Page:Popular Science Monthly Volume 52.djvu/702

682 same proportions in all its parts. The cube of the construction and the cubic dimensions of the rooms, as well as the number of windows and their superficial proportions, might indeed be the same; but we will consider here the details of construction in view of the materials used. Let us reduce the problem to its simplest expression: a beam on two supports in a condition to bear the weight of a man. Let P be this weight; l, b, and h, the length of the beam between the points of support, its breadth, and thickness; and R, the resistance of the wood. According to a well-known formula, we have: $$\scriptstyle P=\frac{2Rbh^2}{3l}$$ which means that the weight that can be supported increases directly in proportion to the resistance of the wood, the breadth of the beam, and the square of its thickness, and inversely as the distance between the supports.

Since on Mars, according to the data of the problem, R suffers no change, while b, h, and l become $$\tfrac{b}{2}$$, $$\tfrac{h}{2}$$, and $$\tfrac{l}{2}$$, we see that the weight which the geometrically reduced apparatus can support will be equal to $$\tfrac{P}{4}$$. We have just seen that the weight of a Martian is $$\tfrac{P}{10}$$. Consequently, the apparatus will be four times as solid as necessary. The Martians could use joists and planks proportionately only half as thick or one quarter as broad, or with supports four times as far apart, or any other combination that would reduce the second member of the equation to one sixteenth.

From what we have said of the lightness of the Martians, it would appear that their division walls and fences would have to be relatively four times, absolutely twice as high as with us.

Now, suppose Megamicros preparing to continue on Mars some work he had begun on the earth. He has a bench, planks, nails, and a hammer. His hammer is of seven eighths less volume and mass, and its weight is reduced to one sixteenth. Himself smaller in size, he can no longer lift the instrument to the same height, so that on a final analysis the living force of the hammer reduced in weight is only one thirty-second. The nail is only half as long, and of only one fourth section; so that, supposing the same rigidity, he meets only one eighth of the resistance in driving it into the board. Megamicros then finds that his hammer is four times too light, and can not understand what makes it so.

If the real Martians have passed, like us, through a stone age and come to an iron age, they have had to work with implements relatively four times larger than ours, and are now using hammers of corresponding dimensions.

To return to our imaginary Martians. It may be objected that