...Statics to the equilibrium of fluids, making allowance for the attendant variability of form. But, before hydrostatics could be comprehended under Statics,...when Lagrange supplied, as the basis of the whole of Rational Mechanics, the single principle of Virtual Velocities. One of its most valuable properties...

...byconsidering its problems dynamically; and before the close of the section M. Comte remarks that " before hydrostatics could be comprehended under statics,...when Lagrange supplied, as the basis of the whole of rational mechanics, the single principle of virtual velocities." In which statement we have two facts...

...of equilibrium of any system of forces applied to the different points of a solid body"—equations which include all cases of levers and an infinity of cases besides. Clearly this is progress towards a higher generality—towards a knowledge more independent of special...

...the section M. Comte remarks that " before hydrostatics could be comprehended under statics, it Mras necessary that the abstract theory of equilibrium...fluids as well as solids. This was accomplished when Lagraiige supplied, as the basis of the whole of rational mechanics, the single principle of virtual...

...equilibrium of any system of forces applied to the different ' points of a solid body'—equations which include all cases of levers and an infinity of cases besides. Clearly this is progress towards a higher generality—towards a knowledge more independent of special...

...could be comprehended under staties, it was necessary that tho abstract theory of equilibrium should bo made so general as to apply directly to fluids as well as solids. This was accomplished when Lagraiige supplied, as tho basis of the whole of rational mechanies, tho single principle of virtual...

...of equilibrium of any system of forces applied to the different points of a solid body"—equations which include all cases of levers and an infinity of cases besides. Clearly this is progress towards a higher generality—towards a knowledge more independent of special...

...calculate, from the amount of residuary motion, the size, distance, and orbit of the unknown planet. D 2 Nothing can better illustrate the statement that scientific...mechanics, the single principle of virtual velocities," — or the principle that whenever weights balance each other, " the relation of one set of weights...

...familiar to the earliest nations known, Archimedes advanced to the more general case of the imequal lever with unequal weights ; the law of equilibrium...mechanics, the single principle of virtual velocities," — or the principle that whenever weights balance each other, of OBJ se: ic F^ris?,- :Iv;r vtlodciw...

...of equilibrium of any system of forces applied to the different points of a solid body—equations which include all cases of levers and an infinity...general as to apply directly to fluids as well as s n lids. This was accomplished when Lagrange supplied, as the basis of the whole of mechanics, the...