CONTENTS.

PRELIMINARY.

ON THE MEASUREMENT OF QUANTITIES.

Article		Page
1.	The expression of a quantity consists of two factors: the numerical value and the name of the concrete unit.	1
2.	Dimensions of derived units.	1
3–5.	The three fundamental units—Length, Time, and Mass.	2, 3
6.	Derived units.	5
7.	Physical continuity and discontinuity.	6
8.	Discontinuity of a function of more than one variable.	7
9.	Periodic and multiple functions.	8
10.	Relation of physical quantities to directions in space.	8
11.	Meaning of the words Scalar A quantity that has magnitude but no direction, such as temperature or mass. and Vector A quantity that has both magnitude and direction, such as velocity or force..	9
12.	Division of physical vectors into two classes: Forces and Fluxes In this context, "Forces" refers to directed intensities (like electric field strength), while "Fluxes" refers to the flow or quantity passing through an area (like current density)..	10
13.	Relation between corresponding vectors of the two classes.	11
14.	Line-integration appropriate to forces; surface-integration appropriate to fluxes.	12
15.	Longitudinal and rotational vectors.	12
16.	Line-integrals and potentials A mathematical function describing the energy state at a point in a field..	13
17.	Hamilton’s expression for the relation between a force and its potential.	15
18.	Cyclic regions Spaces containing loops that cannot be shrunk to a point without leaving the region, like the inside of a ring. and geometry of position An early term for topology..	16
19.	The potential in an acyclic region A "simply connected" space where any loop can be tightened to a single point. is single-valued.	17
20.	System of values of the potential in a cyclic region.	18
21.	Surface-integrals.	19
22.	Surfaces, tubes, and lines of flow.	21
23.	Right-handed and left-handed relations in space.	24
24.	Transformation of a line-integral into a surface-integral.	25
25.	Effect of Hamilton’s operation ∇ The "Nabla" or "Del" operator used in vector calculus to find gradients, divergence, and curl. on a vector function.	27
26.	Nature of the operation ∇² The Laplacian operator, used to describe how a quantity varies across a space..	29