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Fundamental Formulas of Physics (Volume-2) written by
Donald H. Menzel , Harvard College Observatory, Cambridge, Mass.
A survey of physical scientists, made several years ago, indicated the need for a comprehensive reference book on the fundamental formulas of mathematical physics. Such a book, the survey showed, should be broad, covering, in addition to basic physics, certain cross-field disciplines where physics touches upon chemistry, astronomy, meteorology, biology, and electronics.
The present volume represents an attempt to fill the indicated need. I am deeply indebted to the individual authors, who have contributed time and effort to select and assemble formulas within their special fields. Each author has had full freedom to organize his material in a form most suitable for the subject matter covered. In consequence, the styles and modes of presentation exhibit wide variety. Some authors considered a mere listing of the basic formulas as giving ample coverage. Others felt the necessity of adding appreciable explanatory text.
Fundamental Formulas of Physics (Volume-2) written by
Donald H. Menzel
cover the following topics.
16: GEOMETRICAL OPTICS by James G. Baker
1. GENERAL CONSIDERATIONS
1.1. Geometrical optics and wave optics
1.2. Media
1.3. Index of refraction
1.4. Interfaces
1.5. Refraction and reflection. The Fresnel formulas
1.6. Optical path and optical length
1.7. Fermat's principle
1.8. Cartesian surfaces and the theorem of Malus
1.9. Laws of reflection.
1.10. Laws of refraction
1.11. The fundamental laws of geometrical optics
1.12. Corollaries of the laws of reflection and refraction
1.13. Internal reflection and Snell's law
1.14. Dispersion at a refraction
1.15. Deviation
2. THE CBARACTERISTIC FUNCTION OF HAMILTON (EIKONAL OF BRUNS)
2.1. The point characteristic, V
2.2. The mixed characteristic, W
2.3. The angle characteristic, T
2.4. The sine condition of Abbe
2.5. Clausius' equation
2.6. Heterogeneous isotropic media
2.7. Collineation
3. FIRST ORDER RELATIONSHIPS
3.1. Conventions
3.2. Refraction at a single surface
3.3. Focal points and focal lengths
3.4. Image formation
3.5. Lagrange's law
3.6. Principal planes
3.7. Nodal points
3.8. Cardinal points
3.9. The thin lens
3.10. The thick lens
3.11. Separated thin lenses
3.12. Chromatic aberration
3.13. Secondary spectrum
3.14. Dispersion formulas
4. OBLIQUE REFRACTION
4.1. First-order theory
4.2. Oblique refraction of elementary pencils
4.3. The Seidel aberrations
4.4. The Seidel third-order expressions
4.5. Seidel's conditions in the SchwarzschildKohlschutter form
5. RAy-TRACING EQUATIONS
5.1. Meridional rays
5.2. Skew rays
17: PHYSICAL OPTICS by Francis A. Jenkins
1. PROPAGATION OF LIGHT IN FREE SPACE
1.1. Wave equation
1.2. Plane-polarized wave
1.3. Elliptically polarized wave
1.4. Poynting vector
1.5. Intensity
1.6. Partially polarized light
1.7. Light quant
2. INTERFERENCE
2.1. Two beams of light
2.2. Double-source experiments
2.3. Fringes of equal inclination
2.4. Fringes of equal thickness
2.5. Michelson interferometer
2.6. Fabry-Perot interferometer
2.7. Lummer-Gehrcke plate
2.8. Diffraction grating
2.9. Echelon grating
2.10. Low-reflection coatings
3. DIFFRACTION
3.1. Fraunhofer diffraction by a rectangular aperture
3.2. Chromatic resolving power of prisms and gratings
3.3. Fraunhofer diffraction by a circular aperture
3.4. Resolving power of a telescope
3.5. Resolving power of a microscope
3.6. Fraunhofer diffraction by N equidistant slits
3.7. Diffraction of x rays by crystals
3.8. Kirchhoff's formulation of Huygens' principle
3.9. Fresnel half-period zones
3.10. Fresnel integrals
4. EMISSION AND ABSORPTION
4.1. Kirchhoff's law of radiation
4.2. Blackbody radiation laws
4.3. Exponential law of absorption
4.4. Bohr's frequency condition
4.5. Intensities of spectral lines
5. REFLECTION
5.1. Fresnel's equations
5.2. Stokes' amplitude rela-tions
5.3. Reflectance of dielectrics
5.4. Azimuth of reflected plane-polarized light
5.5. Transmittance of dielectries
5.6. Polarization by a pile of plates
5.7. Phase change at total internal reflection
5.8. Fresnel's rhomb
5.9. Penetration into the rare medium in total reflection
5.10. Electrical and optical constants of metals
5.11. Reflectance of metals
5.12. Phase changes and azimuth for metals
5.13. Determination of the optical constants
6. SCATTERING AND DISPERSION
6.1. Dipole scattering
6.2. Rayleigh scattering formula
6.3. Thomson scattering formula
6.4. Scattering by dielectric spheres.
6.5. Scattering by absorbing spheres
6.6. Scattering and refractive index
6.7. Refractivity
6.8. Dispersion of gases
6.9. Dispersion of solids and liquied
6.10. Dispersion of metals
6.11. Quantum theory of disspheres
7. CRYSTAL OPTICS
7.1. Principal dielectric constants and refractive indices
7.2. Normal ellipsoid
7.3. Normal velocity surface
7.4. Ray velocity surface
7.5. Directions of the axes
7.6. Production and analysis of elliptically polarized light
7.7. Interference of polarized light
7.8. Rotation of the plane of polarization
8. MAGNETO-OPTICS AND ELECTRO-OPTICS
8.1. Normal Zeeman effect.
8.2. Anomalous Zeeman effect
8.3. Quadratic Zeeman effect
8.4. Faraday effect.
8.5. Cotton-Mouton effect
8.6. Stark effect
8.7. Kerr electro-optic effect
9. OPTICS OF MOVING BODIES
9.1. Doppler effect
9.2. Astronomical aberration
9.3. Fresnel dragging coefficient
9.4. Michelson - Morley experiment
18: ELECTRON OPTICS by Edward G. Ramberg
1. GENERAL LAWS OF ELECTRON OPTICS
1.1. Fermat's principle for electron optics.
1.2. Index of refraction of electron optics.
1.3. Law of Helmholtz-Lagrange for axially symmetric fields.
1.4. Upper limit to the CUTrent densityj in a beam cross section at potential and with aperture angle alpha"'
1.5. General lens equation
2. AXIALLY SYMMETRIC FIELDS CONTENTS
2.1. Differential equations of the axially symmetric fields in free space
2.2. Potential distribution in axially symmetric electric field
2.3. Behavior of equipotential surfaces on axis
2.4. Magnetic vector potential in axially symmetric field
2.5. Field distribution in axially symmetric magnetic field
3. SPECIFIC AxIALLY SYMMETRIC FIELDS
3.1. Electric field
3.2. Electric field
3.3. Magnetic field
3.4. Magnetic field
4. PATH EQUATION IN AxIALLY SYMMETRIC FIELD
4.1. General path equation in axially symmetric field.
5. PARAXIAL PATH EQUATIONS
5.1. General paraxial path equation.
5.2. Azimuth of electron.
5.3. Paraxial path equation for path crossing axis
5.4. Paraxial ray equation for variable R = r 5.5. Paraxial ray equation in electric field for variable c = -r'/r
5.6. Paraxial ray equation in electric field for variableb = -r,/r+ 1(2z)
5.7. Paraxial ray equation in electric field for arbitrarily high voltage
6. ELECTRON PATHS IN UNIFORM FIELDS
6.1. Path in uniform electrostatic field-6.2. Path in uniform 'magnetic field.
6.3. Path in crossed electric and magnetic field.
7. FOCAL LENGTHS OF WEAK LENSES
7.1. General formula for focal length of a weak lens
7.2. Focal length of aperture lens
7.3. Focal length of electric field between coaxial cylinders
7.4. Focal length of magnetic field ofsingle wire loop
7.5. Focal length of magnetic gap lens
7.6. Focal length of lens consisting of two apertures at potentia! 8. CARDINAL POINTS OF STRONG LENSES
8.1. Strong lens
8.2. Uniform magnetic field, cut Z= off ±d sharply at
8.3. "Bell-shaped" magnetic field
8.4. Electric field (J) = me (4/V3}k arc tan z/d
9. ELECTRON MIRRORS
9.1. Paraxial ray equations
9.2. Displacement of electron
9.3. Approximate formula for focal length of an electron mirror
10. ABERRATIONS
10.1. Geometric aberrations of the third order
10.2. Chromatic aberrations. 445
10.3. General formula for aperture defect
lO.4. Aperture defect of weak lens
10.5. Aperture defect of bellshaped magnetic field
10.6. Aperture defect of uniform magnetic and electric field
10.7. Aperture defect of uniform electric field of length I
10.8. Chromatic aberration of weak unipotential electrostatic lens
10.9. Chromatic aberration of a magnetic lens for large magnification
10.10. Chromatic aberration of uniform magnetic and electric field
10.11. Relativistic aberration of weak electrostatic unipotential lens
11. SYMMETRICAL Two-DIMENSIONAL FIELDS
11.1. Field distributions
11.2. Paraxial path equation in electric field
11.3. Paraxial path equations in magnetic field
1104. Focal length of weak electric cylinder lens
11.5. Focal length of weak slit lens
11.6. Focal length and displacement of focal point in z direction for weak magnetic cylinder lens
12. DEFLECTING FIELDS
12.1. Field distribution in two-dimensional deflecting fields
12.2. Deflection by electric field for electron incident in midplane
12.3. Deflection by magnetic field of length I
19; ATOMIC SPECTRA by Charlotte E. Moore
1. THE BOHR FREQUENCY RELATION
1.1. Basic combination principle
2. SERIES FORMULAS
2.1. The Rydberg equation
2.2. The Ritz combination principle
2.3. The Ritz formula
2.4. The Hicks formula
3. THE SOMMERFELD FINE STRUCTURE CONSTANT FOR HYDROGENLIKE SPECTRA
3.1. Energy states
4. COUPLING
4.1. LS or Russel-Saunders coupling
5. LINE INTENSITIES
5.1. Doublets
6. THEORETICAL ZEEMAN PATTERNS
6.1. Lande splitting factor
6.2. The Paschen-Back effect
6.3. Pauli's g-sum rule
7. NUCLEAR MAGNETIC MOMENTS
7.1. Hyperfine structure
8. FORMULAS FOR THE REFRACTION AND DISPERSION OF AIR FOR THE VISIBLE SPECTRUM
8.1. Meggers' and Peters' formula
8.2. Perard's equation
8.3. The formula of Barrell and Sears.
20: MOLECULAR SPECTRA by L. Herzberg and G. Herzberg
1. GENERAL REMARKS
2. ROTATION AND ROTATION SPECTRA
2.1. Diatomic and linear polyatomic molecules
2.2. Symmetric top molecules
2.3. Spherical top molecules
2.4. Asymmetric top molecules
2.5. Effect of external fields
2.6. Hyperfine structure
3. VIBRATION AND VIBRATION SPECTRA
3.1. Diatomic molecules
3.2. Polyatomic molecules
4. INTERACTION OF ROTATIbN AND VIBRATION: ROTATION-VIBRATION SPECTRA
4.1. Diatomic molecules
4.2. Linear polyatomic molecules
4.3. Symmetric top molecules
4.4. Spherical top molecules
4.5. Asymmetric top molecules
4.6. Molecules with internal rotation
5. ELECTRONIC STATES AND ELECTRONIC TRANSITIONS
5.1. Total energy and electronic energy
5.2. Interaction of rotation and electronic motion in diatomic and linear polyatomic molecules
5.3. Selection rules and spectrum
21: QUANTUM MECHANICS by L. 1. Schiff
1. EQUATIONS OF QUANTUM MECHANICS
1.1. Old quantum theory
1.2. Uncertainty principle
1.3. Schrodinger wave equation
104. Special solutions of the Schrodinger equation for bound states
1.5. Solutions of the Schrodinger equation for collision problems
1.6. Perturbation methods
1.7. Other approximation methods
1.8. Matrices III quantum mechanics
1.9. Many-particle systems
1.10. Spin angular momentum
1.11. Some radiation formulas
1.12. Relativistic wave equations
22: NUCLEAR THEORy by M. E. Rose
1. TABLE OF SYMBOLS
2. NUCLEAR THEORY
2.1. Nuclear masses and stability
2.2. Stationary state properties
2.3. Nuclear interactions
2.4. Properties ofthe deuteron
2.5. Potential scattering
2.6. Resonance reactions
2.7. Beta decay
23: COSMIC RAYS AND HIGH-ENERGY PHENOMENA by Robert W. Williams
1. ELECTROMAGNETIC INTERACTIONS
1.1. Definitions and some natural constants
1.2. Cross sections for the collision of charged particles with atomic electrons, considered free
1.3. Energy loss by collision with atomic electrons
1.4. Range of heavy particles
1.5. Specific ionization
1.6. Cross sections for emisstion of radiation by charged particles
1.7. Energy loss of electrons by radiation.
1.8. Cross sections for scatastering of charged particles
1.9. Scattering of charged particles in matter
l.l0. Compton effect
1.11. Pair production
2. SHOWER THEORY
2.1. Definitions
2.2. Track lengths
2.3. Integral spectrum
2.4. Properties of the shower maxima.
2.5. Stationary solutions,
2.6. Lateral and angular spread ofshowers
3. NUCLEAR INTERACTIONS
3.1. Nuclear radius and transparency
3.2. Altitude variation of nuclear interactions: gross transformation.
4. MESON PRODUCTION
4.1. Threshold energies
4.2. Relativity transformations
5. MESON DECAY
5.1. Distance of flight
5.2. Energy distribution of decay products
5.3. Angular distribution in two-photon decay
6. GEOMAGNETIC EFFECTS
6.1. Motion in static magnetic fields
6.2. Flux of particles in static magnetic fields
6.3. Limiting momenta on the earth's surface
24: PARTICLE ACCELERATORS by Leslie L. Foldy
1. GENERAL DESCRIPTION AND CLASSIFICATION OF HIGH-ENERGY PARTICLE ACCELERATORS
1.1. General description
1.2. Classification according particle accelerated
1.3. Classification according to particle trajectories
1.4. Designation of acceleratotors
1.5. Basic components
2. DYNAMIC RELATIONS FOR ACCELERATED PARTICLES
2.1. Fundamental relativistic relations.
2.2. Derived relations
2.3. Nonrelativistic relations
2.4. Units
3. AGNETIC GUIDING FIELDS
3.1. Specification of magnetic guiding fields
3.2. Force on a charged particle in a magnetic field
3.3. Equations of motion of a charged particle In a magnetic guiding field
3.4. Equilibrium orbit
3.5. Stability of motion in the equilibrium orbit
3.6. Oscillations about the equilibrium orbit
3.7. Coupling of oscillations about the equilibrium orbit
3.8. Damping of radial and vertical oscillations.
4. PARTICLE ACCELERATION
4.1. Electrostatic and quasielectrostatic acceleration
4.2. Induction acceleration
4.3. Traveling wave acceleration
4.4. Impulsive acceleration.
5. PHASE STABILITY AND PHASE OSCILLATIONS
5.1. Phase stability.
5.2. Phase oscillations in circular accelerators
5.3. Phase motion in linear accelerators
6. INJECTION AND FOCUSING
7. ADDITIONAL REMARKS ABOUT SPECIAL ACCELERATORS
7.1. The conventional cyclotron
7.2. The betatron
7.3. The synchrotron
7.4. The synchrotron or fretronquency modulated cyclotron
7.5. Linear accelerators
25 : SOLID STATE by Conyers Herring
1. INTRODUCTION: CRYSTAL MATHEMATICS
1.1. Translations
1.2. The unit cell and the s sphere
1.3. The reciprocal lattice
1.4. Periodic boundary conditions
2. ELASTIC CONSTANTS
2.1. Stress and strain components
2.2. Elastic constants and moduli
2.3. Forms of Cij or Sij for some common crystal classes
2.4. Relation of elastic constants and moduli.
2.5. Forms taken by the condition of positive definiteness, for some common crystal classes
2.6. Relation of Ci; and Si; to other elastic constants
2.7. Thermodynamic Relation
3. DIELECTRICS AND PIEZOELECTRICITY
3.1. Piezoelectric constants.
3.2. Dielectric constants.
3.3. Pyroelectricity and the electrocaloric effect
3.4. Elastic constants of piezoelectric crystals.
3.5. Relations of adiabatic and isothermal piezoelectric and dielectric constants
4. CONDUCTION AND THERMOELECTRICITY
4.1. Conductivity tensor of a crystal
4.2. Matthiessen's rule
4.3. Thomson effect
4.4. Seebeck effect
4.5. Peltier effect
4.6. Entropy flow and Bridgman effect
4.7. Galvanomagnetic and thermomagnetic effects
5. SUPERCONDUCTIVITY
5.1. The London equations
5.2. Field distribution in a steady state
5.3. The energy equation
5.4. Critical field and its relation to entropy and specific heat
5.5. Equilibrium of normal and superconducting phases for systems of small dimensions
5.6. Multiply connected superconductors
5.7. General properties of ime-dependent disturbances in superconductors
5.8. A-c resistance of super conductors.
5.9. Optical constants of superconductors
6. ELECTROSTATICS OF IONIC LATTICES
6.1. Potential at a general point of space, by the method of Ewald
6.2. Potential acting on an ion, by the method of Ewald
6.3. Potential due to an infinite linear array, by the method of Madelung
6.4. Potential acting on an ion in a linear array, by the method of Madelung
6.5. Potential due to a plane array, by the method of Madelung
7. THERMAL VIBRATIONS
7.1. Normal modes of a crystal
7.2. Thermodynamic functions, general case "
7.3. Thermodynamic functions at high temperatures
7.4. Thermodynamic functions at low temperatures
7.5. Debye approximation .
7.6. Equation of state for a crystal.
7.7. Long wavelength optical modes of polar crystals
7.8. Residual rays
8. DISLOCATION THEORY
8.1. Characterization of dislocations.
8.2. Force on a dislocation
8.3. Elastic field of a dislocation in an isotropic medium
9. SEMICONDUCTORS
9.1. Bands and effective
9.2. Density of states .
9.3. Traps, donors, and "acceptors
9.4. The Fermi-Dirac distribution
9.5. Density of mobile charges .
9.6. Fermi level and density of mobile charges, intrinsic case
9.7. Fermi level and density of mobile charges, extrinsic case .
9.8. Mobility, conductivity, and diffusion
9.9. Hall effect
9.10. Thermoelectric effects.
9.11. Mean free time and mean free path
9.12. The space charge layer near a surface
9.13. Contact rectification "
9.14. Differential capacity of a metal-semiconductor contact
9.15. D-c behavior of p-n junctions
9.16. A-c behavior of p-n junctions
10. ELECTRON THEORY OF METALS
10.1. The Fermi-Dirac distribution
10.2. Averages of functions of the energy.
10.3. Energy and electronic specific heat
10.4. Spin paramagnetism
10.5. Bloch waves
10.6. Velocity and acceleration
10.7. Energy levels of almost free electrons
10.8. Coulomb energy
10.9. Exchange energy
10.10. Electrical and thermal
10.11. Orbital diamagnetism
10.12. Optical constants
11. MISCELLANEOUS
11.1. Specific heats at constress and strain
11.2. Magnetocaloric effect and magnetic cooling
11.3. The Cauchy relations .. traps
11.4. The Brillouin and Lanstant gevin functions
11.5. Relation of thermal release to capture of mobile charges by traps
26: THE THEORY OF MAGNETISM by J. H. Van Vleck
1. PARAMAGNETISM
1.1. Classical theory
1.2. Quantum theory
2. FERROMAGNETISM
2.1. Classical theory
2.2. Quantum theory.
2.3. Anisotropic effects
3. DIAMAGNETISM AND FEEBLE PARAMAGNETISM
3.1. Classical theory of diamagnetism.
3.2. Quantum theory of diamagnetism.
3.3. Feeble paramagnetism
27: PHYSICAL CHEMISTRY by Richard E. Powell
1. CHEMICAL EQUILIBRIUM
1.1. Equilibrium constant or "mass action law"
1.2. Equilibrium constant from calorimetric data
1.3. Equilibrium constant from electric cell vol tages
1.4. Pressure dependence of the equilibrium constant
1.5. Temperature dependence of the equilibrium constant
2. ACTIVITY COEFFICIENTS
2.1. The "thermodynamic" equilibrium constant
2.2. Thermodynamic interpretation of the activity coefficient
2.3. Activity coefficients of gases
2.4. Activity coefficient from the "law of corresponding states"
2.5. Activity coefficients of nonelectrolvtes in solution
2.6. The Gibbs-Duhem equation
2.7. The enthalpy of nonideal solutions.
2.8. The entropy of nonideal solutions.
2.9. The activity coefficients of aqueous electrolytes
2.10. The Debye-Hlickel equation
3. CHANGES OF STATE
3.1. Phase rule 650
3.2. One component, solidsolid and solid-liquid transitions
3.3. One component, solidgas and liquid-gas transitions
3.4. Two components, solidliquid transition
3.5. Two components, liquid vapor transition
3.6. Liquid transition
3.7. Osmotic pressure
3.8. Gibbs-Donnan membrane equilibrium
4. SURFACE PHENOMENA
4.1. Surface tension
4.2. Experimental measurement ofsurface tension
4.3. Kelvin equation
4.4. Temperature dependence of surface tension
4.5. Insoluble films on liquids
4.6. Adsorption on solids.
4.7. Excess concentration at the surface.
4.8. Surface tension of aqueous electrolytes.
4.9. Surface tension of binary solutions.
5. REACTION KINETICS
5.1. The rate law of a reaction
5.2. Integrated forms of the rate law
5.3. Half-lives
5.4. Integrated form of rate law with several factors
5.5. Consecutive reactions.
5.6. Multiple-hit processes.
5.7. Reversible reactions
5.8. The specific rate: collision theory
5.9. The specific rate: activated complex theory
5.10. Activity coefficients 1Il reaction kinetics
5.11. Heterogeneous catalysis
5.12. Enzymatic reactions
5.13. Photochemistry
5.14. Photochemistry in intermittent light.
657
6. TRANSPORT PHENOMENA IN THE LIQUID PHASE
6.1. Viscosity: definition and measurement
6.2. Diffusion: definition and measurement
6.3. Equivalent conductivity: definition andmeasurement
6.4. Viscosity of mixtures.
6.5. Diffusion coefficient of mixtures.
6.6. Dependence of conductivity on concentration
6.7. Temperature dependence of viscosity, diffusion and conductivity.
28: BASIC FORMULAS OF ASTROPHYSICS by Lawrence H. Aller
1. FORMULAS DERIVED FROM STATISTICAL MECHANICS
1.1. Boltzmann formula.
1.2. Ionization formula
1.3. Combined ionization and Boltzmann formula
1.4. Dissociation equation for diatomic molecules.
2. FORMULAS CONNECTED WITH ABSORPTION AND EMISSION OF RADIATION
2.1. Definitions
2.2. Specific intensity
2.3. Einstein's coefficients
2.4. Oscillator strength
2.5. Absorption coefficients
2.6. Line strengths
2.7. Definition ofi-values for the continuum
3. RELATION BETWEEN MASS, LUMINOSITY, RADII, AND TEMPERATURE OF STARS
3.1. Absolute magnitude
3.2. Color index
3.3. Mass-luminosity law
3.4. The equation of transfer for gray material
3.5. Non-gray material
3.6. Model atmosphere In hydrostatic equilibrium
3.7. Formation of absorption lines
3.8. Curve of growth
3.9. Equations governing the equilibrium of a star
3.10. Boundary conditions
3.11. Theoretical form of mass-luminosity law
29: CELESTIAL MECHANICS by Edgar W. Woolard
1. GRAVITATIONAL FORCES
2. UNDISTURBED MOTION
2.1. Elliptic motion
2.2. Parabolic motion
2.3. Hyperbolic and nearly parabolic motion
2.4. Relativity correction.
3. DISTURBED MOTION
3.1. The disturbing function
3.2. Variations ofthe elements
3.3. Perturbations of the coordinates
3.4. Mean orbit of the earth
3.5. Mean orbit of the moon
3.6. Mass of a planet from the mean orbit of a satellite.
4. THE ROTATION OF THE EARTH
4.1. Poisson's equations.
4.2. The Eulerian nutation.
30: METEOROLOGY by Richard A. Craig
1. BASIC EQUATIONS FOR LARGE-SCALE FLOW
1.1. The hydrodynamic equation of motion
1.2. Conservation of mass
1.3. Equation of state
1.4. First law of thermodynamICS
2. DERIVED EQUATIONS
2.1. Geostrophic wind
2.2. Hydrostatic equation
2.3. Adiabatic lapse rate.
2.4. The circulation theorem
2.5. The vorticity theorem.
2.6. The energy equation.
2.7. The tendency equation
2.8. Atmospheric turbulence
31 BIOPHYSICS by John M. Reiner
1. INTRODUCTION: ENERGY RELATIONS
2. KINETICS OF ENZYME CATALYZED REACTIONS
2.1. Simple reactions
2.2. Inhibitors
3. THE CELL
3.1. Metabolism and concentration distributions
3.2. Diffusion forces and cell division
3.3. Cell polarity and its maintenance
3.4. Cell permeability
4. THE NEURONE AND BEHAVIOR
4.1. Excitation and conduction in the neurone.
4.2. Behavior and structure of central nervous system
5. THE EVOLUTION AND INTERACTION OF POPULATIONS
5.1. The general laws of populations.
5.2. Equations of biological populations
5.3. Simple populations; fect of wastes, nutriment, and space
5.4. Interaction of two species
5.5. Embryonic growth
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