The fourth dimension

THE SECOND CHAPTER IN THE HISTORY OF FOUR SPACE 53

We can solve the problem in a particular case- In the figure ACDE ak (fig. 30) there are° _ 15 inside . . 1b : 4atcorners . 1 - a total of 16. - Now in the square ABGF, - there are 16—

. Qimside . ne . 12 on sides. . 6 . 4atcorners . lL . 16

+ Hence the square on AB + would, by the shear turner a * + © ing, become the shear square

ve ACDE.

And hence the inhabitant of this world would say that the line aB turned into the line ac. These two lines would be to him two lines of equal length, one turned a little way round from the other.

That is, putting shear in place of rotation, we get a different kind of figure, as the result of the shear rotation, from what we got with our ordinary rotation. And as a consequence we get a position for the end of a line of invariable length when it turns by the shear rotation, different from the position which it would assume on turning by our rotation.

A real material rod in the shear world would, on turning about A, pass from the position aB to the position Ac. We say that its length alters when it becomes Ac, but this transformation of 4B would seem to an inhabitant of the shear world like a turning of aB without altering in length.

If now we suppose a communication of ideas that takes place between one of ourselves and an inhabitant of the