussed at length. 

 In another chapter theorems dealing with the move- 

 ments of two vessels such as may take place in single- 

 ship actions are grouped and discussed fully. In a 

 third chapter the most effective methods of concentra- 

 tion for scattered ships belonging to a fleet sent out 

 for purposes of observation and scouting are dealt 

 with. In another section the " lines of observation " 

 to be patrolled by ships of a fleet, and the organisa- 

 tion required in order that an enemy cannot pass 

 through the line without detection, are discussed; 

 The influences of currents in rivers on the movements 

 of vessels and the effect of wind and sea are also 

 briefly investigated. 



Captain Vidal writes fully as much as a mathe- 

 matician as a naval officer. In his opinion the study 

 of mathematics is both necessary and beneficial to all 

 naval officers, whose duty he considers it to be to lay 

 down conditions for programmes of ship-construction. 

 Consequently he urges that oflicers should under- 

 stand the work of the engineer and the trend of indus- 

 trial progress if they are to give good advice and be 

 the corps directeur of a modern fleet. Naval officers 

 rnust, in his opinion, " make, in war, the synthesis 

 of actual forces and guide them in producing the 

 desired effects." To ensure success in this high mis- 

 sion the study of naval cinematics is essential, in 

 Captain Vidal's judgment, since every advance in 

 that science " enables one to foresee more clearly the 

 results of movements of ships and to employ new 

 combinations with intelligence." There is much 

 force in this contention, but the class of work dealt 

 with by Captain Vidal could be undertaken only by 

 the elite of officers in the Royal Navy. His treat- 

 ment would be over the heads of average naval men, 

 and it is not likely to assist them in their daily work. 

 The fact that the standard of mathematical attainment 

 by average officers in our naval service is not so high 



Is 



