RECENT ADVANCES IN SCIENCE 13 



with applied mechanics. Lecornu is also opposed to any at- 

 tempt to introduce consistency in the positive sense of rotation 

 in two-dimensional and three-dimensional geometry, and con- 

 cludes by urging us to let the astronomer and the applied mathe- 

 matician continue using their respective conventions. 



The necessity for a standardised notation has been recog- 

 nised in the application of mathematics to aeronautical pro- 

 blems, and a committee appointed by the Royal Aeronautical 

 Society has recommended the adoption of a set of conventions 

 and symbols, which, it is hoped, will be used by all workers 

 in the subject. In this system the axes adopted are the 

 ordinary left-handed system mentioned above, with clockwise 

 rotations as seen from the axes, thus following the notation 

 used by Routh and in the books based on his treatises. The 

 actual axes adopted as fixed in the aeroplane, for the purpose 

 of the equations of motion with moving axes, are as follows. 

 Imagine the pilot seated in the aeroplane in flight and facing 

 forwards. If the flight is " normal," i.e. horizontal, then the 

 x axis is from the pilot backwards, the y axis is horizontal and 

 to the left, the z axis is vertically upwards. All velocities and 

 force components are used with the positive sign along the 

 positive directions of the axes, and all rotations and couple 

 components are taken with the positive sign round the cyclic 

 order y — 0, z — x, x — y. These axes and conventions were used 

 by Bairstow and his co-workers in the classical wind-channel 

 work carried out during the past ten years at the National 

 Physical Laboratory. 



It nevertheless seems doubtful whether this choice is a wise 

 one, especially as regards the positive direction of the x axis. 

 There may be some justification for this from the point of view 

 of wind-channel experiments, for in these experiments the 

 model is at rest and the air is made to move past it, in the 

 opposite direction to the actual flight of a machine. But, as 

 is pointed out by Bryan (Aer. Journ. xxii. 191 8, 51-3), the effect 

 of the choice is to make the velocities of all aeroplanes nega- 

 tive, and to make all the air-resistance effects positive alge- 

 braically but actually negative. This seems to be a very just 

 criticism, especially as Bryan, who was the first to develop 

 the rigid dynamics of the aeroplane, had devised a notation 

 which satisfies most requirements and avoids these peculiar 

 and troublesome sign confusions. 



