RECENT ADVANCES IN SCIENCE 185 



(Jour, de Phys. 5, 175-86, 191 6) on the two-dimensional 

 motion of a light sphere moving in air under gravity, having 

 a rotation about a horizontal axis perpendicular to the plane 

 of motion. Carriere found that after an initial part dependent 

 on the initial conditions, the motion becomes practically uniform 

 in a straight line inclined to the downward vertical in the same 

 sense as the rotation, the inclination increasing with the ratio 

 of the rotation to the translational motion. Appell suggests 

 that the motion can be explained if the air resistance is taken 

 to act in a line through the centre of the sphere, making an 

 angle with the backward direction of motion dependent on the 

 angular velocity, and states that he intends to publish the 

 mathematical analysis for the assumption that the air-resistance 

 varies as the velocity. In a paper read at the Royal Society 

 but not yet published (Nature, 98, 483, 191 7), the writer of 

 these notes shows that the centre of a plane lamina moving 

 in two dimensions in air, the law of resistance being the square 

 of the velocity, moves in a manner similar to that found by 

 Carriere for a light sphere. One may even suggest that probably 

 any rigid body moving in air under gravity will after a time 

 approximate to a type of " terminal " motion along a wavy line 

 inclined to the vertical in a sense and to an extent dependent 

 on the relation between the rotational and the translational 

 velocities. It is well known that a particle tends towards a 

 terminal motion in a vertical straight line. 



H. Larose (Comptes Rendus, 165, 545-8, 191 7) investigates 

 the steady motion of a uniform flexible and inextensible string 

 in air under gravity, finding the equations of the various forms 

 of a string moving with a constant velocity along itself and an 

 addition velocity in a horizontal direction. 



Another problem in resisted motion is worked out by J. 

 Prescott in a paper entitled " On the Motion of a Spinning 

 Projectile " (Phil. Mag. (6), 34, 332-80, 191 7). The author 

 takes the air resistance to be proportional to the square of 

 the velocity, the constant of proportionality being one or 

 another according as the velocity is less than or greater than 

 1,060 ft. per sec, thus introducing an important modification 

 into the method of Bashforth, who made the resistance vary as 

 the cube of the velocity, the constant of proportionality varying 

 as the velocity underwent any considerable change. Assuming 

 first that the resistance is always exactly opposite to the direc- 



