Suppose that, in firing a gun, under given conditions of range, etc., the effective skill employed is 10 per cent.  This means that 10 per cent of hits are made.  But it means another thing equally important—­it means that 90 per cent of misses are made.  To what are these misses due?  Clearly they are due to errors made, not necessarily by the man who fires the gun, but by all the people concerned.  If the correct sight-bar range were given to the gun, and if the gun were correctly laid and the pointer pressed the button at precisely the right instant, the shot would hit the target, practically speaking.  But, in actual practice, the range-finder makes an error, the spotter makes an error, the plotting-room makes an error, the sight-setter makes an error, and the gun-pointer makes an error.  The sum total of all of these errors results in 90 per cent of misses.

Suppose that by careful training these errors are reduced in the relation of 9 to 8, so that instead of there being 90 per cent of misses there are only 80 per cent.  This does not seem a very difficult thing for training to accomplish, but note the result:  the hits are increased from 10 per cent to 20 per cent.  In other words, by a decrease in errors in the relation of 9 to 8, the effective skill and the hits are doubled.

Conversely, if the errors increased in the ratio of 9 to 10, the misses would increase from 90 per cent to 100 per cent, and the hits would be reduced from 10 per cent to 0.

Suppose now that the conditions are so very difficult that only 1 per cent of hits is made, or 99 per cent of misses, and that by training the misses are reduced from 99 per cent to 98 per cent.  Clearly, by a decrease of errors of hardly more than 1 per cent the effective skill and the hits are doubled.

Conversely, if the errors increased in the ratio of 99 to 100, the misses would increase from 99 per cent to 100 per cent, and the hits would be reduced from 1 per cent to 0.

But suppose that the conditions are so easy that 90 per cent of hits are made and only 10 per cent of misses.  Clearly, if the errors were divided by 10, so that only 1 per cent of misses was made, instead of 10 per cent, the number of hits would increase only 9 per cent, from 90 per cent to 99 per cent.

Of course, this is merely an arithmetical way of expressing the ancient truths that skill becomes more and more important as the difficulties of handling an instrument increase; and that, no matter how effective an instrument may be when used with perfect skill, the actual result obtained in practice is only the product of its possible performance and the effective skill with which it is used.