30 THE MECHANICS OF THE EARTH'S ATMOSPHERE. 



If we divide these values by the cosines of 40, 20, and degrees, 

 respectively, there results 



109.55, 107.65, and 110.93. 



The resistances are therefore in accordance with the ordinary as- 

 sumption, proportional to the cosine of the inclination. 



In case the plane of the plane disk does not include the axis of rota- 

 tion, we should also have to consider the diminution of the surface 

 opposed to the impinging air in consequence of the projection upon the 

 direction of motion, and for both reasons the resistance diminishes in 

 the ratio of the square of the cosine of the deviation. Since the disks 

 were always adjusted by the plumb line, therefore an error of 2 degrees, 

 by which the resistance would only be diminished by its thousandth 

 part, could not easily remain unnoticed. 



Finally, it still remains to be investigated whether the nature of the 

 surface of the disks, according as they were smooth or rough, had any 

 influence on the resistance. To this end I took two disks, each of which 

 was covered on one side with very smooth paper but on the other with 

 very coarse sandpaper. I allowed these to run with various velocities, 

 exposing each time first the smooth and then the rough side to the 

 impinging air. In both cases the times in which the index described 

 10 inches remained very nearly the same. The differences were very 

 irregular, and not larger than occurred in repeated experiments with 

 equal pairs of disks. Hence the nature of the surface of a plane disk 

 has no iufluence on the resistance of the air when the surfaces are 

 normal to the direction of motion. 



