The Pinatubo Study

Mt. Pinatubo eruption

Glossary of Names, Terms, & Scientific Principles Used in Pinatubo Study Video and Related Papers

Aqueous CO2 gas (in ocean surface)
In solutions of carbon dioxide dissolved in water, most of the carbon dioxide is present as the aquated molecule, CO2(aq), in equilibrium with a small amount of hydronium ion and hydrogen carbonate (bicarbonate) ion. See:
Boltzmann constant
The Boltzmann constant (kB or k) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula See:
Boone, Pat
Patrick Charles (Pat) Boone is the principle funder of the Pinatubo Study Phase I, and is a co-founder of ClimateCite Corporation. Pat is an American singer, composer, screen actor, writer, television personality, motivational speaker, and spokesman. Pat has sold 45 million records worldwide, has 13 gold singles, two gold albums, a platinum album, and has recorded over 2,300 songs…more than any recording artist in recorded music history. He’s starred in 15 movies, including 1957’s Bernardine, and he has three stars on the Hollywood Walk of Fame. In 2003 Boone was inducted into the Gospel Music Hall of Fame, along with Amy Grant and the Blind Boys of Alabama. See:
Bromley, Claire (Bud)
Bud is a retired life sciences executive. Bud's entrepreneurial leadership exceeded three decades. He was the senior business development, marketing and sales executive at four public corporations, each company a supplier of analytical and life sciences instrumentation, software, consumables and service. Prior to those positions, his 19 year career in Hewlett-Packard Company's Analytical Products Group included worldwide sales and marketing responsibility for Bioscience Products, Global Accounts and the International Olympic Committee, as well as international management assignments based in Japan and Latin America. Bud has visited and worked in more than 65 countries and lived and worked in 3 countries. Bud writes extensively about AGW (manmade climate change) and other science subjects at:
The Greek uppercase letter delta is the standard mathematical symbol to represent a change in some quantity or difference in something. delta- v is a change in velocity. For example, if the variable 'x' stands for the movement of an object, then 'Δx' means the change in movement.
Dimensionless units
Dimensionless units are dimensionless values that serve as units of measurement for expressing other quantities, such as radians (rad) or steradians (sr) for plane angles and solid angles, respectively. For example, optical extent is defined as having units of meters multiplied by steradians. See:,of%20metres%20multiplied%20by%20steradians.
In a chemical reactionchemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time (assuming constant temperature and pressure), so that there is no observable change in the properties of the system. See:
Fast Fourier Transform
A fast Fourier transform is an algorithm that computes the discrete Fourier transform of a sequence, or its inverse. Fourier analysis converts a signal from its original domain to a representation in the frequency domain and vice versa. See:
Fick’s Law
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient. In one (spatial) dimension, the law can be written in various forms, where the most common form is in a molar basis.
Fick's second law
Fick's second law predicts how diffusion causes the concentration to change with respect to time. It is a partial differential equation.
First derivative
The first derivative primarily tells us about the direction the function is going. That is, it tells us if the function is increasing or decreasing. See:
Flow rate
In physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, rate of fluid flow, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol Q (sometimes V̇). The SI unit is cubic meters per second (m3/s). See:,(m3%2Fs).
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. See:
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. See:
Frequency domain
The Frequency Domain refers to the analytic space in which mathematical functions or signals are conveyed in terms of frequency, rather than time. For example, where a time-domain graph may display changes over time, a frequency-domain graph displays how much of the signal is present among each given frequency band. See:
Gabor transform
The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis. The window function means that the signal near the time being analyzed will have higher weight. See:
Gibbs free energy
Gibbs free energy (measured in joules in SI) is the maximum amount of non-expansion work that can be extracted from a thermodynamically closed system (one that can exchange heat and work with its surroundings, but not matter) See:,in%20a%20completely%20reversible%20process.
Graham’s Law
Graham's law of effusion (also called Graham's law of diffusion) was formulated by Scottish physical chemist Thomas Graham in 1848. Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the molar mass of its particles.

Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases diffuse more slowly). A complete theoretical explanation of Graham's law was provided years later by the kinetic theory of gases. Graham's law provides a basis for separating isotopes by diffusion—a method that came to play a crucial role in the development of the atomic bomb.

Graham's law is most accurate for molecular effusion which involves the movement of one gas at a time through a hole. It is only approximate for diffusion of one gas in another or in air, as these processes involve the movement of more than one gas.
Helmholtz free energy
In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). See:,a%20constant%20temperature%20(isothermal).
Henry’s Law
In physical chemistryHenry's law is a gas law that states that the amount of dissolved gas in a liquid is proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century. See:
Henry, William
William Henry was born on December 12, 1774 and was an English chemist. He was the son of Thomas Henry and was born in Manchester England. He developed what is known today as Henry's Law. See:
Inflection point
In differential calculus and differential geometry, an inflection point, point of inflection, flex, or inflection is a point on a smooth plane curve at which the curvature changes sign. See:
Inertia is the resistance of any physical object to a change in its velocity. This includes changes to the object's speed, or direction of motion. An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed when no forces act upon them. 
Insolation Solar irradiance
Solar irradiance is the power per unit area received from the Sun in the form of electromagnetic radiation as measured in the wavelength range of the measuring instrument. The solar irradiance is measured in watt per square metre in SI units. See:
Intensive property
An intensive property is a property of matter that depends only on the type of matter in a sample and not on the amount. Color, temperature, and solubility are examples of intensive properties. See:
In the mathematical field of numerical analysis, interpolation is a type of estimation, a method of constructing new data points based on the range of a discrete set of known data points. See:
Joint Time Frequency Analysis. In signal processing, time–frequency analysis is a body of techniques and methods used for characterizing and manipulating signals whose statistics vary in time, such as transient signals. See:
Keeling Curve
The Keeling Curve is a graph of the accumulation of carbon dioxide in the Earth's atmosphere based on continuous measurements taken at the Mauna Loa Observatory on the island of Hawaii from 1958 to the present day. The curve is named for the scientist Charles David Keeling, who started the monitoring program and supervised it until his death in 2005. See:
Keeling, Charles David
born April 28, 1928 was an accomplished classical pianist who almost chose a career in music. However he chose science has a carrier rather than music and piano pedagogy, and graduated from the University of Illinois in 1948. He went on earning a Ph.D. from Northwestern University. While working on his Ph.D., he also studied most of the undergraduate course work for a degree in Geology. He then became a postdoctoral fellow at Caltech and later joined Scripps Institute of Oceanography where he was appointed as professor of Oceanography in 1968.

At Caltech he developed the first instrument able to measure carbon dioxide in atmospheric samples with consistently reliable accuracy. Keeling camped at Big Sur where he used his new device to measure the level of carbon dioxide and found that it had risen since the 19th century.

The well-known plot of “atmospheric CO2 rise” called the Keeling curve is named in his honor. See:

Law of mass action
In chemistry, the law of mass action is the proposition that the rate of the chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dynamic equilibrium. Specifically, it implies that for a chemical reaction mixture that is in equilibrium, the ratio between the concentration of reactants and products is constant. See:
LeChatelier’s principle
Le Châtelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change to reestablish an equilibrium. Read more.
Le Chatelier, Henry Louis
Henry Louis Le Chatelier was a French chemist of the late 19th and early 20th centuries. He devised Le Chatelier's principle, used by chemists and chemical engineers to predict the effect a changing condition has on a system in chemical equilibrium. See:
Low-pass filter.  low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design.  See:
Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration when a net force is applied. An object's mass also determines the strength of its gravitational attraction to other bodies. The SI base unit of mass is the kilogram.
Methane hydrates
Methane hydrates are white, icelike solids that consist of methane and water. They are an untapped potential future energy source. The methane molecules are enclosed in microscopic cages composed of water molecules. See:,cages%20composed%20of%20water%20molecules.
Milankovitch cycles
Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term is named for Serbian geophysicist and astronomer Milutin Milanković. See:
The term "mole" is defined in that one mole of a substance with a molecular (or atomic) mass of one (1), will have a mass of 1 gram. Or 1 mole of a substance will contain Avogadro's number of atoms or molecules of that substance. In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles. The molar mass is an extensive (not an intensive), property of a substance since it depends on the amount of the substance. See:

The base unit of amount of pure substance in the International System of Units (SI units) that is defined as having exactly 6.02214076 x 1023 indivisible units (such as atoms or molecules) of that substance.
Molecular distances
In molecular geometry, bond length or bond distance is defined as the average distance between nuclei of two bonded atoms in a molecule. It is a transferable property of a bond between atoms of fixed types, relatively independent of the rest of the molecule. See:
Molecular mass
The molecular mass (m) is the mass of a given molecule: it is measured in daltons (Da or u). Molecular and atomic mass are intensive properties of matter. Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element.  See:

Difference between mass and weight People often use the words 'mass' and 'weight' interchangeably, but they mean quite different things. Your mass is the same no matter where you go in the universe; your weight, on the other hand, changes from place to place. See:,changes%20from%20place%20to%20place.
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity, then the object's momentum p is \mathbf{p} = m \mathbf{v}.
Net CO2
Net CO2 is the measured amount of total CO2 in the atmosphere. Net CO2 is total CO2 emitted into atmosphere by all sources (natural and human) minus total CO2 absorbed from atmosphere by all sinks (natural and human). An example of net CO2 is diligently reported by the Global Monitoring Laboratories (GML) of the U.S. National Oceanographic and Atmospheric Administration (NOAA) such as the laboratory on Mauna Loa volcano on Hawaii Island. (image below, at the link, and pdf attached). This lab, by general agreement, is the “gold standard” representing a global average for net CO2. At this lab, the average net CO2 for 2022 was 418.57 ppm, or 0.0419% of dry air, which is about 419 molecules of CO2 gas per million gas molecules in air after removing water vapor molecules. Net CO2 is not the amount of human-produced CO2 in the air. NOAA is not measuring human-produced CO2. NOAA measures net CO2. The NOAA-measured average increase in net CO2 was 1.78 ppm for the year 2022, less increase than every year since 2009. That is, the 2022 annual increase in CO2 due to all sources minus all sinks, natural and human, was 1.78 ppm, or 0.000178%. 1.78 ppm divided by 418.57 ppm is 0.4%, which reveals that the annual average increase for the year 2022 in net human-contributed CO2 did not exceed 0.4% of total CO2 and did not exceed 0.000178% of dry air. (Data credit NOAA-Scripps GML. )
The newton is the International System of Units derived unit of force. It is defined as 1 kg⋅m/s², the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion. 
Notch filter
A notch filter is a type of band-stop filter, which is a filter that attenuates frequencies within a specific range while passing all other frequencies unaltered. For a notch filter, this range of frequencies is very narrow. The range of frequencies that a band-stop filter attenuates is called the stopband. See:
In the Pinatubo Study video, obfuscation refers to the scattering and reflection of photons (energy) from the Sun in the Earth’s atmosphere by particles of matter such as those released by the Pinatubo volcanic eruption which reduces the amount of solar irradiance on the surface of the Earth.
Partition coefficient
A partition coefficient is the ratio of the concentration of a substance in one medium or phase (C1) to the concentration in a second phase (C2) when the two concentrations are in contact at equilibrium; that is, partition coefficient = ( C1 / C2) equil. The constant for partitioning between a gas phase and a liquid phase at low concentrations where the gas has not reacted with the liquid is also called a Henry’s law constant, H = (C1/C2)equil. The Henry’s law constant (H) refers specifically to vapor–liquid equilibria. Partition coefficient and ratio are not equivalent to solubility. Solubility is expressed as units of concentration. A partition coefficient and ratio are dimensionless and have no units. See:
Perturbation of trend
A deviation of a system, moving object, or process from its regular or normal state, path, or velocity caused by an outside influence. See:
Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities. See:
This is an abbreviation for "parts per million" and it also can be expressed as milligrams per liter (mg/L) and micromoles per mole. See:
Rate of change
The rate at which a variable changes over a specific period of time. It is generally expressed as a ratio between a change in one variable relative to a corresponding change in another variable. Graphically, this ratio is represented by the slope of a line. See:
To bring to the state of equilibrium again. See:
Professor Murry Salby, Ph.D.

Murry L. Salby is a climate scientist and former chair of climate at Macquarie University, where he worked from 2008 to 2013. He has written two textbooks, Fundamentals of Atmospheric Physics (1996), and Physics of the Atmosphere and Climate (2011), the latter building on his first book, offers an overview of the processes controlling the atmosphere of Earth, weather, energetics, and climate physics. He has also authored over a hundred referenced articles in scientific journals.

Salby got his Bachelors in aerospace engineering in 1973, and his PhD in environmental dynamics from Georgia Tech in 1978, including a Sigma Xi: The Scientific Research Society doctoral research award. He began as an assistant professor at University of Colorado Boulder’s Department of Atmospheric and Oceanic Sciences in 1984, became an associate professor in 1985, and professor in 1991, gaining tenure in 1998, before resigning in 2007. He has also held positions as a visiting professor and scientist at institutions in the U.S., Sweden, Australia, France, and Israel. He became professor of environmental science at Macquarie University, and worked there from 2008-2013.

1978-1980. Fellow, Advanced Study Program, National Center for Atmospheric Research. Independent research.

1980-1982. Scientist, Global Observations, Modeling and Optical Techniques Project, National Center for Atmospheric Research, Pure and applied research in conjunction with remotely sensed fields derived from Nimbus-6 LRIR, and Nimbus-7 LIMS. See High Resolution Dynamics Limb Sounder.

1982-1984. Visiting scientist, Geophysical Fluid Dynamics Program, Princeton University. Independent research.

1984-1985. Assistant professor, Department of Astrophysical, Planetary, and Atmospheric Sciences, University of Colorado.

1985-1990. Associate professor, Department of Astrophysical, Planetary, and Atmospheric Sciences, University of Colorado.

1986-1999. Director, Center for Atmospheric Theory and Analysis, University of Colorado.

1988-2002. Affiliate scientist, Atmospheric Systems and Analysis.

1987. Visiting professor, Meteorological Institute, University of Stockholm, Stockholm, Sweden.

1990-1991. Lady Davis visiting professor, Department of Atmospheric Science, Institute of Earth Sciences, Hebrew University of Jerusalem, Israel.

1991-2007. Professor, Department of Astrophysical, Planetary, and Atmospheric Sciences, University of Colorado.

1997. Visiting senior scientist, Centre Nationale Researches Scientifique/University of Paris, Paris France.

1998. Visiting scientist, Bureau of Meteorology Research Center, Melbourne Australia.

2000. Visiting scientist, Center for Ocean Land and Atmosphere, Washington DC.

2007. Visiting scientist, Bureau of Meteorology Research Center, Melbourne Australia.

2008-2013. Professor of Environmental Science, Macquarie University

Complete books may be read on-line or downloaded as PDFs on our educational 501(c) (3) ClimateCite website. These books are copyrighted material and are placed on our website as a public service and as an educational resource for those interested in the subject. They may be shared so long as no charges apply. Acquisition of the manuscripts placed hereon was originally paid for by Tomer (Tom) D. Tamarkin.

Fundamentals of Atmospheric Physics

Physics of the Atmosphere and Climate

Saw tooth wave form
Regarding the Keeling curve seasonal variation pattern, this is better described as a quasi-triangle wave. A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodicpiecewise linearcontinuous real function. See:
Scalar (Scalar quantity)
Scalar quantities have a size or magnitude only and need no other information to specify them. Thus, 10 cm, 50 sec, 7 liters and 3 kg are all examples of scalar quantities. Vector quantities have both a size or magnitude and a direction, called the line of action of the quantity.
Scale of graph
In physics and math, a scale in graphs can be defined as the system of marks at fixed intervals, which define the relation between the units being used and their representation on the graph.  See:
Scientific Hypothesis
A scientific hypothesis is an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world.
Scientific Principles & Laws
Principle vs. Law

Principles are ideas based on scientific rules and laws that are generally accepted by scientists. They are fundamental truths that are the foundation for other studies. Principles are qualitative.

They aren't really rules that can be written down with mathematical symbols. They are more like guiding ideas that scientists use to make predictions and develop new laws.

Example: Principle of Relativity: Physical laws take the same form in all systems of reference. (Albert Einstein) Principle of Special Relativity: The speed of light is the same for all observers. (Albert Einstein) Pauli Exclusion Principle: No two particles with the same quantum numbers can be at the same position in space and time. (Wolfgang Pauli)

Scientific Law

Newton's law of gravitational attraction describes how objects are influenced by gravity. If you drop an apple, it will fall. If you throw an apple in the air, it will follow a specific path while falling down. Newton's laws don't tell us why the apple falls or what causes it to fall, just that it does fall.

Similarly, the law of conservation of mass and energy says that neither mass nor energy can be created or destroyed but they can be changed from one form (mass) to the other (energy.). A law does not say why this is true, neither does it say how it is true. It just says what happens—mass is always conserved or converted to an equal amount of energy per the formula E=MC2. Scientific laws can be written as mathematical equations, so they are called quantitative. However, there aren't very many laws in biology. They are more common in physics and chemistry. Here are few examples of scientific Lawsdescribed by their formulas:

Newton's 2nd Law: F = ma

Hooke's Law: F = kx

Henry’s Law: C=kP

Gauss' Law: E⃗ p=1/4πϵ0 X q/r2 / r

Sometimes, people use the terms "principle" and "law" interchangeably. This is because both result in reliable predictions of natural phenomena.
Scientific Method
The Scientific method of procedure is a method that has characterized natural science since the 17th century, and consists systematic observation, measurement, experiment, and the formulation, testing, and modification of hypotheses.

"Criticism is the backbone of the scientific method" The steps of the scientific method are:
Scientific Theory
A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results.
Second derivative
The second derivative is the rate of change of the rate of change of a point at a graph (the "slope of the slope" if you will). This can be used to find the acceleration of an object (velocity is given by first derivative). See:
In mathematics, the sign of a real number is its property of being either positive, negative, or zero. See:
In chemistry solubility is the ability of a solid, liquid, or gaseous chemical substance (referred to as the solute) to dissolve in solvent (usually a liquid) and form a solution. The solubility of a substance fundamentally depends on the solvent used, as well as temperature and pressure. See:
Spectroscopy is the study of the absorption and emission of light and other radiation by matter. It involves the splitting of light or more precisely electromagnetic radiation into its constituent wavelengths (a spectrum), which is done in much the same way as a prism splits light into a rainbow of colors. This may be used to identify discrete substances such as gases or elements. See:
Stoichiometric coefficient
The stoichiometric coefficient is the number written in front of atoms, ion and molecules in a chemical reaction to balance the number of each element on both the reactant and product sides of the equation. Though the stoichiometric coefficients can be fractions, whole numbers are frequently used and often preferred.
Surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water to float on a water surface without becoming submerged. See
Tamarkin, Tomer (Tom) D.
In 1971 Tom received the nation’s highest honor for high school students in the field of physics for his work in Nuclear Magnetic Resonance as a Means of Spectroscopy. He did his undergraduate studies in physics, with a dual minor in math and chemistry, at N A U. He has been in the energy generation, pollution control, and utility industry since 1985. Tom was the inventor of electric utility energy conservation instrumentation and measurement devices. He has been granted seven patents in the U.S., Israel, Europe, & China. In the U.S. alone his patents are practiced by the nation’s largest utility companies on over 90 million installed devices. Tom’s personal website is at:
Thermal momentum
Thermal Momentum is an inaccurate term often used to state the degree of the tendency of a given mass to retain its heat. However, energy and momentum are two different things. They are related in special relativity, in the way that time and space are related, but they aren't the same. See Thermal Mass:
Thorpe, Sir Thomas E.
Great grandfather of Tom Tamarkin, Sir Thomas Edward Thorpe (born Dec. 8, 1845, Manchester—died Feb. 23, 1925, Salcombe, South Devon, England. He received his early education in Manchester and in 1863 entered Owens College, Manchester, as a chemistry student under Henry Enfield Roscoe’s guidance. Much of his four years at Owens College was spent as Roscoe’s private assistant, and he participated in the classical work on vanadium (which resulted in determining its true atomic weight.) During this early time in his carrier, Thorpe participated with Roscoe in numerous studies of carbon dioxide, its accurate percentage of the Earth’s atmosphere, and its toxicity (or lack thereof) in public buildings such as theaters.

After graduation Thorpe worked with Bunsen at the University of Heidelberg, where he received his doctorate. Best known for his numerous textbooks and histories of chemistry, Thorpe was also an important figure in inorganic chemical research. His doctoral dissertation on the oxychlorides of chromium and sulfur led to a study of similar phosphorus compounds, resulting in the discovery of thiophosphoryl chloride (PSCI3), phosphoryl fluoride (POF3), and phosphorus pentafluoride (PF5). His atomic weight determinations of silicon and gold were the most accurate at the time for those elements. He also determined the weights of titanium, strontium, and radium. He carried out extensive studies of the critical temperatures, viscosities, and molecular volumes of liquids. His investigation of the vapor density of hydrofluoric acid revealed that at lower temperatures it is polymerized. Thorpe is most remembered for the large number of popular textbooks he wrote. Most of the following went through several editions: A Dictionary of Applied Chemistry, 3 vols. (London, 1893); the 3rd ed. (1921–1927), which he was preparing until a few days before his death, contained 7 vols. His other chemistry books were A Manual of Inorganic Chemistry, 2 vols. (London, 1898); Qualitative Chemical Analysis and Laboratory Practice, 8th ed. (London, 1894), written with M. M. Pattison Muir; Coal, Its History and Uses (London, 1879); and A Series of Chemical Problems With Key (London, 1907). He was knighted in 1909. See: Google Books, Wikipedia, Britannica online & Many of Sir Thomas E. Thorpe’s books have been reprinted and are now available on From 1894 to 1909 he was Chief Chemist to the British Government, as Director of the Government Laboratory. Early in his carrier Thorpe extensively studied the properties of carbon dioxide and published several papers on CO2.
Specific impulse
The specific impulse formula is Isp = F / (ṁ × g) , the unit of Isp = 1 N/((kg/s) × (m/s²)) = 1 N/(kg⋅m/s³) . But since 1 N = kg⋅m/s² , the units of specific impulse becomes (1 kg⋅m/s²) / (kg⋅m/s³) = s 
The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapor and aerosols, and is where most weather phenomena occur. See:
Vector (Vectorial Quantity)
A directed quantity, one with both magnitude and direction; the signed difference between two points.
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion.
Half the product of the stress due to the attraction or repulsion between two particles in space times the distance between them or in the case of more than two particles half the sum of such products taken for the entire system. The virial theorem relates the total kinetic energy of a self-gravitating body due to the motions of its constituent parts, T to the gravitational potential energy, U of the body. See: