hundred parts; a portion, Bx = a, is then measured off, and represents the amount of A present. Similarly, a portion, Ax′ = b, is measured off and represents the fractional amount of B, while the remainder, xx′ = c, represents the amount of C. From x and x′ lines are drawn parallel to the sides of the triangle, and the point of intersection, P, represents the composition of the ternary mixture of given composition; for, as is evident from the figure, the distance of the point P from the three sides of the triangle, when measured in directions parallel to the sides, is equal to a, b, and c respectively. From the division marks on the side AB, it is seen that the point P in this figure also represents a mixture of 0.5 parts of A, 0.2 parts of B, and 0.3 parts of C. This gives exactly the same result as the previous method. The employment of a right-angled isosceles triangle has also been suggested,[[319]] but is not in general use.
In employing the triangular diagram, it will be of use to note a property of the equilateral triangle. A line drawn from one corner of the triangle to the opposite side, represents the composition of all mixtures in which the relative amounts of two of the components remain unchanged. Thus, as Fig. 82 shows, if the component C is added to a mixture x, in which A and B are present in the proportions of a : b, a mixture x′, which is thereby obtained, also contains A and B in the ratio a : b. For the two triangles ACx and BCx are similar to the two triangles HCx′ and KCx′; and,
therefore, Ax : Bx = Hx′ : Kx′. But Ax = Dx and Bx = Ex; further Hx′ = Fx′ and Kx′ = Gx′. Therefore, Dx : Ex = Fx′ : Gx′ = b : a. At all points on the line Cx, therefore, the ratio of A to B is the same.
If it is desired to represent at the same time the change of another independent variable, e.g. temperature, this can be done by measuring the latter along axes drawn perpendicular to the corners of the triangle. In this way a right prism (Fig. 83) is obtained, and each section of this cut parallel to the base represents therefore an isothermal surface.