ON GRAPHIC METHODS IN MECHANICAL SCIENCE. 607 



(2) Elastic Line and Curve of Deflection. — Neutral axis. Construction 

 of the elastic line. 



Cases of a beam resting on two points of support for various forms 

 of section. 



Cases of a beam encastre at one extremity and at two extremities. 



(3) Continuous Girders. — Construction of the elastic line of beam 

 resting on supports. 



Theorem of three moments interpreted graphically. 

 Unfavourable conditions of loading. 

 Influence of variable cross-section of frame and trusses. 

 Curve of maximum bending moment and shearing force in a con- 

 tinuous girder under concentrated loads. 



(4) Elastic Arch. — Reactions on supports and figure of elastic arch. 

 Elastic arches of parabolic form. 



Cases in which the reactions of the supports pass through the fixed 

 points. Hinged archwork. 



Arches encastre at two extremities. Arches encastre at one support 

 and on rollers at the other. 



Professor Eddy's method of treating the elastic arch. 



Arches ribbed with stiffening truss. 



Spherical and conical domes in metal. 



Construction of central ellipse for the elastic arch with three hinges. 



Influence of wind upon the arch. 



3. MACHINES. 



The graphical treatment of problems for the relative position of dif- 

 ferent parts of a machine. Zeuner's diagrams. 

 Construction for diagrams of effort. 

 Linear and radial diagrams of velocity. 



Use of virtual or instantaneous centre and centrodes, and of axodes. 

 Relative linear and angular velocities of different links of a machine. 

 Graphical treatment of the dynamics of machinery. 

 Graphical constructions for finding the outline of different parts. 

 Teeth of wheels. 



Miscellaneous problems in connection with machines, such as — 



Governors. 



Flywheels. 



Tension in belting. 



Pressure transmitted through the spokes of wheels. 



Resistance of railway trains. 



4. HYDEO-MECHANICS AND NAVAL AECHITECTDRE. 



Constructions for the form of jets. 



Impact and reaction of the water on vanes of vai'ious forms. 

 Graphical constructions in connection with turbines, water-wheels, 

 centrifugal pumps. 



Metacentre and the centre of gravity of ships. 



Stability curves. Graphical construction for the resistance of ships. 



