Issues and Problems

The reference staff is called upon to answer a great variety of questions pertaining to the value of physical magnitudes, mathematical constants, and formulas relating these quantities. They arise in problems ranging from everyday situations to sophisticated scientific and engineering contexts. The most common questions fall within 5 general classes:

1.	Conversion Problems. Given a quantity expressed in one system of units find its equivalent in another system (e.g. 2 lbs = 0.907 kg).
2.	Value Problems. Find the value of a physical magnitude under given circumstances (e.g. what is the resistivity of graphite at room temperature?).
3.	Formula Problems. Find the value of a quantity as a function of other quantities (e.g. what is the volume of a cylinder if the radius of the base is 0.5m and its height is 3m?).
4.	Statistics. Most of these questions concern values recorded for some quantities or their averages during a given time lapse and/or at a given location (e.g. how many days with temperatures above 90° F were recorded in Pawhuska, OK during August, 1998).
5.	Astronomical Phenomena. Questions concerning time and space coordinates of celestial events (e.g. ephemeris of moon and planets, dates and times of eclipses, comets, etc.).

Conversion Problems

There are two main sources of difficulties in finding conversions: conceptual and technical. Special problems will also be considered.

1.	Conceptual Misunderstandings for both seekers and providers of conversion information often arise from insufficient grasp of some basic notions and facts about measurements. Most of these relate to matters of precision and dimensions:
	a. Precision. Only mathematical constants and a few physical magnitudes determined by convention have exact values. Allother quantities result from measurements (comparison with a standard unit) and have the form: [quantity] X [unit] ± [error]. Usually when the error is not explicitly stated it is assumed to be 1/2 of the first decimal figure not included (e.g. 7.456 means 7.456 ± 0.0005).
	b. Dimensions. The units inch, meter, and mile fall into a single class of magnitudes, called their dimension, which is length [L], in this case. A quantity expressed in one unit can be converted to an equivalent expression in some other unit if and only if both units have the same dimensions. Many conceptual problems encountered in dealing with conversions turn out to be less obvious examples of the same confusion as that of trying to convert gallons to hours or years to pints. In principle the values of all physical magnitudes can be expressed as combinations of three basic dimensions: length [L], time [T] and mass [M] (e.g. volume: [L3]; speed: [L/T]; energy: [M.L2/T2]). In practice a few other dimensions are also considered among the basic ones. The dimensions of all other quantities are expressed in terms of the basic ones.
2.	Technical. Most of the technical difficulties arise from the diversity of units and systems of measurement. An extremely concise review follows.
	Systems of Units. There are many systems and kinds of units in use but most requests will fall within 3 main classes:
	a. SI System. This is universally used by scientists at present. Its base units are the m (meter ) for length, the s (second ) for time and the kg (kilogram) for mass (not weight), the K (Kelvin) for temperature, the A (ampere) for current, the mol (mole) for quantity of substance and the cd (candela) for luminous intensity. All other units are called derived because they are defined in terms of the base units (e.g. the unit of force, the newton, equals m.kg-²).
	b. Engineering Units. In the U.S.A. engineers employ a mixture of SI units and traditional units of commerce and industry. Different branches of engineering may use different units for the same magnitude (e.g. calories in food technology, B.T.U.'s in refrigeration, kWh in electrical engineering).
	c. Traditional Units. In the U.S.A. there are many units used in commerce, land surveying, etc. ( pound, acre, foot, bushel, etc.) which sometimes descend from British traditional units, but may differ from their current values (e.g. 1 U.S.A. gallon = 0.83267 UK gallon).
	Other Technicalities. In order to read quantities from tables it is necessary to be familiar with 1) the prefixes of the SI units (kilo, micro, etc.) and 2) the scientific (exponential) notation for quantities (e.g. 123.4 X 10³ = 123400; 123.4 X 10-³ = 123.4/1000 = 0.1234)
3.	Special Problems. Some examples of problems which recur frequently in practice:
	Example 1: Density and Specific Gravity. Density is the ratio mass / volume (e.g. aluminum under normal conditions has a density of 2.70 g/ cm³) while specific gravity is a dimensionless quantity, the ratio of the mass of a given volume of a substance to the mass of the same volume of water at 4°C (e.g. the specific gravity of aluminum is 2.70). The SI units have been so chosen that the numerical values are always the same, and one can use tables of density or of specific gravity interchangeably.
	Example 2: Resistance and Resistivity. The electrical resistance to the flow of current in a conductor, measured in ohms () depends on its geometrical dimensions and on an intrinsic characteristic of the material, called resistivity, which is measured in ohms meter [m]. Therefore, when somebody requests e. g. the resistance of graphite, what is meant is its resistivity.
	Example 3: Inverse Quantities. Sometimes the value of a quantity X can only be found in terms of its inverse 1/X ( e.g. conductivity is the inverse of resistivity; conductance is the reciprocal of resistance, etc.).
Master Rule It is impossible to give rules for solving all conversion problems, but the following one may prove useful in most cases: look up the definition of the quantities and properties involved. Understanding the quantities will help finding the conversion or determine if it is possible. The original quantity and its converted value into another unit must have the same dimensions.

Value Problems

Many questions in science and engineering involve finding the value of physical quantities, which are usually recorded in tables. The most frequently requested include the following:

1.	Values of physical constants and coefficients (e.g. proton mass, speed of light in a vacuum, Planck's constant, etc.).
2.	Solubility data of different solutes in various solvents at given temperatures, pressures, etc., as percentages of the masses of solutes and solvents (e.g. solubility of potassium chloride in water at 15 C and at 100 C is 32.5 and 56.7, respectively, meaning 32. 5 kg or 56.7 kg of KCl per 100 kg of H2O).
3.	Thermodynamic data for chemical substances, mixtures and systems (melting and freezing points, boiling points, specific heats, etc.).
4.	Properties of materials used in engineering (tensile strength of alloys, flammability of liquids, thermal conductivity, dielectric strength, etc.).
5.	Properties of dangerous substances: toxicological data (e.g. LD50 - median lethal dose); flammability data (e.g. flash point, ignition temperature, etc.).

Formula Problems

There are many different types of questions involving formulas. Here is a list of the most frequent or important:

1.	Mathematical Formulas. These are formulas which do not involve reference to physical properties or substances. The most frequently requested belong to geometry, calculus and statistics (e.g. volume of a torus, integrals of functions, regression coefficients, etc.).
2.	Physics Formulas. Most of them fall within three main classes:
	a. definitions of quantities (e.g. F = m.a -- definition of "force")
	b. expressions of laws or principles ( F =- G M1 M2 / r² -- Newton's law of gravitation)
	c. formulas for the transformation of other formulas (e.g. Lorentz transformations).
3.	Chemistry Formulas. Chemical substances are either elements (represented by symbols (e.g. H, Cl, Au, P, etc., and arranged in the Periodic Table ) or compounds, represented by formulas made up of element symbols and numerals (e.g. H2O, C6H6, etc.). There are two classes of compounds: organic (all compounds of carbon, except carbonates and some of their relatives, as CO2, which are traditionally considered inorganic) and inorganic (all others). Formulas of organic compounds are extremely numerous and may be very complex, involving rings, side chains, etc. The most important distinction is between those of cyclic (with rings) and acyclic (no rings) formulas.
4.	Engineering Formulas. Most of these are special cases of physics and chemistry formulas as applied in different technologies, such as 1) properties of specific materials ( metals, polymers, fuels, adhesives, lubricants, etc.) and 2) relations between components of systems (of electric and electronic circuits, engines, structures, etc.

Statistics

Finding statistical data does not usually present problems beyond finding a source. Some requests pertaining to economic statistics of technologies fall beyond the scope and resources of this library.

Astronomical Phenomena

Finding coordinates and dates of astronomical events does not usually present problems beyond finding a source. Some requests concerning astrological calculations fall outside the scope of a science library.

Some Suggested Resources

In many cases the information needed to answer questions covered by this guideline is to be found in many alternative sources, and the choice of resources is mainly dictated by one's familiarity with the collections and subject matter. For this reason the following list of references only attempts to suggest some useful sources coordinated with the various problems treated above, and it is in no way exhaustive or sufficient for all of them.

Conversion Problems:

Scientific unit conversion : a practical guide to metrication. [QC94.C37 1997 Ref. Desk] Not only scientific units, but also a comprehensive source of practical, local, ancient and obsolete units.

The Macmillan dictionary of measurement ,[QC82 .D37 1994 Ref. Desk] Gives definitions of all types of quantities and measurement terms.

CRC handbook of chemistry and physics. [QD65 .H3 {latest date} Ref. Desk] Conversions in Chemistry, Physics and some branches of Engineering.

A Physicist's desk reference.[QC61 .P49 1989 Ref. Desk]

Value Problems:

CRC handbook of chemistry and physics.[QD65 .H3 {latest date} Ref. Desk] Quantities in Chemistry, Physics and some branches of Engineering. Most comprehensive one-volume source.

International critical Tables.[Q199.N3 quarto v.1-7. Ref. Rm.] Old but comprehensive, reliable source of physical, chemical and engineering measurements hard to find elsewhere.

Sax's dangerous properties of industrial materials .[T55 .S3 2000 quarto v.1-3 3. Ref. Desk] Toxicological and flammability data.

Metals handbook .[ TA459 .A5 1978 v. 1-18. Ref. Rm.] Followed on the shelves by ASM handbook, in preparation. Data on metals, alloys.

Many handbooks on each of the major branches of engineering at Ref. Desk, Ref. Rm. and open stacks.

Formula Problems:

Mathematics
The VNR concise encyclopedia of mathematics.[QA40 .V18 1989 Ref. Desk]
CRC standard mathematical tables and formulae. [QA47 .C141 1996 Ref. Desk]

Physics
A Physicist's desk reference. [QC61 .P49 1989 Ref. Desk]
Encyclopedia of physical science and technology.[Q123 .E497 1992 v. 1-18 Ref. Rm.]

Chemistry
Dictionary of inorganic compounds.[QD148 .D52 v. 1-7 Ref. Rm.]
Dictionary of organic compounds.[QD251 .D47 1996 quarto v. 1-17 Ref. Rm.]
The elements.[QD466 .E48 1991 Ref. Desk]

Engineering
Gieck's Engineering formulas.[TA151 .G47 1990 Ref. Desk]

Many handbooks on each of the major branches of engineering at Ref. Desk, Ref. Rm. and open stacks.

Statistics:

Statistical Abstracts of the United States.[HA202 .A3 {latest year} Ref. Desk]

The World Almanac.[AY40 .W6 {latest date} Ref. Desk]

Astronomical Phenomena:

Astronomical Almanac.[D213.8:{current year} Doc. Bib.]

Astronomical Phenomena for the year...[D213.8/3:{current and forthcoming year}]