XXII
velocity of 20′ and has traversed a space, which a body by an
uniform motion would have gone through in two seconds with
an average velocity of O X 20/2 = 10′. Hence space in 2 seconds
will be 2 x 10 = 2. 2. 5 = 22. 5. The same calculation will show,
that for 3 seconds space will be O X 30 / 2 . 3 = 3. 15 = 3 . 5 = 32.
5. For 4 second we get O X 40/2 X 4 = 20. 4 = 4. 4. 5 = 42 5
For 5 seconds 52. 5 and for H second H2.5.
Having proved laws 1 and 3, law 2, may be easily derived
either from law 1 or 3. For, knowing the space traversed in any
second we have only to add the 5' which a falling body traverses
in consequence of gravity to the velocity acquired in the pre
ceding second, f. e. In the 7th second the space must be
6 x 10 + 5= 65'. Arranging the spaces of subsequent seconds
according to this calculation we shall see law 2 verified too.
§ 48. The laws of falling bodies may be verified by means of
the “Inclined plane”. Although the force, with which something
rolls down an inclined plane, is not the full action of gravity (but
according to the degree of inclination of the plane, a greater or
smaller fraction or one of the components of gravity) the pro
portion, in which velocity increases, remains unaltered and the
slackening of the fall by the inclined plane enables us to observe
the progress in velocity, if the inclined plane is graduated in
inches. The same inclined plane may be used as a loader (see
§ 37) on account of the decomposition, which takes place, if
a cask is laid upon it. By Alwoods machine all the laws of
falling may be demonstrated. It consists of a wooden pillar
with a clock work on the top and a graduated scale for measur
ing the spaces traversed by a weight suspended by a silk thread.
§ 49. 2) Projection. a) If a body is thrown perpendi
