Notwithstanding these counter-currents of speculation, which should make the wise man speak smilingly of his wisdom, this summary remains incomplete without a reference to the pressure of higher space upon those adventurous minds that essay to deal with the profound problems of the greater universe, and a statement of the reasons for their feeling this pressure.  These reasons are well suggested by Professor B.G.  Harrison, in his Popular Astronomy.  He says:  “With the idea of a universe of finite dimensions there is the obvious difficulty of the beyond.  The truth is that a universe of finite proportions is equally difficult to realize as one of infinite extent.  Perhaps the nearest analogy to infinity that we can understand lies in our conception of a closed curve.  It seems easier to imagine the endless movement of a sphere in a circular path than the case of one travelling in a straight line.  Possibly this analogy may apply in some way to fourth-dimensional space, but the manner of its application is certainly not easy to understand.  If we would imagine that all co-ordinates of time and space were curved, and eventually return to the same point, it might bring the ultimate comprehension one degree nearer.”

A HINT FROM ASTRONOMY

The physical evidence that our space is thus curved in higher space, some have considered astronomy to furnish in what is called the “negative parallax” of certain distant stars.  This cannot be passed by, though it is too deeply involved with the probable error of the observers themselves to be considered more than an interesting fact in this connection.  Every one knows that the difference of angle under which an object is seen from two standpoints is called its parallax.  The parallax of the stars—­and the consequent knowledge of their distance—­is obtained by observing them from opposite points of the earth’s orbit around the sun.  When a star is within measurable distance, these angles are acute, and the lines from the star to the earth at opposite sides of its orbit converge, therefore.  But when these lines, as sometimes happens, appear to be divergent, the result is called a negative parallax, and is explainable by higher space relationships.  Obviously, the divergence of the lines would indicate that the object lies behind the observer instead of in front of him.  This anomaly can be explained by the curvature of space in the fourth dimension.  If space is so curved, the path of light itself is curved also, and a man—­were his vision immeasurably keen, not to say telescopic—­could see the back of his own head!  It is not worth while to give this question of negative parallax too much importance, by reason of the probability of error, but in this connection it should be stated that there appears to be an undue number of negative parallaxes recorded.

GRAVITATION