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Updated: May 20, 2025
Practical examples of the solution of these and a number of other problems involving proportions or averages were given by the author. The engine represented in Figs. 1 to 4 herewith is intended for a mill, and is of 530 to 800 indicated horse-power, the pressure being seven atmospheres, and the number of revolutions forty-five per minute.
Nature's methods, we say, are blind, haphazard; the wind blows where it listeth, and the seeds fall where the winds and waters carry them; the frosts blight this section and spare that; the rains flood the country in the West and the drought burns up the vegetation in the East. And yet we survive and prosper. Nature averages up well.
"Only here," he says, "I reckon the man I send will do all round; for Pike County has its claims as well as Boston." "What does that mean?" asked the mill-owner. "I reckon he means he don't want Pine Clearing to get too high-toned any more than he wants it too low down. He's mighty square in his averages is Sam."
The higher we go in the scale the truer this individualism holds. We are forced to reason not from the bulk of observations, but from their averages. If we find ten bucks who will go a mile wounded to two who succumb in their tracks from similar hurts, we are justified in saying tentatively that the species is tenacious of life.
The Colorado is still deepening its gorge. In the Grand Canyon its gradient is seven and one half feet to the mile, but, as in all ungraded rivers, the descent is far from uniform. Graded reaches in soft rock alternate with steeper declivities in hard rock, forming rapids such as, for example, a stretch of ten miles where the fall averages twenty-one feet to the mile.
I. to IV. the hauling machine develops on an average 150 indicated horse, while in the tugs No. V. to VIII. the power developed averages 180 indicated horse power. V. to VIII. will take a load of 2,600 tons of cargo in the same number of wooden barges at the same speed and against the same current.
May we not be pardoned for treating all estimates as utterly fallacious that are not based upon known facts and figures? Why do we hear so much of the "approximate correctness" of so many statistical tables, when, in point of fact, the primary data are incapable of proof, and the averages and conclusions built upon them are all assumed?
Let people who have to observe sickness and death look back and try to register in their observation the appearances which have preceded relapse, attack, or death, and not assert that there were none, or that there were not the right ones. A want of the habit of observing conditions and an inveterate habit of taking averages are each of them often equally misleading.
We are golden averages, volitant stabilities, compensated or periodic errors, houses founded on the sea. The wise skeptic wishes to have a near view of the best game, and the chief players; what is best in the planet; art and nature, places and events, but mainly men.
As the river in its swiftest parts is never less than half a mile wide, and averages a mile, it can readily be seen that it is a grand waterway, well deserving its name. Nine miles were made this day and camp was reached at the beginning of rough water on the Horse Shoe Rapid. Here the first evidence of shoes giving out was seen.
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