26 THE GROUNDWORK OF SCIENCE

mics, Thermodynamics, Chemistry, Optics, Acoustics, and

the sciences of Electricity and Magnetism), which again

necessitates recourse to Mathematics, and once more to

Logic and Psychology.

In a word, all the sciences are connected by such a

labyrinth of interrelations that the construction of a really

satisfactory classification of them appears to be an insuper-

able task. Anyhow, it is a task beyond our powers.

But for our special purpose the explorations of the

foundations of science a systematic classification of the

sciences does not appear necessary. We will therefore aim

at nothing but to place before our readers a catalogue of the

sciences in what seems, to our judgment, a not inconvenient

order. It will also, we think, be well to here assume the

existence of real, external independent bodies, as they are

commonly supposed to exist, reserving all questions as to

the truth of that supposition for our next chapter.

Accepting then, provisionally, the existence of a world of

real and independent external bodies, generally exhibiting

some definite shape and figure, with powers of intrinsic

motion, of motion due to external causes, and in all cases

capable of enumeration, we may thus set down the series.

On account of this last characteristic we will place first

on our list the science of Mathematics. This, as the reader

of course well knows, consists of Arithmetic, or the study

of definite quantities of things of whatever kind; of Algebra,

or the use of definite symbols to investigate undefined

quantities of undefined things ; and of Geometry, which

studies the properties of figures, the direction of lines, and

the conditions of space in its three dimensions (length,

breadth, and thickness), including the properties of the sphere,

the cone, and the cylinder. Though Geometry appears to

have arisen through the desire to measure land accurately

(for which the properties of triangles and their angles

mics, Thermodynamics, Chemistry, Optics, Acoustics, and

the sciences of Electricity and Magnetism), which again

necessitates recourse to Mathematics, and once more to

Logic and Psychology.

In a word, all the sciences are connected by such a

labyrinth of interrelations that the construction of a really

satisfactory classification of them appears to be an insuper-

able task. Anyhow, it is a task beyond our powers.

But for our special purpose the explorations of the

foundations of science a systematic classification of the

sciences does not appear necessary. We will therefore aim

at nothing but to place before our readers a catalogue of the

sciences in what seems, to our judgment, a not inconvenient

order. It will also, we think, be well to here assume the

existence of real, external independent bodies, as they are

commonly supposed to exist, reserving all questions as to

the truth of that supposition for our next chapter.

Accepting then, provisionally, the existence of a world of

real and independent external bodies, generally exhibiting

some definite shape and figure, with powers of intrinsic

motion, of motion due to external causes, and in all cases

capable of enumeration, we may thus set down the series.

On account of this last characteristic we will place first

on our list the science of Mathematics. This, as the reader

of course well knows, consists of Arithmetic, or the study

of definite quantities of things of whatever kind; of Algebra,

or the use of definite symbols to investigate undefined

quantities of undefined things ; and of Geometry, which

studies the properties of figures, the direction of lines, and

the conditions of space in its three dimensions (length,

breadth, and thickness), including the properties of the sphere,

the cone, and the cylinder. Though Geometry appears to

have arisen through the desire to measure land accurately

(for which the properties of triangles and their angles