It is interesting to observe that the first term of the second member of equation (56) is the deflection of the point of application of _W₂_ as a point in the frame, while the second term is the deflection of the point of application of _W₁_ considered as a point of the beam. In other words, the condition resulting from the application of the principle of least work is equivalent to making the elastic deflections by _W₁_ and _W₂_ equal. Indeed equation (53) expresses the equivalence of deflections whenever the features of the problem are such as to involve concurrent deflections of two different parts of the structure. =116. Removal of Indetermination by Methods of Least Work and Deflection.=—The indetermination existing in connection with the computations for such trusses as those shown in Fig. 22 and Fig. 23 can be removed by finding equations of condition by the aid of the method of least work or of deflections. It is evident that the component systems of bracing of which such trusses are composed must all deflect equally. Hence expressions may be found for the deflections of those component trusses, each under its own load. Since these deflections must be equal, equations of condition at once result. A sufficient number of such equations, taken with those required by statical equilibrium, can be found to solve completely the problem. Such methods, however, are laborious, and the ordinary assumption of each system carrying wholly the loads resting at its panel-points is sufficiently near for all ordinary purposes. The method of least work can be very conveniently used for the solution of a great number of simple problems, like that which requires the determination of the four reactions under the four legs of a table, carrying a single weight or a number of weights, and many others of the same character. CHAPTER X. =117. The Arched Rib, of both Steel and Masonry.=—During the past ten or fifteen years the type of bridge structure called the arched rib has come into much use, and its merits insure for it a wider application in the future. It partakes somewhat of the nature of both truss and arch; or it may be considered a curved beam or girder. The ordinary beam or truss when placed in a horizontal position and loaded vertically yields only vertical reactions. Under the same conditions, however, the arched rib will produce both vertical and horizontal reactions, and the latter must either be resisted by abutments of sufficient mass, or by a tie-rod, usually horizontal, connecting the springing points of the rib.