386 



THE POPULAR SCIENCE MONTHLY 



Fig. 6. 



Three-space 



Let us next direct our attention to 3-space, an inhabitant of which 



we might call an animal, but which, to continue the nomenclature 



adopted, we shall sometimes in a general way speak of as a iridim. 



Here freedom of life is much more augmented, even more so than in 



passing from 1-space to 2-space. 

 For here we have added the up- 

 and-down motion to the right-and- 

 y^ left and the forward-and-backward 



motions. Here any point is located 

 by means of its distances from 

 three mutually perpendicular planes, 



each plane being formed by two of 



the three lines that can be drawn 

 mutually perpendicular to one an- 

 other. In Fig. 7, Ox, Oy, Oz— 

 representing directions to the right, 

 hitherward and upward, respectively 

 — are the axes of reference, each 

 being perpendicular to the other 

 two, forming the mutually perpen- 

 dicular planes, xOy, yOz, zOx. 

 We saw that in 2-space the axes xx', yy' divided the space into four 

 equal parts of indefinite extent. A straight line in 2-space divides that 

 space into two parts. In 3-space, it is evident that the coordinate planes 

 divide space into eight equal parts of indefinite extent. Any point 

 in 3-space is definitely determined when its distances from the three 

 planes of reference is known. Distances perpendicular to the yz plane, 

 denoted by x, are positive if measured to the right, negative if measured 

 to the left; distances perpendicular to the xz plane, denoted by //, are 

 positive if measured towai-ds us, negative if measured away from us; 



4^ 



Fig. 7. 



