be to any other so-called "force," which like centrifugal force, is independent of the nature of the matter? Again, here on the earth our sensation of weight is interpreted mathematically by combining expressions for centrifugal force and gravity; we have no distinct sensation for either separately. Why then is there any difference in the essence of the two? Why not consider them both as brought into our equations by the agency of mathematical transformations? This is Einstein's point of view. Granting, then, the principle of equivalence, we can so choose axes at any point at any instant that the gravitational field will disappear; these axes are therefore of what Eddington calls the "Galilean" type, the simplest possible. Consider, that is, an observer in a box, or compartment, which is falling with the acceleration of the gravitational field at that point. He would not be conscious of the field. If there were a projectile fired off in this compartment, the observer would describe its path as being straight. In this space the infinitesimal interval between two space-time points would then be given by the formula $$ds^2 = dx^2_1 + dx2_2 + dx^2_3 + dx2_4,$$ where ds is the interval and $x_1, x_2, x_3, x_4$ are coordinates. If we make a mathematical transformation, i.e., use another set of axes, this interval would obviously take the form $$ds^2 = g_{11}dx^2_{33} + g_{22}dx^2_2 + g_{33}dx^2_3 + g_{44}dx2_4 + 2g_{12}dx_1dx_2 + \rm{etc.},$$ where $x_1, x_2, x_3$ and $x_4$ are now coordinates referring to the new axes. This relation involves ten coefficients, the coefficients defining the transformation.