AN ENUMERATION OF THE SCIENCES 27

served, and still serve), Greek geometers occupied them-

selves, in a purely speculative manner, with the different

methods in which a circular cone may be cut. The in-

vestigation of the various kinds of curves which may be

produced by cutting across it in different directions, gave

rise to the study we know as Conic Sections.

By various other processes the most varied properties of

objects have been investigated, including complex reciprocal

relations of increase, decrease, and variation. When two

quantities vary they may do so equally or in different pro-

portions or ratios. The Differential calculus deals with

computations concerning the rates of change between quanti-

ties. The Integral calculus passes from the relation between

such rates back to the relations which exist between the

changing quantities themselves.

We may next pass to the science of Mechanics, with its

subdivisions, Statics, Dynamics, Hydrostatics, Hydrodynamics,

and Pneumatics.

" Mathematics " is, as we have seen, concerned with num-

ber, space, and direction ; " Mechanics " also with time, motion,

and force, and especially the action or effects of gravity.

Mechanics deals also not only with solids but also with

fluids, whether liquids or aeriform (or gaseous) substances ;

and these whether apparently at rest or in a state of

motion.

Statics concerns itself with equilibrium, the composition

of forces, the lever, the balance, the inclined plane, etc.

Dynamics considers motion, its velocity, duration, extension,

and direction (according to Newton's three laws), its quantity,

acceleration and retardation, and the law of falling bodies

due to the action of centrifugal and centripetal forces.

In Mechanics it is assumed that solids consist of par-

ticles cohering stably in some definite order, but liquids are

supposed to consist of particles which possess freedom of

served, and still serve), Greek geometers occupied them-

selves, in a purely speculative manner, with the different

methods in which a circular cone may be cut. The in-

vestigation of the various kinds of curves which may be

produced by cutting across it in different directions, gave

rise to the study we know as Conic Sections.

By various other processes the most varied properties of

objects have been investigated, including complex reciprocal

relations of increase, decrease, and variation. When two

quantities vary they may do so equally or in different pro-

portions or ratios. The Differential calculus deals with

computations concerning the rates of change between quanti-

ties. The Integral calculus passes from the relation between

such rates back to the relations which exist between the

changing quantities themselves.

We may next pass to the science of Mechanics, with its

subdivisions, Statics, Dynamics, Hydrostatics, Hydrodynamics,

and Pneumatics.

" Mathematics " is, as we have seen, concerned with num-

ber, space, and direction ; " Mechanics " also with time, motion,

and force, and especially the action or effects of gravity.

Mechanics deals also not only with solids but also with

fluids, whether liquids or aeriform (or gaseous) substances ;

and these whether apparently at rest or in a state of

motion.

Statics concerns itself with equilibrium, the composition

of forces, the lever, the balance, the inclined plane, etc.

Dynamics considers motion, its velocity, duration, extension,

and direction (according to Newton's three laws), its quantity,

acceleration and retardation, and the law of falling bodies

due to the action of centrifugal and centripetal forces.

In Mechanics it is assumed that solids consist of par-

ticles cohering stably in some definite order, but liquids are

supposed to consist of particles which possess freedom of