Notation

The author’s system of italic/bold/sans serif should be adhered to unless there is a very good reason for change. The author’s system may well be very involved, and there is no benefit to making changes without purpose. The Royal Society style is for bold-italic vectors and sans-serif tensors; however, unless there is inconsistency or a lack of style, the RS style should not be (ad hoc) applied. Judgement by the copyeditor is obviously required – as it is elsewhere – and changes should only be made where absolutely necessary. In most circumstances, the author should be queried as to whether a change is appropriate – either apply the style and query for confirmation or, if less sure, formulate an alternative and request its inclusion.

In cases where style must be applied consistently across a Trans A or Trans B issue, please query the RS office for which style to follow.

Contents:

A B C D E F G H I J K L M

N O P Q R S T U V W X Y Z

A

• α (alpha): roman for labels, italic for variables; may be confused with ∝ (proportional to)
• axis: when referred to in text should be x-axis, y-axis, etc.
• asterisks in equations should be queried, as their usage may not denote multiplication; note that when asterisks are to be used, their presentation must be consistent throughout the article – in both equations and text
• the word ‘asterisk’ should be written out, e.g. “the asterisk is…”, in any explanation of its meaning
• about, ca, tilde (~), approximately: discourage use of ‘about’ and ~, but with caution in respect to the mathematical meaning; abbreviate ‘approximately’ to ‘approx.’ when in parentheses

B

• brackets: order of brackets is usually {…[…(…)…]…}, with <…> being used for mean, although functions should always be set with (…) – however, in most texts involving mathematics, it is best to leave the order of brackets as is; the left and right brackets should balance, but be aware of (…], etc., constructions

C

• constant: use ‘const.’ in equations
• commas should always be followed by a fixed space, except in a mathematical range, e.g. θ = [0,π]
• c_p: specific heat per unit mass at a constant pressure
• c_v: specific heat per unit mass at a constant volume
• C_p: specific heat (or heat capacity) for 1 mole of a substance at a constant pressure
• C_v: specific heat (or heat capacity) for 1 mole of a substance at a constant volume

D

• δ, Δ: variable delta
• Δ: difference (‘change in’) sign
• ∂: partial differential sign
• d, the differential sign in dx/dy, or abbreviation for ‘days’, should be set in roman type
• dashes: mark distinctions between en-dashes and minus signs clearly (minus signs should have thin spaces around them when used as operators and be closed up when denoting negative values/variables)
• decimals should be written as 0.125 rather than .125; no thin spaces should be inserted for decimals (e.g. use 0.00035, 0.002345).
• degrees should be written as ° following a number (no space, e.g. 10°C); note: (i) Kelvin (temperature) is just K (thin space) rather than °K; (ii) 273 K = 0ºC
• degrees of freedom should be set subscripted without enclosing parentheses (i.e. F_22,92; not F_(22,92) or F(22,92))
• dots between variables: centred dots usually mean multiplication or dot product (but only between vectors); dots on the line usually denote multiplication and may be deleted after confirmation from the author

E

• e, the base of the natural logarithm, should be set in roman type
• equals (=), when an author is explaining terms in an equation, then use ‘is’; when referring to a scale bar, use a comma (e.g. ‘Scale bar, 2 mm’)
• exp (exponential) may be used where superscripts of ‘e’ may not be displayed, e.g. exp(x + iωt) or with large fractions
• Exp: statistical expectation

F

• as a general rule, fractions should be written in-line (e.g. 1/x) if there are few terms on either the numerator (top) or denominator (bottom) and displayed (stacked) if there are several terms
• infrequent standard function names: inf; sup; lim; dist; meas; a.e.; min; max; tr; Re; Im; diam; div; supp; a.s.; proj; ad
• fractions, i.e. 1/2: When there's a fraction build up or large integral, summation etc. either before or after 1/2, the 1/2 will be in the larger font (same size as built up fractions), in other instances 1/2 will be in the smaller font size.

G

• greater than (>) or less than (<) or greater than/less than or equal to (≥, ≤) signs should not be used in either running text or in parenthetical statements within running text unless used in an inequality (i.e. ‘x > 3’)
• Greek characters should be roman where they are labels (e.g. α-helix, γ-ray) and italic when they represent a variable (e.g. wavelength – λ, frequency – ν); see also special cases for mu, pi and sigma
• geographical coordinates: degree and prime symbols are closed up to the numbers and standard inter-word spaces are inserted between the minutes and the compass direction (e.g. in 20°7′ S, 161°13′ E)

I

• ∞: infinity
• i (=√−1), should be set in roman type
• imaginary parts may also be denoted in equations or on axes by ‘Im’ (preferred to ℑ)
• integrals may be written in-line where the terms following the sign are on one line, and should be displayed if the terms are stacked; limits of the integral should appear to the right-hand side of the integral sign

L

• log₁₀ is usually just written as ‘log’ – not to be confused with ‘ln’, natural logarithm. However, log₁₀ is admissible for clarity in a paper where logs of various bases are used
• labels: super-/subscripts acting as labels, e.g. ‘t’ for ‘total’, should be roman
• lists should include fixed spaces after commas and around ellipses, e.g. x = 1, 2, …, x_n
• litres should be lowercase ‘l’, so e.g. use ‘ml’ not ‘mL’.

M

• M denotes molar when used as a unit of measure (not small cap), mega when used in compound units
• matrices, in general, should be denoted using italics – however, follow the author’s system if it is logical and consistent; matrix elements should be surrounded by square or round brackets; avoid breaking matrices over two lines, if necessary the font size can be reduced
• mean is denoted by n with an overbar or <n>, where n is any variable
• micrometres (avoid ‘microns’), i.e. 10⁻⁶ metres, are denoted by μm. Note that the μ should be upright, as it is not a variable here

N

• n is preferred to N when used to mean a number of observations/sample size – change to n, provided the author has not used n for another variable; N is more often used when referring to population size (e.g. N_t is often used to denote the total size of a population)
• tables of nomenclature should be given the title ‘Table 1. Nomenclature.’ and set as close to the start of the article as possible. The author should be queried to provide a citation for the table

O

• O(…) or o(…) denotes ‘order’. Avoid confusion between this and 0 or ° symbol
• operator: common term for symbols such as +, −, ×, ÷; these should be applied in the following order: brackets, order, division or multiplication, addition or subtraction; where +, −, ±, etc., are used to denote the sign of a variable, these should be closed up; fixed spaces should be added on either side of an operator

P

• pi can occur in two forms: Π denotes product and π is the ratio of the circumference to the diameter of a circle (= 3.142…)
• p or Pr denotes probability
• p(a|b) denotes the probability of a given b
• product (see pi): limits written at top and bottom (displayed equation) or as super-/subscripts to the right (in-line text)
• points: labels for geometrical points in n-dimensional spaces should appear in roman (and usually appear as capitals)
• p-values: where there are more than four p-values given, the most significant value should be given three asterisks (e.g. ***p=0.001), the next two asterisks (e.g. **p=0.01), then one asterisk (e.g. *p=0.1), then ^# symbols should be used.

R

• ratios are written a : b (with thin spaces either side of the colon)
• Re: real number in equations or on axes (preferred to ℜ)
• Re: Reynolds number
• root mean square (r.m.s.)
• ℝ: the set of real numbers

S

• scale bars in a list: Scale bars, (a) 500 µm, (b, c) 10 µm, and (d, e) 50 µm. Or the scale bar measure should appear as ‘Scale bar, 500 µm’ within each section of the legend, e.g. Figure 1. (a) Histogram of total species. Scale bar, 500 µm. (b) Histogram of control. Scale bar, 500 µm.’
• sigma can occur in several forms: σ – variable or standard deviation (‘s.d.’ preferred); Σ – sum; Σ – variable
• solidi (‘/’) (or ‘per’) are not permitted in compound units (e.g. m s⁻¹ not m/s)
• standard form is the preferred notation for numbers with large digits in tables/figures. e.g. 1000 should be written as 1 x 10³, 0.000003 should be written as 3 x 10⁻⁶ (as thresholds, convert e.g. 1000 and 0.001 to 1 x 10³ and 1 x 10⁻³, but use 10 and 0.01 not 1 x 10² and 1 x 10⁻²; however, the context must be taken into account and common sense should prevail)
• sum: limits written at top and bottom (displayed equation) or as super-/subscripts to the right (in-line text)
• sets (e.g. where M is the set of maternal genotypes) should be treated as variables (i.e. italicize the set’s name)
• spaces should always be fixed in display and in-line equations and terms; en-spaces should be used when dealing with ranges or in-line vectors without commas, e.g. ‘x = [x_1, x₂, x₃]’; geometric functions, such as sin/cos/tan, should be followed by a fixed thin space
• subscripts: when explaining subscripts in the text, use quotation marks for labels, e.g. “subscript ‘b’ is”, and leave as is for variables, e.g. “subscript i is”
• square root: the symbol √ should be used, not words “sqrt”

T

• transpose of a matrix is denoted by superscript roman T
• tensors are denoted by sans serif; components of tensors are usually written in italic with subscripts
• thin spaces: always before units (e.g. 10 mm, 4 s), but not in a split expression such as ‘10 million people’; between operators and numbers, i.e. before/after =, <, >, etc.; in ratios (e.g. 12 L : 12 D cycle), i.e. between all the elements; to demarcate tens of thousand quantities or above (10 000, 1 000 000), but not in decimals (e.g. use 0.24847, 0.034384)
• Avoid use of tilde (~), replace with "approx."

V

• ‘Van der Waal’ should be written in sentence case (e.g. The van der Waal force acting on…; Van der Waal forces act on …).
• variables (italic) can take any value – this includes constants, e.g. speed of light c, Planck’s constant h; any integer number is commonly referred to as n
• variance (statistics) is normally written as var(x), etc.
• vectors are denoted by bold italic and not by over arrows (^→) or underline; vector zero is written as 0; components of vectors are usually written in italic with subscripts, e.g. x = (x_1, x₂, x₃)

Y

• Year can be shortened to yr when referring to a time span (e.g. 100 yr) but year can be retained when referring to durations of time (e.g. the experiment lasted for 10 years). Thus, 10 k years can be shortened to 10 kyr.
• However, Earth scientists use ‘a’ for annum in compound units (e.g. Ga or Ma) when referring to a specific point in geological history.
• Events per year are usually written as x yr⁻¹.

Z

• zero (0) should be marked clearly to distinguish it from O, O, o, o or °