12 SCIENCE PROGRESS 



English books to choose a set of axes which can be denned at 

 any point on the earth's surface by the instructions : take the 

 x axis due east, the y axis due south, and the z axis vertically 

 upwards. In considering rotations about these axes, we adopt 

 the cyclic order x — y, y — z, z — x, so that the screw motions 

 symbolised by positive x, y, z components of velocity and 

 positive x, v, z components of rotation are necessarily on 

 left-handed screws. But this clashes with some fundamental 

 physical ideas in electromagnetism in which we use right-handed 

 screws. Thus in mechanics a rotation in the y z plane is posi- 

 tive when it is clockwise as seen from the x axis ; in electro- 

 magnetism the rotation is positive when it is seen anti-clock- 

 wise. 



One is led to speculate whether it would not be an advan- 

 tage to adopt a uniform notation in this respect. Although 

 the matter is of little importance as regards the prosecu- 

 tion of new research, it is nevertheless of great importance 

 both from the point of view of pedagogy and from the 

 point of view of economy of mental effort, which is so vital 

 to progress in mathematics. It is taken up by Lecornu (Comptes 

 Rendus, 166, 630-32, 191 8) in a paper " Sur le signe de rota- 

 tion." He mentions the fact that in mechanics rotations are 

 reckoned positive when seen clockwise by the observer from 

 the positive direction of the " axis " of rotation, whilst the 

 reverse is the case in astronomy. Yet he decides against any 

 attempt to bring mechanics and astronomy into line with one 

 another. He bases himself on the fact that the apparent 

 diurnal revolution of the important heavenly bodies, such as 

 the sun and moon, is clockwise when seen from the north : 

 east to south to west. Thus shadows cast by the sun, as in 

 the case of the gnomon, move on the earth in a clockwise 

 direction, and in this way all mechanical rotations have assumed 

 the clockwise sense. But theoretical astronomy, which con- 

 siders the actual revolutions and rotations in the heavenly 

 bodies, necessarily adopts the opposite direction, namely, the 

 anti-clockwise sense, for positive. 



Lecornu considers that it would be contrary to all the 

 usages of practical life to impose on applied mechanics a con- 

 vention derived from astronomy and opposed to the practical 

 convention that we all adopt almost automatically in practice, 

 and of course theoretical mechanics must not be inconsistent 



