120 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



must be considered as well as in the case where it is negligible. Let 

 AB represent the section of the fixed plane just considered by the 

 plane of the paper. Likewise, let C D represent the similar section of 

 the moving plane. Let the moving plane have a velocity of one cen- 

 timeter per second in the direction C D, and let the distance between 

 the planes be one centimeter. If the layer of gas next to the solid 

 moves with the same velocity with which the solid moves, the line of 

 particles represented by X Y at the beginning of any second will, if 

 X equals X Y, be represented by X at the end of this second. 

 That the particles will at the end of the second lie in the line X is 

 seen by considering the forces acting on any layer of the gas between 

 the planes and parallel to them. The layer above the one in question 

 exerts a tangential force on the latter which tends to move it in the direc- 



D 



B 



Figure 1. 



tion C D, but the layer below it holds it back with a force just equal 

 to this. Otherwise there would be a net constant force acting on the 

 layer parallel to C D, which would produce an acceleration. Clearly 

 there can be no acceleration of the layer while the moving plane 

 maintains its uniform velocity. Moreover, since action and reaction 

 are equal, the layer which is tjius holding back the layer above it is 

 being dragged forward with the same force. It in turn exerts the 

 same forward force on the next succeeding layer, and so on. It thus 

 appears that the force exerted by the layer of gas next to the fixed 

 solid, AB, in the direction AB, is just the same and in the same 

 direction as that exerted by any layer of gas upon that layer just be- 

 neath it ; and also that the force with which the fixed solid resists the 

 motion of the gas is the same as the force with which any layer resists 

 the motion of the layer above it. Clearly, a similar statement may be 



