The Mathematics of Measurement: A Critical History (Google eBook)

Front Cover
Springer Science & Business Media, 1998 - Mathematics - 330 pages
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The Mathematics of Measurement is a historical survey of the introduction of mathematics to physics and of the branches of mathematics that were developed specifically for handling measurements, including dimensional analysis, error analysis, and the calculus of quantities.
  

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Contents

Symbolic algebra and the calculus in kinematics
110
Symbolic algebra in geometrical optics and astronomy
112
The language of Newtons Principia
113
MATHEMATICS IN EIGHTEENTHCENTURY EXACT SCIENCE
117
Quantity of matter
118
The concept of inertia
122
Newtons laws of motion and his law of gravity
124
Abbreviated ratio equations units and functional equations
126

Early weights and measures
23
Limitations of the technology of measurement
26
Angle and time measurements in astronomy
27
Quantification without metrology
30
Quantitative laws in antiquity and in the middle ages
31
EARLY APPLICATIONS OF GEOMETRY AND PROPORTION
32
The character of greek theoretical geometry
34
Euclidean geometry
35
Abstract points lines and surfaces
36
Applying idealized geometry to nature
38
Configurations for physical quantities and relations
39
Proportion
41
Homogeneous and heterogeneous proportions
42
Physical laws and compound ratios
44
Proportion in Medieval exact science
45
Ratio reduced to a single number
46
Features of laws stated as proportions
47
Applications of early trigonometry
48
Trigonometry during the Renaissance
50
THE PROGRESS OF QUANTIFICATION
51
The basic reference quantities of measurement
52
Applications of measurement and mathematics from the Renaissance
56
Sensitivity to observational error
57
Improvements in clockwork
58
Balances to the eighteenth century
59
The discovery of quantitative laws
61
Galilean abstraction
62
The quantification of electric charge tension and current
63
ARITHMETICAL ALGEBRA AND SYMBOLIC GEOMETRY
66
Verbal geometrical algebra
68
Applications of arithmetical algebra to natural philosophy
70
Analytical trigonometry
74
The growing competence of number
75
The promotion of heterogeneous ratios
77
Opposition to algebra
78
Justifications of algebra
80
The infinitesimal calculus
82
Algebra in physics in the seventeenth century
86
The influence of geometry
87
Comparative measurement
89
Points of entry of algebra into technology and physics
90
Thomas Harriot
94
The concept of the moment of a force
96
The algebraic representation of the moment of a force
98
Varieties of force
99
Components of a force
100
Dynamical momentum
105
Mechanical work and vis viva
108
Varignons analytical kinematics and dynamics
127
Algebra in scientific engineering
131
Euler to Lagrange
132
Celestial mechanics
136
Algebra in magnetism and electricity
138
The beginnings of the analytical theory of heat
142
THE METRIC REFORM AND THE UNITS OF PHYSICS
145
The centigrade scale of temperature
147
The impact of the metric movement
148
Absolute units and equations in the theory of heat
149
Biots Traité de physique
154
Absolute units in mechanics
155
Work kinetic energy and thermodynamics
159
Absolute units in dynamical astronomy
160
ABSOLUTE QUANTIFICATION IN ELECTRICITY AND MAGNETISM
163
Poisson and magnetic units
164
Gauss and absolute units in magnetism
166
Ampère and analytical electrodynamics
168
Biot Savart Laplace and analytical electromagnetism
170
Wilhelm Weber and absolute electric current
171
Absolute units for electrical resistance and for electromotive force
172
The concept of energy in electricity
175
The proliferation of unit systems in electromagnetism
177
The British Association standards
179
The practical system of electrical units
183
The Giorgi system and the Systèms International
184
DIMENSIONAL ANALYSIS AND THE QUANTITY CALCULUS
188
The dimensional analysis of Fourier
191
Gauge invariance conversion factors dimensions
193
The quantity calculus
197
Webers base calculus
200
Maxwells dimensional analysis
202
Multiple ambiguity
205
DIMENSIONAL EXPLORATION
208
The optimum number of base quantities
214
Dimensionless quantities
215
The status of dimensional theory
217
INTERPRETING THE ALGEBRA OF PHYSICS
219
Formal algebra and formal arithmetic in modern physics
221
Debates over the quantity calculus
224
A symbolic mimicry of nature?
229
Conclusion
236
UNITS IN THE SYSTÈME INTERNATIONAL
237
A coherent system of measurement
238
Notes
240
Bibliography
282
Index
308
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Roche, Linacre College, Oxford, UK.

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