THE DYNAMOMETER-CHRONOGRAPH. 87 



may be expressed in terms of the amount of work done per unit quantity of air 

 passing within the radius of the arms. If any air passes within the perimeter 

 winch does not strike the arms and do its work, it is so much loss of an attainable 

 efficiency. This practical conclusion is continued by experience, since modern 

 American wind-mills, in which practically the entire projection area is covered 

 with the blades, are well known to be more efficient than the old wind-mills of 

 four arms. 



Turning now to the propeller, it will b? seen that the expression for its 

 efficiency, viz., the ratio of useful work done to power expended, involves quite 

 different elements. Here the useful work done (in a unit of time) is the product 

 of the resistance encountered by the distance advanced, which is entirely different 

 in character from that in the fan-blower, and almost opposite conditions conduce 

 to efficiency. Instead of aiming to set in motion the greatest amount of air, as 

 in the case of the fan-blower, the most efficient propeller is that which sets in 

 motion the least. The difference represents the difference between the screw 

 working in the fluid without moving it at all, as in a solid nut, and actually 

 setting it in motion and driving it backward — a difference analogous to that which 

 in marine practice is technically called " slip," and which is a part of the total 

 loss of efficiency, since the object of the propeller is to drive itself forward and 

 not to drive the air backward. It may now be seen why the propeller with few 

 blades is more efficient than one with many. The numerous blades, following- 

 after each other quickly, meet air whose inertia has already yielded to the blades 

 in advance, and hence that does not offer the same resistance as undisturbed air 

 or afford the same forward thrust. In the case of the propeller with two blades, 

 each blade constantly glides upon new strata of air and derives from the inertia 

 of this fresh air the maximum forward thrust. The reader will observe the 

 analogy here to the primary illustration of the single rapid skater upon thin ice, 

 who advances in safety where a line of skaters, one behind the other, would 

 altogether sink, because he utilizes all the sustaining power to be derived from 

 the inertia of the ice and leaves only a sinking foothold for his successors. The 

 analogy is not complete, owing to the actual elasticity of air and for other reasons, 

 but the principle is the same. A second observation relating to aerial propellers, 

 and one nearly related to the first, is that the higher the velocity of advance 

 attained, the less is the percentage of " slip," and hence the higher the efficiency 

 of the propeller. The propeller of maximum efficiency is in theory one that 

 elides through the air like a screw in an unyielding frictionless bearing, and 

 obtains a reaction without setting the air in motion at all. Now, a reaction from 

 the air arising from its inertia increases, in some ratio as yet undetermined, with 

 the velocity with which it is struck, and if the velocity is high enough it is 

 rendered probable, by facts not here recorded, that the reaction of this ordinarily 



