As we have already seen, there is another point to consider. Not only must we be able to support the mirror when inclined to the horizon, but we must support it bodily at the end of the tube when it is horizontal. We will next examine an arrangement adopted by Mr. Grubb, similar to that adopted by others, for supporting the Melbourne speculum, and we cannot do better than quote Mr. Grubb’s own explanation of it. He says:— “To understand it, suppose the speculum to be divided into forty-eight portions, as in Fig. 74, each of them being exactly equal in area, and consequently in weight. Now, if the centre of gravity of each of these pieces rested on points which would bear up with a force = the weight of each segmental piece, it is evident that there would be no strain in the mass from segment to segment. [Illustration: FIG. 74.—Division of the speculum into equal areas. ] “This is exactly what is accomplished by this system; in fact, if when the speculum is resting on these supports it could be divided up into segments corresponding to those lines, they would have no inclination to leave their places, showing a perfect absence of strain across those lines. Suppose now the points representing the centres of gravity of these segments were supported on levers and triangles, so as to couple them together, as at A, Fig. 75, and each of these couplings to be supported from a point _a_, representing the centre of gravity of the sum of the segments supported by that particular couple, and it is evident that there can be no strain between the components of these couples. Again, let these points, _a_, be coupled together by the system shown at B, Fig. 75, and their centres of gravity, _b_, coupled as at C, and it is evident that the whole weight of the speculum ultimately condensed by this system into these points is supported on forty-eight points of equal support being the centres of gravity of the forty-eight segments at Fig. 75. In Fig. 76 is seen the whole system complete. It consists of three screws passing through the back of the speculum box (which serve for levelling the mirror), the points of which carry levers (_primary system_) supporting triangles on their extremities (_secondary system_), from the vertices of which are hung two triangles and one lever (_tertiary system_). All the joints of this apparatus are capable of a small rocking motion, to enable them to take their positions when the speculum is laid upon them. [Illustration: FIG. 75.—Primary, secondary, and tertiary systems of levers shown separately. ] [Illustration: FIG. 76.—Complete system consolidated into three screws. ]