Chapter IV

.--Editor.

[5] A. Einstein: Die Grundlage der allgemeinen Relativitätstheorie. Ann. d. Physik. 4, vol. 49, page 776.

[6] At this point we have again used the blue pencil on Dr. Davis' text, his discussion of the three observational tests of the General Theory adding nothing to Dr. Pickering's.--The Editor.

[7] Commander McHardy uses the term "event" in a sense somewhat different from that seen in a majority of the essays. He reserves for the four-dimensional element--the instant of time at a point in space--the name "point-event"; and the term "event" he applies to a collection of these forming, together, an observable whole. An actual physical happening, like a railroad wreck or a laboratory experiment, it will be realized is of the latter sort, occupying an appreciable region of space rather than a single point, and an appreciable interval of time rather than a single second. To the element, the "point-event" of Commander McHardy's essay, this bears the same relation that the geometer's solid bears to his point. This comment is in no sense to be taken as criticism of Commander McHardy's terminology, which rather appeals to us; we make it merely to guard against confusion in the reader's mind.--Editor.

[8] This paragraph is the result of an editorial revision of the author's text, designed to retain the substance of his presentation, while tying up what he has to say more definitely with the preceding essays, and eliminating the distinction between finite and infinitesimal intervals, which we believe to be out of place in an essay of this character. We will not apologize to our mathematical readers for having used finite and differential notation in the same equation, in violation of mathematical convention.--Editor.

[9] Although gravitational force in a small region can be imitated or annulled by accelerating motion, there remains the disturbing influence of gravitational matter already referred to and expressed in the fabric curvature. It is this that defines how unique tracks run, or rather, how bodies progress.--Author.

[10] Not all gravitational fields may be transformed away by a proper choice of coordinates. If this were so, the space, whose nature is independent of any choice of coordinates, would always be Euclidean.--Author.

[11] Thus when it it said that a body contracts or that a clock runs slow when it is put in motion no actual physical change is implied. The judgment of different observers--one at rest with respect to the body and one not--are different.--Author.

[12] The balance of Dr. Royds' essay is given to a discussion of the phenomena of Mercury's perihelial advance, the deflection of light under the gravitational field of the sun, and the shift in spectral lines, in connection with which alone Einstein's theory makes predictions which are sufficiently at variance with those of Newtonian science to be of value in checking up the theory observationally. In the interest of space conservation and in the presence of Dr. Pickering's very complete discussion of these matters we omit Dr. Royds' statement.--Editor.

[13] There is, on any view, no difference as regards observation of position only.--Author.