We have so little positive knowledge in regard to the ultimate constitution of matter and even in regard to the actual character of the objects around us, which are revealed to us through our senses, that the field in which our imagination may revel is boundless. Perhaps some day the humanity of the present will merge itself into a new race, endowed with new senses, whose revelations are to us, for the present, at least, utterly inconceivable. The possibility of such a development may be rendered more clear if we imagine the existence of a race devoid of the sense of hearing, and without the organs necessary to that sense. They certainly could form no idea of sound, far less could they enjoy music or oratory, such as afford us so much delight. And, if one or more of our race should visit these people, how very strange to them would appear those curious appendages, called ears, which project from the sides of our heads, and how inexplicable to them would be the movements and expressions of intelligence which we show when we talk or sing? It is certain that no development of the physical or mathematical sciences could give them any idea whatever of the sensations which sound, in its various modifications, imparts to us, and neither can any progress in that direction enable us to acquire any idea of the revelations which a new sense might open up to us. Nevertheless, it seems to me that the development of new senses and new sense organs is not only more likely to be possible, but that it is actually more probable, than any revelation in regard to a fourth dimension. FOOTNOTES: [5] "History of Civilization in England." American edition, Vol. II, page 342. [6] "The Natural History of Hell," by John Phillipson, page 37. [7] "Flatland," by E. A. Abbott. London, 1884. [8] "From Adam's Peak to Elephanta--" page 160. HOW A SPACE MAY BE APPARENTLY ENLARGED BY CHANGING ITS SHAPE The following is a curious illustration of the errors to which careless observers may be subject: Draw a square, like Fig. 19, and divide the sides into 8 parts each. Join the points of division in opposite sides so as to divide the whole square into 64 small squares. Then draw the lines shown in black and cut up the drawing into four pieces. The lines indicating the cuts have been made quite heavy so as to show up clearly, but on the actual card they may be made quite light. Now, put the four pieces together, so as to form the rectangle shown in Fig. 20. Unless the scale, to which the drawing is made is quite large and the work very accurate, it will seem that the rectangle contains 5 squares one way and 13 the other which, when multiplied together, give 65 for the number of small squares, being an apparent gain of one square by the simple process of cutting. [Illustration: Fig. 19.] [Illustration: Fig. 20.]