The fact that the speed of the propeller depends on the density of the air has an interesting corollary, which is that a propeller adequate at low altitudes will fail at high ones. The density of the air varies with altitude according to the following figures: At 3000 meters, 72 per cent. of sea level 5000 meters, 59 per cent. of sea level 6000 meters, 52 per cent. of sea level If we take the r. p. m. at 90 miles per hour at sea level as 6000, then at the above altitudes the speeds will be 4300, 3500, and 3000, respectively. The last figure is below that for which this size of propeller stalls with its normal load, as noted in the last paragraph. Consequently, if flying is to be done at these altitudes a larger propeller must be carried, which will still deliver enough power at the lower density. The next factor to be considered is the _power furnished by the propeller_. As a representative figure may be quoted the performance of the L propeller. This gives 27 watts at 3600 revolutions per minute (56 miles per hour). From this figure the performance of other propellers may be deduced from the basic laws, which are: that the _power varies as the density of the medium_ and as the _cube of the velocity_ (assuming constant efficiency). Since the power delivered by the six inch diameter L propeller is already adequate at 60 miles per hour, the necessary dimension to function satisfactorily at 100 miles per hour would need to be only a little more than three inches, except for the desirability of a safety factor for high altitudes and low air densities. The _efficiency_ of the propeller is defined by the relation— power delivered by the propeller Efficiency = ———————————————————————————————— power supplied to the propeller The denominator of this fraction is the thrust times the velocity, for which the curves of Fig. 66 supply us data for the L propeller. Using the figures 3600 r. p. m., 56 miles per hour, and 27 watts, we find the efficiency to be about 50 per cent. This increases with the velocity, with a possible upper limit of 70 to 80 per cent. Since the main propeller of the plane is not over 80 per cent. efficient we have at most an efficiency of 64 per cent. in using a propeller drive, as compared with taking the power directly off the engine. In considering the use of _spring and clock-work motors_ we meet at once with the problem of comparing the effect on the performance of a plane of a carried weight, as against a head resistance. The efficiency of a spring motor is measured in terms of its weight, that of a propeller in terms of its head resistance. The general answer to this question is given by the relation that _a pound of dead weight is equivalent to ⅕ pound head resistance_.