There is a simple one, and before Galileo’s time it had been discovered by Stevinus, an engineer. Stevinus’ solution was as follows. Suppose that _A B C_ is a wedge-shaped block of wood. Let a loop of heavy chain be hung over it, and suppose that there is a little pulley at _C_ and no friction anywhere. Then the chain will hang at rest. But the lower part, from _A_ to _B_, is symmetrical; that is to say, it is even in shape on both sides. Hence, so far as any pull it exerts is concerned, the half from _A_ to _D_ will balance the other half from _B_ to _D_. Therefore, like weights in a scale, you may remove both, and then the force of gravity acting down the plane on the part _A C_ will balance the force of gravity acting vertically on the part _C B_. Now the weight of any part of the chain, since it is uniform, is proportional to its length. Hence, then, the gravitational force down the plane of a piece whose weight equals _C A_ is equal to the gravitational force vertically of a piece whose weight equals _C B_. In other words, the force of gravity acting down a plane is diminished in the ratio of _C B_ to _C A_. But when a body falls vertically, then, as we have seen, S = 1/2 GT², where S is the space it will fall through, G the number of feet per second of velocity that gravity, acting vertically on a body, will produce in it in a second, and T the number of seconds of time. If then, instead of falling vertically, the body is to fall obliquely down a plane, instead of G we must put as the accelerating force G × (vertical height of the end of the plane)/(length of the plane). To try the experiment, he took a beam of wood thirty-six feet long with a groove in it. He inclined it so that one end was one foot higher than the other. Hence the acceleration down the plane was 1/36 G, where G is the vertical acceleration due to gravity which he wanted to discover. Then he measured the time a brass ball took to run down the plane thirty-six feet long, and found it to be nine seconds. Whence from the equation given above 36 feet = 1/2 acceleration of gravity down the plane × (9 seconds)². Whence it follows that the acceleration of gravity down the plane is (36 × 2)/(9)² feet per second. But the slope of the plane is one thirty-sixth to the vertical. Therefore the vertical acceleration of gravity, _i.e._, the velocity which gravity would induce in a vertical direction in a second, is equal to thirty-six times that which it exercises down the plane, _i.e._, 36 × (36 × 2)/(9)²; and this equals 32 feet per second. Though this method is ingenious, it possesses two defects. One is the error produced by friction, the other from failure to observe that the force of gravity on the ball is not only exerted in getting it down the plane, but also in rotating it, and for this no allowance has been made. The allowance to be made for rotation is complicated, and involves more knowledge than Galileo possessed. Still the result is approximately true.