Let us suppose that the body on which we wish to measure lengths is moving relatively to ourselves, and that in one second it moves the distance =OM=. Let us draw a circle round =O= whose radius is the distance that light travels in a second. Through =M= draw =MP= perpendicular to =OM=, meeting the circle in =P=. Thus =OP= is the distance that light travels in a second. The ratio of =OP= to =OM= is the ratio of the velocity of light to the velocity of the body. The ratio of =OP= to =MP= is the ratio in which apparent lengths are altered by the motion. That is to say, if the observer judges that two points in the line of motion on the moving body are at a distance from each other represented by =MP=, a person moving with the body would judge that they were at a distance represented (on the same scale) by =OP=. Distances on the moving body at right angles to the line of motion are not affected by the motion. The whole thing is reciprocal; that is to say, if an observer moving with the body were to measure lengths on the previous observer’s body, they would be altered in just the same proportion. When two bodies are moving relatively to each other, lengths on either appear shorter to the other than to themselves. This is the Fitzgerald contraction, which was first invented to account for the result of the Michelson-Morley experiment. But it now emerges naturally from the fact that the two observers do not make the same judgment of simultaneity. The way in which simultaneity comes in is this: We say that two points on a body are a foot apart when we can _simultaneously_ apply one end of a foot rule to the one and the other end to the other. If, now, two people disagree about simultaneity, and the body is in motion, they will obviously get different results from their measurements. Thus the trouble about time is at the bottom of the trouble about distance.