Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/21

Contents.

Preliminary.

On the Measurement of Quantities.

Art. 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 and Vector 9
12. Division of physical vectors into two classes, Forces and Fluxes 10
13. Relation between corresponding vectors of the two classes 11
14. Line-integration appropriate to forces, surface-integration to fluxes 12
15. Longitudinal and rotational vectors 12
16. Line-integrals and potentials 13
17. Hamilton's expression for the relation between a force and its potential 15
18. Cyclic regions and geometry of position 16
19. The potential in an acyclic region 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 $\nabla$ on a vector function 27
26. Nature of the operation $\nabla^2$ 29