L E C T U R E S A T U N I V E R S I T Y O F B U E N O S A I R E S 9 5 5 us consider one example, he went on. Let us suppose that a disk spins with respect to a sys- tem K and that an observer is found in that system. If the observer is located at the midpoint, he is at rest with respect to K that is, he does not move with the disk’s matter. If he has identical clocks, operating identically, and he places them on the disk at different distances from the rotational axis, he will verify that the clocks run more slowly the farther they are from the center of the disk, since the velocity of movement grows proportionally to the dis- tance of the points from the axis. That is, the clocks run at different speeds in different plac- es, and the same thing will occur in a gravitational field. In the case we have been discussing, the centrifugal force can be attributed to that sort of field. In other words, a rea- sonable definition of time by using identical clocks at rest with regard to the body of refer- ence (disk) is impossible. Similarly, the definition of the coordinates, he continued, presents serious difficulties. If the observer located on the disk draws a circle with its center at the axis, and, using a material ruler, small with respect to the radius, measures the length of its circumference and its diameter and calculates the ratio between them, he will get a number greater than π = 3.14…. In effect, when placed on that circumference, the little ruler, seen from K, grows shorter in length, according to the principle of relativity, while that does not occur when it is on the radius, since it is perpendicular to the direction of movement. Further, the obser- vations that are made from the center of the disk are identical to what happens from the cen- ter of the disk that constitutes system K’. What we have just said proves that Euclidean geometry is not applicable to the spinning disk O, which is the same in a gravitational field. Thus, he added, we cannot define the coordinates x, y, z relative to the spinning disk O, which is the same in a gravitational field, in the same way it is used in the Special Theory of Relativity. It is clear, he said, that while the coordinates and times of the events are not defined, the natural laws in which they appear have no meaning. In order to demonstrate how to resolve the difficulties we have just pointed out, Dr. Ein- stein continued, and to be able to apply the general principle of relativity, we need to con- sider certain questions of geometry, beginning with the Gaussian coordinates, a topic I will leave for the next lecture. Professor Einstein Delivered His Sixth Lecture on Relativity Yesterday [15 April 1925] Distance and Duration in a Gravitational Field (In the previous lecture it was demonstrated that, given a system moving with rotational movement, it is not possible to define the time between two events and the distance between the locations where they take place the same thing occurs when the body of reference is moving with rectilinear, uniform motion. That is to say, not even by using identical clocks