In the other class of gauges, shown in fig. 79, the steam acts upon a bent metal tube, _a b c_, usually of a flattened or elliptical section. It may not be known to all readers that if a tube bent, say in the form of the letter ~U~ or ~C~, is subjected to the pressure of a liquid or gas on the inside, the force exerted by the pressure has a tendency to straighten out the tube. This is due to the tendency which a tube of an elliptical or flat section has to change the shape of the latter and approximate to a circular form when the inside is subjected to a pressure. Thus let _A B_, fig. 80, represent a cross section, and _a b d c_, a longitudinal section of a part of such a tube contained between two radii, _O a_ and _O b_, drawn from the centre _O_ of the curve in which the tube is bent. If now we subject the inside of _A B_ to a pressure it will have a tendency to assume the form of the circle _C D_, and would then be represented in the longitudinal section by the dotted lines _a′ b′ d′ c′_. If now we draw radial lines through _a′ c′_ and _b′ d′_, it will be found that they intersect at _O′_, instead of _O_, which was the original centre of the curve of the tube. It will be seen that as the section of the tube approximates to the form of a circle, the portion _a b_ which is outside the curve will be moved farther from the centre, while the other side, _c d_, is moved nearer to it. As indicated by the radial lines, when this occurs either the outside must be lengthened and the inside shortened, to conform to the radial lines _a O_ and _b O_, or else the tube will be straightened so that the radial lines will assume the position _a′ O′_ and _b′ O′_. The phenomenon of the straightening of the bent tubes of steam gauges is frequently attributed to the difference between the area of the inside and outside of the curve. This error was shared by the writer, until the fallacy of the reasoning which supported it was pointed out to him. In the gauge represented in fig. 79, (in which the dial-plate is removed), one end, _c_, of the tube is attached at _d_ to a lever which has a toothed segment, _e_, at the other end. The end _a_ of the tube is connected with the lever at _f_. The connection at _d_, therefore, forms the fulcrum of the lever. It is obvious that as the two ends of the bent tube are forced apart by the steam pressure, the lever and the segment have motion imparted to them. The latter gears into a pinion on the spindle of the index or pointer, _r r_, which thus indicates on the dial the degree of pressure in the tube. The latter is connected with the boiler by a tube attached at _g_. Various forms of this kind of steam-gauge are also made, but all act on essentially the same principle. The position of the steam-gauge on the engine is shown at _M_, in fig. 71. QUESTION 147. _Why is the pipe which connects the steam-gauge with the boiler bent as shown in fig. 71?_