[The Reader is strongly advised, in reading this Chapter, _not_ to refer to the above Diagram, but to draw a large one for himself, _without any letters_, and to have it by him while he reads, and keep his finger on that particular _part_ of it, about which he is reading.] pg023 Secondly, let us suppose that we have selected a certain Adjunct, which we may call "x," and have divided the large Class, to which we have assigned the whole Diagram, into the two smaller Classes whose Differentiæ are "x" and "not-x" (which we may call "x'"), and that we have assigned the _North_ Half of the Diagram to the one (which we may call "the Class of x-Things," or "the x-Class"), and the _South_ Half to the other (which we may call "the Class of x'-Things," or "the x'-Class"). [For example, we might say "Let x mean 'old,' so that x' will mean 'new'," and we might suppose that we had divided books into the two Classes whose Differentiæ are "old" and "new," and had assigned the _North_ Half of the table to "_old_ books" and the _South_ Half to "_new_ books."] Thirdly, let us suppose that we have selected another Adjunct, which we may call "y", and have subdivided the x-Class into the two Classes whose Differentiæ are "y" and "y'", and that we have assigned the North-_West_ Cell to the one (which we may call "the xy-Class"), and the North-_East_ Cell to the other (which we may call "the xy'-Class"). [For example, we might say "Let y mean 'English,' so that y' will mean 'foreign'", and we might suppose that we had subdivided "old books" into the two Classes whose Differentiæ are "English" and "foreign", and had assigned the North-_West_ Cell to "old _English_ books", and the North-_East_ Cell to "old _foreign_ books."] Fourthly, let us suppose that we have subdivided the x'-Class in the same manner, and have assigned the South-_West_ Cell to the x'y-Class, and the South-_East_ Cell to the x'y'-Class. [For example, we might suppose that we had subdivided "new books" into the two Classes "new _English_ books" and "new _foreign_ books", and had assigned the South-_West_ Cell to the one, and the South-_East_ Cell to the other.] It is evident that, if we had begun by dividing for y and y', and had then subdivided for x and x', we should have got the _same_ four Classes. Hence we see that we have assigned the _West_ Half to the y-Class, and the _East_ Half to the y'-Class. pg024 [Thus, in the above Example, we should find that we had assigned the _West_ Half of the table to "_English_ books" and the _East_ Half to "_foreign_ books."