Ought we to smile at the man and say that he errs in his conclusion ?  I do not believe we ought to if we wish to remain consistent ; we must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws.  Even though it is being accelerated with respect to the “Galileian space” first considered, we can nevertheless regard the chest as being at rest.  We have thus good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity.

We must note carefully that the possibility of this mode of interpretation rests on the fundamental property of the gravitational field of giving all bodies the same acceleration, or, what comes to the same thing, on the law of the equality of inertial and gravitational mass.  If this natural law did not exist, the man in the accelerated chest would not be able to interpret the behaviour of the bodies around him on the supposition of a gravitational field, and he would not be justified on the grounds of experience in supposing his reference-body to be " at rest.”

Suppose that the man in the chest fixes a rope to the inner side of the lid, and that he attaches a body to the free end of the rope.  The result of this will be to strech the rope so that it will hang " vertically " downwards.  If we ask for an opinion of the cause of tension in the rope, the man in the chest will say:  “The suspended body experiences a downward force in the gravitational field, and this is neutralised by the tension of the rope ; what determines the magnitude of the tension of the rope is the gravitational mass of the suspended body.”  On the other hand, an observer who is poised freely in space will interpret the condition of things thus :  " The rope must perforce take part in the accelerated motion of the chest, and it transmits this motion to the body attached to it.  The tension of the rope is just large enough to effect the acceleration of the body.  That which determines the magnitude of the tension of the rope is the inertial mass of the body.”  Guided by this example, we see that our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass.  Thus we have obtained a physical interpretation of this law.

From our consideration of the accelerated chest we see that a general theory of relativity must yield important results on the laws of gravitation.  In point of fact, the systematic pursuit of the general idea of relativity has supplied the laws satisfied by the gravitational field.  Before proceeding farther, however, I must warn the reader against a misconception suggested by these considerations.  A gravitational field exists for the man in the chest, despite the fact that there was no such field for the co-ordinate system first chosen.  Now we might