HOGG. — FRICTION AND FORCE DUE TO TRANSPIRATION. 119 



continually applied in the direction of motion in order that a uniform 

 velocity may be maintained. That is, during the motion there is a 

 certain tangential stress exerted by the gas on the solid which opposes 

 the motion of the solid. If the layer of gas which is in contact with the 

 moving plane moves with the same velocity with which the solid moves, 

 the tangential stress between the gas and the solid, that is, the resist- 

 ance experienced by the solid, must depend upon the force required to 

 cause one layer of the gas to move with a certain velocity relative to the 

 next layer. Experiment shows that the relative velocity of contigu- 

 ous layers is a measure of the tangential force. If, however, the solid 

 and the gas in contact with it do not move together, then, for the same 

 velocity of the moving solid, the velocity of a layer of gas relative to 

 its contiguous layer is less than before, and hence the friction between 

 them is less, and therefore the stress at the solid is less. In the case 

 considered, when the moving plane and the layer of gas next to it move 

 together the force per square centimeter of the plane necessary to keep 

 up a uniform velocity of one centimeter per second in the given direction 

 is the coefficient of viscosity or internal friction. If the moving plane and 

 the layer of gas next to it have not the same velocity, the gas is said 

 to slip on the solid. The force per unit area of the plane which must 

 be applied in a given direction in the plane to maintain a uniform rela- 

 tive velocity between the plane and the layer of gas is proportional to 

 this relative velocity. When the relative velocity is one centimeter 

 per second the force required is the coefficient of external friction. 



Maxwell showed that the internal friction of a gas is constant for 

 pressures varying from atmospheric to one sixtieth of atmospheric 

 pressure. In his paper ^ he defines the coefficient of slip to be the 

 ratio /a/o", where /x is the coefficient of viscosity of the gas, and o- the 

 coefficient of external friction. The coefficient of slip is then a quan- 

 tity which decreases as o- increases and ft decreases, and which increases 

 as o- decreases and /x increases. In order that there should be no 

 sHpping, o- must be infinitely great compared with fx. As this is 

 probably never the case, there is some slip under all circumstances. 

 Maxwell also showed that when the conditions are such that slip must 

 be considered, the resistance to the moving solid in the foregoing dis- 

 cussion is the same as it would be were the fixed surface removed a 

 distance 2 /3 farther from the moving surface where /3 is the coefficient 

 of slip. 



A consideration of Figure 1 will probably help to make the motion of 

 the gas between the planes better understood in the case where slip 



* Sci. Papers, 2, 1. 



