544 SCIENCE PROGRESS 



to consist largely in the handling of rotating bodies, so that 

 the student might observe and test the laws of precession and 

 nutation, and acquire an instinctive appreciation of the results 

 of rotational theory. There can be no doubt that Prof. Gray's 

 complaint of the appalling lack of knowledge of the principles 

 of rotational dynamics is abundantly justified. Even bona-fide 

 students of mechanics know far too little of this subject. The 

 traditional treatment and sequence in applied mathematics 

 leaves the theory of rotation at a stage that is reached by 

 few students, and when reached the theory is presented in a 

 form difficult of comprehension by any but the most gifted of 

 the remnant. 



The remedy suggested is to do away with the teaching 

 which as a beginning contents itself with rectilineal motion. 

 Prof. Gray would make the consideration of the manner of 

 growth of vectors the main subject of dynamical pedagogy. 

 Whilst one is inclined to agree that this would be very desirable 

 and advantageous, it is yet doubtful whether such treatment 

 is possible with beginners. Ordinary, untutored experience, 

 which is what the teacher of elementary dynamics has to deal 

 with in the early stages of the course, cannot be worked up at 

 once into a scientific theory of rates of variation of directed 

 quantities. The simplest and most intelligible scientific 

 problems are undoubtedly those on rectilineal motion, and the 

 teacher must begin with them. As he proceeds, however, he 

 should gradually instil into his pupils a comprehension of 

 vectors and their variations, following the valuable suggestions 

 offered by Prof. Gray in his Bournemouth address and elsewhere. 



The fact is that the beginner in mechanics is usually ham- 

 pered by an insufficient equipment of geometrical experience. 

 This necessitates the mingling with the strictly dynamical part 

 of the subject — the doctrine of force, work, and energy — of a 

 modicum of geometrical doctrine, called kinematics. There is 

 a prospect that matters will improve somewhat as the result 

 of the popular interest in aerial flight. In ordinary travelling 

 the question of relative motion and addition of simultaneous 

 motions is not of very immediate importance. A train follows 

 a prescribed path, a motor-car is restricted to definite road- 

 ways, even a ship is not so very dependent on the currents in 

 the sea, at least as far as the ordinary passenger is aware. 

 With aerial flight matters are not so simple. An unknown 

 current in the upper air may be the cause of the ignominious 

 failure of an otherwise formidable air-attack by an enemy 

 power ; an uncertainty in the direction of the wind may bring 

 disaster to a transoceanic flight, whilst the success of such an 

 attempt is hailed as a marvellous exhibition of piloting skill. 

 An interesting account of Air Navigation is given by H. E. 



