History of the Math

The potter's wheel — inertia smooths intermittent power.

Law of the lever proven from first principles.

Law of the lever — moment as force times arm.

Areas and volumes of curved figures — the segment's ancestry (circa).

Volume of the cylinder — the formula, permanently (circa).

Chord tables lock in the 360° Babylonian circle.

Antikythera mechanism — geared ratios compute the heavens.

Friction laws found experimentally — and left in notebooks.

Observes the area–velocity trade in channels (circa).

'Nova Scientia' — 45° named the range-maximizing elevation.

Chip log described — speed counted in literal knots.

Isochronism of small swings observed.

Describes real-image formation and the converging-lens telescope in Dioptrice.

Publishes the first logarithm tables — the mathematical machinery under every dB.

Logarithms — the machinery.

Logarithms — arithmetic for multiplicative quantities.

Nova stereometria — wine-barrel gauging done with proto-calculus.

Third law: T² ∝ r³.

States Q = A·V — continuity as a law.

Poses the cantilever strength problem in Two New Sciences — brilliantly, and wrongly.

Projectile path proven parabolic.

The cantilever problem posed — beam strength becomes science.

Air resistance identified as why falling bodies differ.

Mercury barometer — pressure measured as a column height.

The barometer — pressure measured as fluid height.

Efflux law — the √ in the formula.

Puy de Dôme experiment proves pressure falls with altitude.

Puy de Dôme experiment: pressure falls with altitude.

Pressure transmits equally in a confined fluid.

Pendulum clock — timekeeping improves a hundredfold.

P·V constant at fixed temperature.

PV = constant at fixed temperature.

Compound pendulum solved — rotational inertia in practice.

First demonstration that light has a finite speed, from Jupiter's moons.

'Ut tensio, sic vis' — the linear spring law published.

Linear elasticity — 'ut tensio, sic vis'.

The linear spring — the oscillator's restoring force.

Vis viva — motion's measure proportional to v².

Theorem of moments — lever law becomes general statics.

Principia adds drag — and takes the parabola away.

First theoretical sound speed (air) in the Principia.

Principia — resistance proportional to V².

V² drag regime quantified.

Orbits derived from gravitation; the cannonball argument.

The cannonball argument defines escape.

Principia embeds moments in the laws of motion.

Publishes the iterative root-finding method later paired with Newton's name.

Links beam curvature to bending moment.

Friction laws published: load-proportional, area-independent.

231 in³ wine gallon — ancestor of the US gallon.

231 in³ wine gallon — still the US gallon.

First recorded sign test, comparing yearly counts of male vs. female births.

Neutral axis located correctly.

Identifies the natural (radian) measure of angle.

Reproducible mercury thermometers and the °F scale.

Gridiron pendulum cancels expansion with brass against steel.

Early quantified ventilation — air per occupant (circa).

The pitot tube measures flow by its dynamic pressure.

Derives the normal curve as the limit of the binomial distribution.

Hydrodynamica — ½ρV² enters the pressure budget.

Hydrodynamica — the pressure-velocity-height budget.

Pressure-to-velocity budget underpinning the meter.

Hydrodynamica — head, velocity, and pressure unified.

Hydrodynamica establishes the pressure–velocity trade that orifice metering exploits.

'Institutions de Physique' unites theory with the clay-ball experiments.

Centigrade scale proposed (inverted; flipped by 1745).

Critical buckling load derived via calculus of variations.

Publishes the elastica — the beam curvature theory under every deflection formula here.

The Leyden jar — first capacitor, discovered twice.

The Leyden jar — capacitive energy storage.

Circular-function machinery — ω = 2πf.

e and the exponential function formalized.

Formalizes compound-interest and annuity series in Introductio in analysin infinitorum.

The Euler–Bernoulli beam equation — the math under this card.

Charge conservation analysis of the jar.

Involute tooth profile analyzed — the modern gear tooth.

Euler's turbomachine equation.

Turbomachine equation — pumps deliver head, not pressure (circa).

Hydraulic lime identified for the Eddystone Lighthouse — modern concrete's starting gun.

Equations of compressible fluid motion.

Continuity embedded in the general flow equations.

The equation in its modern form.

Specific and latent heat distinguished (circa).

'Moment of inertia' defined; rigid-body dynamics founded.

Vena contracta explains C_d ≈ 0.61.

First slope–radius channel formula (circa).

Wedge theory of earth pressure — soil mechanics begins.

Crank-and-flywheel patent turns steam strokes into rotation.

Measures V–I proportionality using shocks to his own body; never publishes.

Systematic dilatometer measurements of expansion coefficients.

Horsepower defined — pumping becomes a priced commodity.

Introduces the transform in work on probability — the s-domain is born.

Defines the horsepower to price steam engines against horses.

Defines the horsepower to sell steam engines against horses.

Torsion of wires quantified — the torsion balance.

Static vs kinetic friction; the engineering model completed.

Sound velocities in solids from resonating rods and plates.

'Mécanique analytique' — virtual work subsumes the lever.

Conservation of mass — the bookkeeping behind dilution.

Metre defined from the Earth's meridian.

Gradian — the right angle decimalized to 100.

Hydraulic press patented — force multiplication by area.

The metre — the metric flow units' ancestor.

Litre defined as the cubic decimeter.

'Dark stars' — escape velocity meets light speed (circa).

The converging-diverging meter principle.

First parachute descent from a balloon.

Constricted-tube effect behind flow metering.

Cannon-boring: friction makes heat without limit.

Platinum Mètre des Archives deposited.

Kilogramme des Archives — the kilogram realized.

The voltaic pile — the first battery.

The pile — cells in series, the first battery.

Voltaic pile demonstrates dissimilar-metal EMF — and dissolution of the anode.

Discovers infrared radiation with a thermometer past the red end of a prism spectrum.

Flat-belt line shafting becomes the standard factory transmission.

Volume–temperature law.

Volume–temperature law published (crediting Charles).

Partial pressures and the saturation curve of water vapor.

Early experiments on conduction in bars (circa).

The barometric formula — pressure vs. height, mathematically.

Elastic modulus defined as a material property.

Times sound racing through an iron water main vs air.

Formalizes the distribution for measurement error in Theoria Motus.

Central limit theorem explains why so many things go normal.

Equal volumes, equal molecules — n enters the equation.

Molar volume concept — density becomes PM/RT.

Early derivation of rocket motion — forgotten for a century.

Reversible pendulum measures g with precision.

Zone construction in the prize memoir on diffraction.

'Principles of Carpentry' — section design for practitioners.

Macadam road construction — engineered aggregate layers (circa).

Elementary Principles of Carpentry rationalizes iron-strengthened timber construction.

Prony brake — the first practical shaft-power dynamometer.

The stress tensor — stress made rigorous.

Théorie analytique de la chaleur — heat flow proportional to ΔT.

Théorie analytique de la chaleur — the law and the series.

Publishes the conduction law that makes thermal resistances add in series.

Establishes that periodic signals decompose into harmonic components.

Imperial gallon defined — the US/imperial fork is permanent.

Patents Portland cement.

Volumetric analysis; the burette and pipette named (circa).

Fits sacrificial iron/zinc anodes to Royal Navy copper hulls.

Establishes the maximum efficiency bound any heat cycle can approach.

Publishes the reversible-cycle argument that efficiency depends only on reservoir temperatures.

Establishes the temperature-only limit on cycle efficiency — the Carnot COP.

Establishes the reversible-cycle temperature limit on heat-to-work conversion.

Analyzes the reversible heat-engine cycle underpinning entropy.

Turns beam theory into usable engineering design formulas.

Linear bending theory: σ = M·c/I.

Publishes Die galvanische Kette — V = IR, to initial ridicule.

V = IR — the law the divider applies twice.

Resistance defined — the quantity being combined.

Die galvanische Kette — V = IR.

Work defined; the ½mv² form fixed.

Electromagnetic induction — the transformer's physics.

Self-induction discovered (the henry remembers him).

Invents the four-arm bridge circuit.

Exact thick-cylinder stress solution published.

Negative temperature coefficient observed in Ag₂S — the first semiconductor effect.

Observes the temperature-dependent resistance of silver sulfide — the first recorded thermistor behavior.

Geometric picture of free rotation — the inertia ellipsoid.

Combined ideal gas equation PV = nRT.

Combines the laws into PV = nRT.

Recasts Carnot's cycle in analytic P–V form, reviving the idea.

Patents a working vapor-compression refrigeration machine.

Describes the diffraction disk that sets the physical resolution limit.

Derives the circular-aperture diffraction pattern and its central disk.

Dielectrics and the measure of capacitance.

Derive compressible orifice flow and discover the mass-flow ceiling below the critical pressure ratio.

Maximum power transfer theorem — why matching matters.

Wrought-iron flitch girders become standard practice for long floor spans.

Quantifies electrical heating — the P = VI power relation.

Awards Ohm the Copley Medal; the law finally sticks.

I²R heating — the physical meaning of RMS.

'Principles of Mechanism' systematizes gear-train kinematics.

Formalizes paraxial optics and cardinal points in Dioptrische Untersuchungen.

Proposes the frequency shift of moving sources.

States the mechanical equivalent of heat.

Bakerian Lecture popularizes the bridge (crediting Christie).

Falling-weight experiments price mechanical energy in heat.

Paddle-wheel experiments price heat in work, refined through 1850.

Mechanical equivalent of heat — energy accounting unified.

The Magnus saturation-vapor-pressure formula.

Circuit laws, published at age 21, formalize series-parallel analysis.

Current law — why parallel conductances add.

Confirms it with musicians on a moving train.

Modern head-loss equation with f.

Precision gas-density measurements (circa).

Head-loss equation in the modern f·(L/D)·V²/2g form.

Hydraulic crane launches industrial fluid power.

Conservation of energy stated in full generality.

Absolute thermodynamic temperature scale.

Bourdon-tube gauge puts a pressure dial on every boiler.

Patents the Bourdon-tube pressure gauge, the basis of dial gauge grading.

The term 'kinetic energy' coined.

Formalizes the energy equation that links thermal and kinetic energy in a flow.

Induction coil — stored magnetic energy as a product.

Pendulum demonstrates the Earth's rotation.

Viscous-flow theory — the µ in the denominator.

Curved-vane impeller shows efficiency is design, not luck.

Defines the absolute temperature scale that puts T in the efficiency ratio.

Describes running a heat engine in reverse to heat buildings — the heat pump concept.

Licenses Bourdon's design in the US, spreading the mechanical gauge industry.

Predicts LC oscillation mathematically.

The term 'potential energy' coined.

LC oscillation predicted — the reactive tug-of-war.

RC law of the telegraph cable — the time constant's debut.

RC transient law from telegraph cable theory.

General torsion theory; circular-section formula's limits mapped.

Builds an early industrial heat-pump evaporator for salt drying.

Discovers resistance changes with strain.

Dijon experiments make roughness part of the law.

Stress-state earth pressure theory; Ka in closed form.

Brown & Sharpe gauge — the geometric series adopted as AWG.

AWG standardizes the copper in the denominator.

Dijon experiments make wall roughness part of the friction law.

Early analysis of pipe-surge pressure (circa).

Proposes a CO₂ concentration limit — the first quantitative ventilation dilution target.

Formalizes matrix algebra and the characteristic equation.

Rechargeable lead-acid cell.

Photographs oscillatory spark discharge — theory confirmed.

Fahrenheit-sized absolute scale for engineering.

Lead-acid rechargeable cell; the 12 V series string to come.

Defines the blackbody and proves its spectrum is a universal function of temperature alone.

Publishes the vapor-cycle analysis in his steam-engine manual.

Manual of the Steam Engine treats expansion curves of the form PVⁿ = constant.

Double bridge extends null measurement to milliohms.

Four-terminal (Kelvin) sensing removes lead error.

Field equations predict EM waves at the speed of light.

Deadliest US maritime disaster — steam's cost made plain.

Formalizes entropy, giving the isentropic turbine/pump steps their footing.

Introduces entropy, grounding the Carnot bound in the second law.

Names entropy and formalizes dS = dQ_rev/T.

Introduces momentum theory for the marine screw propeller.

Proposes the 2/3-power law.

Patents wire-reinforced concrete — planters first, structures soon after.

Reinforced concrete patented — steel goes into the pour.

Publishes systematic rotating-bending fatigue data from railway-axle testing — the first S-N curves.

Rotating-bending axle tests establish the S-N curve and the role of stress amplitude.

Publishes the empirical 4.56"/inch double-star splitting limit.

'On Governors' launches the analytic study of feedback stability.

Whirling speed identified — and supercritical running wrongly forbidden.

Shock jump conditions from thermodynamics.

Field-energy formulation — ½LI² formalized.

Coins 'radian' at Queen's College Belfast.

Defines numerical aperture and links it to resolution in the microscope.

Fits a parabolic mean-stress relation to Wöhler's data.

First documents that acid-charged iron loses ductility and recovers after baking.

Dimensionless resistance coefficient (circa).

Builds practical ammonia refrigeration plants, launching industrial cooling.

Casts entropy into state-property relations for gases and mixtures.

'Theory of Sound' founds engineering vibration analysis.

Preferred-number series — geometric sizing of standard parts.

Homogeneous immersion objectives push NA above 1.0 using oil.

Finds total emission scales as T⁴; Boltzmann derives it thermodynamically in 1884.

Formalizes the θ = 1.22·λ/D diffraction resolution criterion.

States the resolution criterion using the first Airy null.

Coaxial cable patented.

Coaxial line patented.

Coins 'hysteresis' and maps the B-H loop that stores the loss.

Equivalent-circuit theorem — the divider's output impedance.

Skin effect derived for spherical conductors.

Dye-filament experiment finds the transition criterion.

Manganin — the near-zero-tempco resistance alloy.

Energy flux of the EM field — S itself.

Coins 'torque' for twisting effort in machinery.

Twisted rebar patent; reinforced concrete becomes buildable in America.

Twisted rebar patent — mechanical bond by geometry.

Temperature dependence of equilibrium — the exponential form.

Operational circuit analysis normalizes the conductance view.

Operational calculus makes filter math tractable.

Transmission-line theory — reflections quantified.

General conductor case; the effect named and tamed.

Closed-core practical transformer.

Cone clutch on the first automobiles.

Publish presumptive allowable bearing tables for footing design.

Names and formalizes inductance; reactive behavior theorized.

AC distribution demo at Great Barrington — the grid begins.

Coins 'impedance' for AC opposition.

Generates and measures radio waves — λf = c confirmed on a lab bench.

Transmission-line theory explains velocity factor in cables.

Resonant circuits generate and detect radio waves.

AC resistance of practical conductors quantified.

Measures EM oscillation periods experimentally.

The dipole — the first antenna.

Independent derivation — the Rankine-Hugoniot relations.

Schlieren photograph of a bullet's shock wave.

Photographs supersonic shock waves; identifies the speed ratio.

Commercial venturi meter for waterworks.

Commercial venturi meter — flow becomes a billable number.

Photographs shock waves; the sonic ratio gets its physics.

Ionic dissociation theory — concentration becomes physical chemistry.

The dipole — radio's first and reference antenna.

Develops the 1:4 trapezoidal weir to eliminate end-contraction correction.

Coins 'polytropic' in Technische Thermodynamik, unifying isothermal and adiabatic as special cases.

Establishes the platinum resistance thermometer and its quadratic R–t fit.

The converging–diverging nozzle goes supersonic.

Adds the diverging section — the convergent-divergent nozzle — to drive steam turbines supersonic.

The watt adopted as the unit of power, honoring Watt.

Tangent-modulus theory extends buckling past the elastic range.

Runs turbine shafts above critical on flexible spindles.

Presents the formula that takes his name.

The joule named in Joule's honor.

The watt named as the unit of power.

Activation energy and the rate equation.

Refines the actuator-disk model; induced velocity splits half fore and half aft.

First energy solution for buckling of a simply supported plate in compression.

AC instrument era forces peak-vs-RMS bookkeeping.

Monolithic reinforced-concrete frame system — column, beam, and slab as one.

Operational calculus for circuit transients; the value theorems in embryonic form.

Publishes 'On the Law of Hysteresis' — loss per cycle ∝ B^1.6.

Acquires Eickemeyer's firm to bring Steinmetz and his hysteresis work in-house.

Complex/phasor method tames AC calculation.

Portable precision instruments make shunt measurement standard practice.

Complex phasor method — reactance becomes arithmetic.

US customary units legally defined from the meter.

'Impedance' paper — complex Z formalized.

Phasor method makes RLC arithmetic routine.

Displacement law — λ_peak·T is constant, the 2898 µm·K rule.

Empirical formula for critical speeds of loaded shafts.

Argon discovered from a 0.5% density anomaly.

Founded, formalizing heating and ventilating engineering practice in the US.

Builds the first cavitation tunnel to study propeller bubble collapse on Turbinia.

AC power transmission wins; RMS becomes the lingua franca.

Invar discovered — near-zero expansion alloy.

Radioactivity discovered in uranium salts.

Publishes the radiation distribution law that yields the exponential band approximation.

Capacity vs. discharge-rate law.

Patents syntonic (tuned) wireless telegraphy.

Propeller cavitation discovered at sea; first cavitation tunnel.

First NEC — wire size becomes a safety regulation, circa.

First NEC; drop guidance enters wiring practice, circa.

ΔP = ρ·a·Δv established on Moscow's mains.

Proposes measuring impact energy of metals with a swinging pendulum.

Cosine-bell smoothing later formalized as the Hann window.

Publishes the linear σₐ–σₘ trade-off in Mechanics Applied to Engineering.

Patents the hollow-block molding machine — the CMU is born.

Demonstrates the ball-indentation hardness test at the Paris Exposition.

Presents the quantized radiation law that fits Rubens and Kurlbaum's cavity data at all wavelengths.

Publishes the χ² goodness-of-fit test in the Philosophical Magazine.

f-stop scale standardized in √2 steps for exposure control.

Transatlantic radio makes path loss an engineering question.

Over-the-horizon mystery starts propagation science.

Wind-tunnel lift measurements replace bad tables.

Mass vs weight separated; g₀ = 9.80665 m/s² fixed.

Litre tied to 1 kg of water — off by 28 ppm.

Standardizes the notched-bar pendulum test — specimen, anvil, and energy bookkeeping.

Full spectral radiance law — the exact parent of the Wien approximation.

Build the practical optical (disappearing-filament) pyrometer.

Balloon soundings discover the tropopause and stratosphere.

Systematic ball-bearing load-capacity experiments.

Circulation condition at the trailing edge.

General theory of hydraulic transients.

Exponential decay law and transmutation theory — the half-life.

Measures pressure along a Laval nozzle — theory confirmed (circa).

The rocket equation published, with liquid fuel proposed.

11.2 km/s framed as spaceflight's price of exit.

Exhaust velocity identified as rocketry's key metric.

Ton of refrigeration standardized from melting ice.

Publishes nozzle pressure traverses experimentally confirming the sonic throat.

Trim the Flyer with movable ballast, an early CG-management practice.

Founds modern compressible aerodynamics, making stagnation properties practical design quantities.

Göttingen program makes supersonic flow an engineering science.

Force coefficients normalized by q — modern aerodynamic bookkeeping (circa).

Boundary-layer theory explains why Re governs.

Boundary layer explains where drag comes from.

Block-making machinery industrializes; blocks become a commodity.

Patents the telemobiloscope — first radio echo detection of ships.

Patents the thermionic diode valve — the first reliable AM rectifier.

Coins 'eigenvalue' in his theory of integral equations.

Multi-plate oil-bath clutch developed.

Lift = ρVΓ — the circulation theorem.

Introduces Markov chains — the two-state up/down model behind steady-state availability.

Silicon cat's-whisker crystal detector puts envelope detection in every crystal set.

First observation of electroluminescence (SiC).

Coated stick electrode makes structural arc welds possible.

Ideal aggregate gradation curve published.

Electroluminescence observed in silicon carbide.

Oblique-shock θ-β-M theory in his dissertation under Prandtl.

Coins the name 'Reynolds number'.

Publishes the distribution of the sample mean, groundwork for interval estimation.

Small-sample theory that underpins confidence-based sizing.

Publishes the t-distribution for small-sample inference, writing under a pseudonym for Guinness.

Publishes the t-distribution — the reason small-n uncertainties need k > 2.

First codified lateral-force coefficient for earthquake design.

Relates film stress to substrate curvature — the first bonded-layer stress formula.

Publishes the first queueing analysis of telephone traffic congestion.

Lays the groundwork for traffic intensity in telephone trunk sizing.

Shows S-N data is linear on log-log axes and fits the power law this card evaluates.

First systematic characterization of creep as a time-dependent flow law in metals.

Tabulates buckling coefficients k for practical edge conditions and load cases.

A15 standardizes reinforcing bars; the numbered size system follows.

Rational psychrometric formulae — air conditioning gets its chart.

Scientific management puts machine-time accounting on the shop floor.

Standardizes orifice-plate flow measurement, whose square-law DP inherently limits turndown.

Wind-tunnel C_d measurements; the drag crisis found.

First ready-mixed concrete delivered — the cubic yard becomes a commodity.

International Annealed Copper Standard fixes ρ = 1.7241 µΩ·cm.

Moving assembly line makes equal-time task allocation an economic necessity.

Publishes the original square-root lot-size derivation in a trade magazine.

Coins Q for coil quality at Western Electric (published usage 1920s).

Boiler & Pressure Vessel Code — hoop stress becomes law.

Patent the differential-depth tester for rapid bearing-race checks.

Dimensional analysis (Π-theorem) grounds the flow/head/power coefficients.

Industry standard reference conditions emerge (circa).

Convective heat-transfer theory; LMTD framework matures (circa 1910s).

States cube-root blast scaling; Cranz reaches the same law independently.

States cube-root blast scaling law from wartime charge tests.

Introduces the cardinal (sinc) interpolation series.

Rubber V-belt invented — the compact machine drive.

Pump test standards make efficiency claims comparable.

Standards body that codified NPSH practice.

Introduces the constant-life (Haigh) diagram for plotting mean-stress criteria.

Develops the thallous sulfide photoconductor — the first practical IR detector cell.

Derives the collapse dynamics of a vapor bubble, grounding cavitation theory.

Torque wrench invented for NYC water-main flange bolts.

Lifting-line theory — finite wings computed.

Torque wrench patented — tightening becomes a number.

Water–cement ratio law; aggregate science enters mix design.

Coins the term 'variance' and its partitioning in his paper on Mendelian inheritance.

Superheterodyne fixes detection at a known IF, making the RC a real design number.

Lifting-line theory derives induced drag from trailing vortices.

Whirling rotor theory — self-centering above resonance explained.

First premeditated free-fall parachute jump — V_t survived by design.

'A Method of Reaching Extreme Altitudes' — measured nozzle efficiency.

The multivibrator — two-state RC timing circuits.

Multivibrator circuits, including the one-shot.

Image-parameter network design matures.

Two-port image design formalized.

Nobel Prize for Invar and precision metrology.

Image-parameter design; matching becomes systematic.

Energy-balance theory of brittle fracture from flaws in glass.

Derives the ideal actuator-disk power limit for extracting/adding energy to a stream.

Begins standardizing gauge dimensions and accuracy under the B40 committee.

Introduce the diamond-pyramid (Vickers) test spanning soft to hardened metals.

Corrects the degrees-of-freedom rule for estimated parameters.

Formulates three-term (PID) control while analyzing ship steering.

Systematic matched-network (pad/filter) synthesis.

Pad synthesis equations in modern form.

Roughness coefficient tied to physical wall texture.

'Die Rakete zu den Planetenräumen' — the German school begins.

The book that made orbital mechanics a movement.

Define the Transmission Unit (TU), replacing 'miles of standard cable' with a clean log ratio.

First international standard atmosphere for aviation.

Load–life exponent and statistical bearing life at SKF.

Standard atmosphere fixes T(h) — Mach from altitude becomes arithmetic.

Cavitation similarity number σ (circa).

Transmission Unit replaces miles-of-standard-cable.

Relates signaling rate to bandwidth, seeding the capacity idea.

Invents the control chart, defining process spread as ±3σ.

Rates bearings by 90%-survival life — the original B10/L10.

Sketches the first control chart in a one-page Western Electric memo.

Single dry-plate clutch standardizes the modern form.

Proves the minimum-energy two-impulse transfer.

Erdbaumechanik — modern soil mechanics, effective stress, and the limits of the classics.

Bimetal thermostat analysis: two bonded strips bending under ΔT.

Publishes the enthalpy-potential theory of evaporative cooling that underlies tower performance analysis.

Publishes Statistical Methods for Research Workers — ANOVA for experimenters.

Formalizes degrees of freedom and popularizes the t-test in Statistical Methods for Research Workers.

Adds the cubic term extending the fit below 0 °C.

468/f enters amateur canon.

First liquid-fuel rocket flight, Auburn, Massachusetts.

First liquid-fuel flight — Isp leaves the test stand.

Independently derives the same scaling — hence Hopkinson-Cranz.

Flies a de Laval nozzle on the first liquid-fueled rocket.

Unifies momentum and blade-element theory for aircraft airscrews.

Introduces loading and balance requirements into airworthiness rules.

First liquid-propellant rocket flight — gasoline and LOX proportioned by hand.

Negative feedback, sketched on a ferry-ride newspaper.

Describes the extreme-value form underlying the distribution.

TU renamed the decibel, honoring Alexander Graham Bell.

Standardizes the resistor color code.

Sampling rate theorem groundwork.

Decibel adopted; the 10·log/20·log power-voltage pair standardizes.

Measures thermal noise in resistors.

Derives kTB from thermodynamics.

Quartz crystal clock — Q as a timekeeping technology.

First structural welding code — throat stress made law.

'Vibration Problems in Engineering' — the working handbook.

The TU renamed the decibel.

Defines information logarithmically and links it to bandwidth.

Develop acceptance sampling and LTPD tables at Bell Labs.

Relates signaling rate to bandwidth in telegraph transmission.

Fixes the sampling limit at half the sample rate — the top bin of any FFT.

Shows telegraph channels need ≥2 samples per cycle of the highest frequency — the Nyquist rate.

Broadband coax system — the modern cable.

Curvature correction factor for helical spring stress.

Names the Mach number.

Nautical mile fixed at 1852 m; 'Mach number' named.

Broadband coaxial transmission system.

Publishes calibrated Cipoletti coefficients for irrigation delivery.

Maximally flat filter paper starts modern filter design.

'Strength of Materials' canonizes modern practice.

Torsion design practice standardized in the classic texts.

Uses Takt as the interval for advancing airframes through assembly.

Zero-and-span adjustment established as the standard two-knob calibration for analog meters and bridges.

Publishes the maximally-flat amplifier filter response in Experimental Wireless.

Formalizes autocorrelation and its link to the power spectrum.

The Theory of Interest formalizes present value and the rate of return.

Principles of Engineering Economy establishes interest-factor methods for engineers.

Payback ratio adopted as a rule-of-thumb capital screen in manufacturing.

Principles of Engineering Economy establishes the discrete factor notation for engineers.

Patents practical metal-oxide NTC thermistor elements.

Large calibration campaigns fix discharge coefficients for square-edged plates.

C90 standardizes load-bearing CMU dimensions and strength.

First commercial microwave link, Calais–Dover — clearance becomes engineering.

Publishes Economic Control of Quality, founding statistical process control.

Establishes statistical control theory underpinning measurement variation analysis.

Publishes the maximally-flat filter response, A = 10·log₁₀(1 + (f/fc)^2N).

Develops the elliptic filter, framing Butterworth's design within general approximation theory.

Radio Engineering spreads the quantitative treatment of detector distortion.

Publishes the encirclement stability criterion around the −1 point.

Stability criterion that made frequency-domain loop shaping possible.

Effective-width concept — plates carry load beyond σ_cr.

Effective-earth-radius (4/3) refraction model.

Systematic airfoil families catalogue C_L for designers.

First issues E23, the standard test method for notched-bar impact testing of metallic materials.

Apply the same function to particle-size distributions.

States the sampling theorem independently in the USSR.

Sand-grain roughness experiments at Göttingen map the turbulent friction regimes.

NACA Report 408 introduces the airplane efficiency factor e.

Long Beach earthquake makes seismic base shear mandatory via the Riley Act.

Interference measurement standardizes on field-strength/µV language.

'Mechanical Vibrations' and the tuned damper canon.

Quantum-tunneling theory of electrical breakdown in solids.

US licensing regime; ERP becomes broadcast's yardstick.

Popularizes the formula in practice — hence 'Wilson EOQ'.

h–s diagrams and standardized steam tables make state-point lookup routine.

Formalizes confidence intervals, giving E and z their meaning.

Tabulates the variance ratio directly and names the F distribution for Fisher.

Report to the UK Steel Structures Research Committee that high-strength bolts can develop clamping force equal to rivets.

Transition-state theory explains the barrier.

Daventry experiment proves aircraft detection by radio; British radar program launches.

The Design of Experiments formalizes randomization and replication behind the F test.

Gives a formal statement of the internal rate of return.

Introduces wing sweep as a means to delay compressibility drag rise.

Durand's Aerodynamic Theory publishes the definitive propeller treatment.

'Theory of Elastic Stability' — the working engineer's reference.

12C welded storage-tank standard; gauging becomes contractual (later API 650).

12C welded tank standard — steel verticals standardized.

Patents PCM — digitized analog signals.

Centrifugal-pump texts formalize similarity scaling for design use.

Formalizes the confidence interval as a repeated-sampling procedure.

Theorie und Anwendung der Laplace-Transformation — rigorous conditions for the final-value theorem.

Tests on commercial pipe show real roughness transitions gradually, unlike uniform sand.

Formulas for Stress and Strain — the compilation on every stress engineer's shelf.

Bonded strain gauge makes the bridge the universal sensor front end.

Bonded wire strain gauge, invented independently at Caltech and MIT.

Publish measured galvanic series of alloys in seawater.

The Smith chart — reflection made graphical.

Implicit transition formula for f.

Smith chart — L-network design as geometry.

Frames the birthday coincidence problem in probability terms.

Proposes the distribution in a Swedish engineering academy paper on material strength.

Implicit transition formula for f across the turbulent range.

Publishes the implicit transition formula this card solves.

F-correction charts for multi-pass exchangers.

50 Ω standardized as the loss-power compromise, circa.

Operational radar forces quantitative range prediction from reflected power.

Summing amplifier for the M9 gun director — the op-amp's war job.

First shell-and-tube exchanger standards.

Duty balance formalized on every exchanger datasheet.

Publishes the moving-heat-source solution giving weld temperature fields.

3–15 psi live-zero signaling standardizes process control.

Ultrasonic reflectoscope — sound speed becomes an NDT tool.

Publish the ultimate-gain and reaction-curve tuning rules at Taylor Instrument.

First systematic PID tuning rules from step and oscillation tests.

Technical Paper 410 puts the correlation and roughness tables in every process engineer's toolkit.

Systematic fuel-rich mixture tuning on the V-2 engine.

The etched printed circuit board.

Rigorous antenna theory explains the shortening factor.

Standardized RG-series cables and connectors.

Moving-target indication — Doppler goes operational.

Brittle fracture of welded ships forces the toughness revolution.

Publish the three-parameter stress-strain curve used here.

National Association of Corrosion Engineers formed, standardizing field corrosion practice.

Line-of-sight-rate guidance formalized for anti-aircraft use.

Bearing capacity theory puts soil pressure limits on a mechanistic footing.

Noise-figure convention fixes T₀ = 290 K.

Noise figure defined; 290 K reference set.

Cascade formula — first-stage dominance proven.

'Mechanical Springs' — the standard design text.

The Moody chart — f at a glance.

Plots Colebrook as the famous Moody chart in Transactions of the ASME.

First National Design Specification for wood construction — codified E values and connection design.

Introduces Cv, the flow coefficient rating valves against water at 1 psi drop.

Geostationary orbit proposed for communications.

R-value insulation rating popularizes L/k commerce (circa).

Tempering parameter T·(C + log t) — the mathematical seed of LMP.

Publish the tempering parameter T·(C + log t) in Transactions of AIME.

Ties Liberty ship brittle fractures to the ductile-to-brittle transition, measured by Charpy energy.

Publishes the round-duct friction chart that became the ASHRAE standard.

Popularizes the R-value — resistance instead of conductance — for rating insulation.

Rank-based nonparametric tests renew interest in distribution-free inference.

Notice airframe vibration improves mechanical integrator accuracy — accidental dither.

Formalizes the magnitude/phase plots and gain- and phase-margin readings.

Gain/phase relations underpinning lead-lag magnitude and phase tradeoffs.

First national U.S. minimum-load standard including wind.

J429 grade system codifies bolt strength classes including Grade 8 (150 ksi tensile).

Founded; begins standardizing how instrument performance including rangeability is specified.

The Friis transmission formula — FSPL formalized.

Transmission formula — the budget's physics.

50 Ω becomes the RF impedance — fixing the 107 dB offset.

Helical antenna; the practical-antenna era.

Isotropic-referenced link budgets — EIRP's home turf.

'Properties and Uses of Thermistors' — the modern NTC component.

Refines 2-D thin-plate and 3-D thick-plate forms used for cooling estimates.

Publishes the point-source blast-wave solution grounding the scaling physics.

Independently derive the effective-degrees-of-freedom approximation for combined variances.

Resolves the inelastic column paradox.

Stressed-volume fatigue theory of rolling contact.

First piloted supersonic flight — the relations flown.

Mach 1.06 flown — the ratio becomes a milestone.

First level supersonic flight — Mach 1 crossed.

Devises position-parity error correction on Bell Labs relay machines.

'The Maximum Range of a Radar Set' formalizes the range equation term by term.

Rad Lab Series codifies the radar range equation in usable engineering form.

Adopt circular error probable as the standard bombing accuracy metric.

Flight past Mach 1 confirms the drag rise is a peak, not a wall.

Research Council on Riveted and Bolted Structural Joints founded to standardize bolted connection design.

Quantization noise analysis — the 6.02N + 1.76 dB line.

Quantization noise law — the forward direction.

Joule adopted for heat — the calorie officially deprecated.

IIW founded to standardize welding practice across borders.

Publishes the channel-capacity theorem C = B·log₂(1+S/N).

Defines information entropy in bits — H = -Σ p log₂ p.

Constructs one of the first ground-source residential heat pumps.

Formalizes sampling theory, making sample-timing error a quantifiable noise source.

Servomechanism theory formalizes second-order transient specs.

Principles of Servomechanisms formalizes system type and the Kp/Kv/Ka static error constants.

Systematic hydrodynamic cavitation experiments establish σᵢ scaling.

Sampling theorem formalized.

Radiocarbon dating — the half-life as a clock.

Publish the ideal-gas ΔS working form as the ChemE standard.

Publishes exact distribution-free confidence intervals for the median from order statistics.

Gives the reconstruction condition its information-theory proof.

Optimized raised-cosine window minimizing the largest side lobe.

Ties sinc reconstruction to the sampling theorem for communications.

Formal proof of the sampling theorem; aliasing gets its mathematical footing.

Correlation methods applied to signal detection and delay estimation in noise.

Publish the separated-flow correlation and the Martinelli parameter X.

Rocket Propulsion Elements codifies O/F ratio and its link to Isp.

First edition of Rocket Propulsion Elements codifies TVC gimbal torque budgeting.

*Antennas* — the beamwidth-gain approximation canonized.

TD-2 transcontinental microwave relay; path profiling standardized.

Publishes 'Error Detecting and Error Correcting Codes' in the Bell System Technical Journal.

Adopts takt as the demand-pacing core of the Toyota Production System.

Issues MIL-STD-105A to standardize attribute sampling across suppliers.

Founded to standardize tower testing, terminology, and thermal ratings.

Reports σy ∝ d^(-½) for the yield point of mild steel in Proc. Phys. Soc. B.

Dislocation pile-up analysis gives the d^(-½) exponent a physical basis.

Estimates the redundancy of English, foreshadowing weak human passwords.

ASME paper 'A Statistical Distribution Function of Wide Applicability' makes the case with seven datasets.

ASME paper demonstrates 'wide applicability' across failure data.

Capital Budgeting argues for discounted cash flow over payback rules.

Capital Budgeting popularizes IRR as a corporate investment criterion.

First specification permits A325 bolts to replace rivets one-for-one.

Etched-foil gauges bring precision manufacture to the bridge arm.

International color-code standard (now IEC 60062).

K2-W — the first commercial op-amp.

Microstrip introduced.

IEC 63 standardizes the E-series, circa.

GE engineers publish the time-temperature rupture parameter with C ≈ 20.

Adapt the same form to creep-rupture life — the Larson-Miller parameter.

Advisory Group on Reliability of Electronic Equipment formalizes exponential-model reliability prediction.

Publishes CEP approximation notes relating CEP to the range/bearing sigma ratio.

Advisory Group on Reliability of Electronic Equipment formalizes reliability prediction.

Gyrobus — flywheel-powered public transport.

Report 1135 tabulates the isentropic-flow relations.

Report 1135 charts the θ-β-M relation for working engineers.

Stress Concentration Design Factors compiles elastic Kt charts.

Alternative linear time-temperature parameter, sparking decades of comparison studies.

Independently finds the same law for cleavage strength of polycrystalline iron.

Introduces the A/B/c notation that names the M/M/1 queue.

First Sidewinder guided flight; PbS seeker performance predicted with the point-source range equation.

Sampling Techniques codifies n₀ = z²pq/E² and the finite-population correction.

Refine open-loop tuning for processes with significant dead time.

Tabulates isentropic T₀/T for compressible-flow work.

Metric Kv (m³/h at 1 bar) adopted alongside Cv in Europe.

Original current-capacity charts (later MIL-STD-275).

Silicon junction diodes show stable reverse breakdown — 'zener' diodes, circa.

Independently add the plastic strain-life term, completing the strain-life equation.

Use L = λW informally without a general proof.

L = λW circulates as an unproven but widely used queuing identity.

Detection statistics for fluctuating targets — the rigorous meaning of S_min.

Crest factor becomes a shaker-system spec.

Defines the R, R′, R″, R‴ thermal-shock resistance parameters for brittle ceramics.

First formal (linear-programming) statement of the assembly line balancing problem.

Racking-test programs decompose shear-wall deflection into bending, shear, nail-slip, and anchorage terms.

Publish hardness-vs-HP correlations for carbon and alloy steels.

Popularizes the capability ratio comparing tolerance to process variation.

Statistical Quality Control Handbook standardizes run rules and constants.

AIM-9 Sidewinder fields practical PN homing with a passive IR seeker.

Formalizes quantization as additive noise and the quantizing theorem.

Current-loop transmitters replace air lines.

The equation, staged, reaches orbit with Sputnik.

First artificial satellite proves the arithmetic.

Commercial SCR — hard switching, and the snubber's job, arrives.

Formalizes the stress-intensity factor K, the basis for ΔK.

Introduces the stress-intensity factor K and the plastic-zone correction.

Publish series/parallel network reliability combination methods.

Reliability report establishes MTBF as a specifiable, demonstrable requirement.

Handbook methods make block-diagram reliability standard engineering practice.

Handbook of Structural Stability compiles the coefficient charts airframers still use.

First issues E140 standard hardness conversion tables from paired-measurement data.

Formalizes inventory theory, cementing EOQ in the operations-research canon.

Three-term cosine window with deep side-lobe suppression.

Tabulates normalized Butterworth pole locations and element values for practical synthesis.

Show blunt (low-β) shapes minimize reentry heating — the physical case for the parameter.

1 ft = 0.3048 m exactly; the conversion becomes exact.

First spacecraft to reach Earth escape velocity.

International yard: 1 in = 25.4 mm exactly.

1 lb = 0.45359237 kg exactly.

Defines specific detectivity D*, normalizing detector noise to area and bandwidth.

ASHAE–ASRE merger; the Handbook of Fundamentals codifies layer R-values and film coefficients.

Principles of Optics codifies the modern derivation of the 1.22 λ/D limit.

Switching step-down regulators adopted to cut heat versus linear designs.

Formalize payback in Principles of Engineering Economy with its limitations noted.

Blue Book introduces the period-dependent base-shear coefficient.

The hertz adopted as the SI unit of frequency.

SI adopted — m³/h and L/s standardized.

The watt enshrined in the new SI.

Introduction to Ceramics codifies the parameters as standard practice.

Frames hydrogen-enhanced decohesion and the threshold-stress behavior of high-strength steels.

First working laser (ruby) at Hughes Research Labs — and the first laser eye hazard.

CEP becomes the headline accuracy figure in ICBM and cruise-missile specifications.

Puts the state vector at the center of modern control theory.

Defines controllability and observability and the rank criteria in the new state-space framework.

θ_jc adopted as the standard junction-to-case thermal resistance metric for packaged devices.

API 650 — the modern welded storage-tank standard.

Proves Kσ·Kε = Kt² for notches beyond yield.

Proposes da/dN correlates with ΔK, after rejection by mainstream journals.

Link K to fatigue crack growth (the Paris law), extending LEFM to cyclic life.

Proposes da/dN = C·ΔKᵐ, the power-law heart of crack-growth prediction.

Proves L = λW, the law tying queue length to wait time.

Publishes the first distribution-free proof of L = λW.

SECDED variants adopted for computer memory reliability.

Proves L = λW, the identity that underlies the utilization result.

Publishes heuristic methods for balancing large lines by computer.

Publishes the general proof of L = λW for steady-state queues.

Publishes zero-acceptance-number (c=0) sampling plans.

Applies ballistic-coefficient trajectory design to the first US crewed reentries.

F-1 engine gimbal actuators sized against thrust-arm, inertia, and duct loads.

Theory of Elastic Stability, 2nd edition — the canonical reference for this formula.

First practical visible LED (red, GaAsP).

Satellite links make dB-column budgeting standard practice.

First practical visible (red) LED.

Issues MIL-HDBK-217 with part failure rates and system rollup rules.

MIL-HDBK-217 issued — standardized component failure-rate prediction.

Introduction to Radar Systems makes the range equation chapter 2 of every radar education.

Introduction to Radar Systems standardizes the R⁴ equation and RCS as taught today.

Formalizes availability alongside reliability and maintainability for military systems.

Popularize repeatability/reproducibility study methods in industrial texts.

Demonstrates the first practical visible LED, seeding solid-state lighting.

ASME paper extends polytropic compressor analysis to real gases — the industry-standard method.

MIL-C-45662 formalizes traceable calibration systems for defense hardware.

Three-op-amp differential topology in common use.

Cryogenic first stages exploit the formula for radio astronomy.

Hydrogen-LOX flies — chemical Isp near its ceiling.

Publish the power-law form da/dN = C·(ΔK)ᵐ.

Mechanical Engineering Design standardizes the modified-Goodman + Langer workflow used here.

Introduce the related estimator refining nonparametric location intervals.

Canonical decomposition separating a system into its (un)controllable and (un)observable subspaces.

A 3.5 K unexplained noise temperature = the cosmic microwave background.

SR-71 inlets stage oblique shocks to fly Mach 3.2 efficiently.

First geostationary satellite.

GTO — the Hohmann transfer as commercial routine.

Litre restored to exactly 1 dm³.

Applies queueing theory to data networks, seeding packet switching.

Publish the erf rational approximation (7.1.26) used here.

Structural bolting spec formalizes minimum pretension for slip-critical joints.

µA709 monolithic op-amp; the IC era begins.

Conformal-mapping analysis of strip lines.

Near-Hohmann trajectory reaches Mars.

Proposes the 'slave memory' — the concept of a cache.

Publish Mathematical Theory of Reliability, giving the renewal-theory basis for A.

Builds the University of Arizona reliability program and codifies the RBD formulas.

Publish the fast Fourier transform, making N-point spectra cheap.

Offset and gain error become the dominant specified nonidealities of successive-approximation converters.

FFT algorithm makes frequency-domain FIR design and analysis practical.

4–20 mA standardized.

First US RF exposure standard.

Publish the standard engineering treatment of cross-correlation on random data.

'Laser Beams and Resonators' fixes the Gaussian propagation and ABCD framework.