218 Scientific Intelligence. 



when struck by a current of air directed at right angles to its 

 axis. The expression which has been commonly used to formu- 

 late the resistance to motion in a fluid is F = 1/2 cApv 2 where v 

 represents the velocity of the body, A the area of the outline of 

 the body projected on a plane normal to this direction, p the 

 density of the fluid and c is a coefficient to be experimentally 

 determined, and presumably depending only on the nature of 

 the medium and the geometric form A, but independent of 

 its absolute magnitude and of the velocity v, in which case the 

 formula once completed would be applicable to geometrically sim- 

 ilar bodies and different velocities in the same medium. It is 

 however now known that c is constant only for similar flow lines 

 and these may differ even with geometrically similar figures. 



The condition for geometrically similar flow lines was first 

 determined by Osborne Reynolds and requires that the expression 

 R ==. vpd/ji shall be the same for cases to be compared. Here p, 

 is the viscosity, d, some similar linear dimension of the body and 

 v and p have the previous signification. It is thus evident that c 

 will not in general be a constant but will vary with v, and the 

 size and shape of the body. The smallest departure is found to 

 occur in the case of bodies with sharp edges which stand at right 

 angles to the direction of the current, as for example, flat disks 

 met perpendicularly by an air stream. Here, for a considerable 

 range in the values of B the coefficient c remains constant at 

 about 1.1. On the other hand bodies with rounded convex sur- 

 faces show notable variation. When B is small compared to 

 unity the resistance, as in Stokes' law for falling spheres, 

 increases linearly with the velocity. 



The aim of the author's experiments was to trace the connec- 

 tion between c and B throughout a large range of the Reynolds ' 

 number. They were carried out upon cylinders of circular cross- 

 section which were suspended transversely to a plane current of 

 air, i. e., the stream lines were the same in all planes at right 

 angles to the axis of the cylinder. The air velocities ranged from 

 1.2 to 36 meters per second which is from about 4 to 80 miles an 

 hour. Nine cylinders were used varying from .05 to 300 mm. in 

 diameter so that the range of the Reynolds' number investigated 

 was from 4.2 to 800,000. The resistance for the small cylinders 

 was measured by weighting them and observing the pendulum 

 displacement from the vertical. In the case of the larger ones 

 the force was determined by the aid of a system of threads con- 

 nected to a balance. Any disturbance due to the effect of the 

 ends was corrected by a proper experimental arrangement. The 

 results show a number of interesting things : 1st, that the 

 formula of Lamb derived on the theory of fluid friction, is appli- 

 cable only when B is small compared with unity. 2d, c is a 

 decreasing function of B for values of the latter up to about 2,000 



