where $r$ is the distance from the earth's center, $m$ the mass of the earth, $c$ the velocity of light, and $G$ the Newtonian gravitational constant. Tangential measurements require no correction, but intervals of time as measured by our clocks must be multiplied, for each particular place, by the above factor. Then, in terms of the corrected measures so obtained, the particle will be found to describe a straight line with constant velocity although, in terms of our actual measures, it appears to fall with an acceleration. XXI THE EQUIVALENCE HYPOTHESIS The Discussion of This, With Its Difficulties and the Manner in Which Einstein Has Resolved Them, from the Essay by PROF. E. N. DA C. ANDRADE, ORDNANCE COLLEGE, WOOLWICH, ENGLAND Having shown that, of several systems all moving with reference to one another with uniform motion, no one is entitled to any preference over the others, and having deduced the laws for such systems, Einstein was confronted with a difficulty which had long been felt. A body rotating, which is a special case of an accelerated body, can be distinguished from one at rest, without looking outside it, by the existence of the so-called centrifugal forces. This circumstance, which gives certain bodies an absolute or preferential motion, is unpalatable to the relativist; he would like there to be no difference as regards forces [13] between the case when the earth rotates with reference to outside bodies (the stars) considered as fixed, and the case when the earth is considered fixed and all outside bodies rotate around it. This point cannot be investigated by direct experiment; we can spin a top but we cannot keep a top at rest and spin the world round it, to see if the forces are same. In considering the problem of how to devise laws which should make all rotations relative, Einstein conceived the brilliant yet simple idea that gravitation could be brought into the scheme as an acceleration effect, since both ordinary accelerational forces and gravitational forces are proportional to the same thing, the mass of a body. The impossibility of separating the two kinds of effect can be easily seen by considering the starting of an elevator. When the elevator is quickly accelerated upwards we feel a downward pull, just as if the gravitational pull had been increased, and if the acceleration continued to be uniform, bodies tested with a spring balance would all weigh more in the elevator than they did on firm ground. In a similar way the whole of the gravitational pull may be considered to be an accelerational effect, the difficulty being to devise laws of motion which will give the effects that we find by actual observation.