Toluene and hexane were purified by standard procedures, and benzene was redistilled from calcium hydride.
No dielectric constants are available for concentrated acids, so it is difficult to give a quantitative explanation
for the results.
[but]
The experiment was successful and the results were analyzed.

Notes: (1) In a compound sentence composed of a series of short independent clauses the last two of which are joined by a conjunction, the clauses should be separated by commas. If the clauses themselves contain commas, semicolons should be used to separate all of them.

Harris presented the proposal to the governor, the governor discussed it with the senator, and the senator made an appointment with the president.

Harris presented the proposal, along with a feasibility study, to the governor; the governor discussed it with the senator, who regarded it favorably; and the senator made an appointment with the president.

(2) The comma should be omitted before a conjunction connecting two independent clauses if an introductory prepositional phrase or dependent clause “controls” both main clauses.

For reactions of the order n, a = b and c = d.

No comma is needed before and because, although the equations function as main clauses, they are both “controlled” by the prepositional phrase; to put a comma after a = b upsets the logical balance in the sentence; i.e., theoretically, c = d could be seen as an entirely separate statement: (For reactions of the order n, a = b) and (c = d).

(3) No comma is required between two dependent clauses connected by a coordinate conjunction. A comma may be used for clarity.

We know that the pressure rises and the temperature increases when the pot is covered.
In this case, Qc = v + 2x, where v = y and Qc is the last term.

3.4.3 Use comma(s) to set off an adverbial clause (or long phrase) that precedes or interrupts the main clause.

Because of the known reactivity of x-chloro sulfides, it is not surprising that compound 10 is easily converted
to the x-hydroxy sulfide by water.
After an hour of exposure to light, the cells died.

Note: Often a sentence can be improved by moving an interrupting adverbial clause to the beginning of the sentence.

Poor
The report, after being read aloud, was put up for consideration.
Better
After being read aloud, the report was put up for consideration.

3.4.4 (1) Use a comma to set off an introductory phrase or dependent clause before the main clause if it is long or confusing. A good rule of thumb is to use a comma if the introductory phrase consists of four or more words.

In 1977 the maximum allowable concentration of NOx¬¬ was revised … [no comma needed]
In our case the confidence function is piecewise linear … [no comma needed]
Before we can make a decision, we must have all the facts. [long introductory clause; comma needed]

Note: Omit the comma after an introductory phrase or dependent clause if the word order in
the rest of the sentence is inverted.
Only after we have analyzed the data can we make a recommendation.
In precisely this case were the results satisfactory.
Note: Always use a comma to set off a transitional adverb or expression (however, therefore,
consequently, on the contrary, on the other hand, etc.—see also 3.4.9) that begins a sentence.

(2) Use two commas to set off an introductory phrase at the beginning of a dependent clause or omit the commas altogether. If the phrase is long or breaks the flow of the sentence, then commas should be used.

Our experiments showed that, at low temperature, all of the compounds became brittle. (or)
Our experiments showed that at low temperature all of the compounds became brittle.

Such a structure of the melt bath should be considered because of the metallic layer,
which, due to its high thermal conductivity, redistributes the heat flux.

(3) An introductory word, phrase, or clause following a coordinate conjunction in a compound sentence may be punctuated as illustrated in the following sentence.

The curves in Fig. 2 are derived from a coarser approximation of the method than
those in Fig. 1, but, other than the top curve, they have a reasonable shape. (or)
… in Fig. 1, but other than the top curve, they have a reasonable shape. (or)
… in Fig. 1, but other than the top curve they have a reasonable shape.

(4) Use two commas to set off a word, phrase, or clause that interrupts the clause.

The report, after being read aloud, was put up for consideration.
The analysis, as far as I know, contained no errors.

(5) Phrases beginning with the prepositions as well as, together with, along with, in addition to, and accompanied by should be separated by commas when they fall between the subject and verb. Such phrases are not part of the grammatical subject.

The governor, as well as his press secretary, was shot.

(6) When two or more complementary or antithetical phrases refer to a single word following, the phrases should be separated from one another and from the following word by commas.

A similar, but even more striking, difference in the gas exchange level was observed in experiments
with grass carp.
The most provocative, if not the most important, part of the statement came last.
We had hoped that the mayor himself, not his assistant, would be present.

3.4.5 Use commas both before and after nonrestrictive clauses and phrases. Do not use commas before or after restrictive clauses or phrases when they fall within the main clause or follow the main clause. A restrictive clause or phrase is necessary to complete the meaning of the sentence. A nonrestrictive clause or phrase provides additional descriptive or explanatory detail, but could be omitted without changing the meaning of the sentence.

The products that were produced at high temperatures were unstable. [restrictive: This sentence implies that specifically only those products produced at high temperatures were unstable; there may have been others that were stable. This is specific information that is part of the subject and therefore must be “restricted” to the subject, that is, not separated from it by a comma.]

The products, which were produced at high temperatures, were unstable. [nonrestrictive: This sentence gives additional information about the products referred to here, that they were produced at high temperatures.]

The report that the committee submitted was well documented. [restrictive]
The June financial report, which was well documented, was discussed in great detail. [nonrestrictive]
Mr. Jones, sitting comfortably before the fire, slowly and ceremoniously opened his mail. [nonrestrictive]
The elderly woman sitting beside Mr. Jones was his nurse. [restrictive]
Tom was astonished when he heard the terms. [restrictive]
Tom will meet Mike at 7 p.m., when the train arrives. [nonrestrictive]
I plan to visit the town where I used to live. [restrictive]
I plan to stop off in St. Louis, where I used to live. [nonrestrictive]
The figures for last year cover urban areas only, whereas those for this year include rural areas as well. [nonr.]
The union has decided not to strike while negotiations are still going on. [restrictive]
In 1998–1999, we observed a significant reduction of the river area occupied by young salmon.
[restrictive: This refers to specific area of the river occupied by young salmon]
In 1998–1999, we observed a significant reduction of the river area, occupied by young salmon.
[nonrestrictive: Additional information about the river is given, that it was occupied by young salmon.]

3.4.6 Use a comma before, but not after, the subordinating conjunction (as, while, since, although, because, whereas) in a nonrestrictive clause. Do not use a comma after a subordinating or coordinating conjunction unless an interrupting element appears.

Incorrect
The bryopyran ring system is a unique requirement for anticancer activity, whereas, the ester substituents influence the degree of cytotoxicity.
Correct
The bryopyran ring system is a unique requirement for anticancer activity, whereas the ester substituents influence the degree of cytotoxicity.

3.4.7 Do not use a comma before and, or, or nor as part of a compound predicate unless one is needed for clarity.

Incorrect: The reversal of the central-field polarity could also take place on Mercury, and
lead to the formation of variously oriented local fields.
Correct: The reversal of the central-field polarity could also take place on Mercury and
lead to the formation of variously oriented local fields.

Incorrect: Discussions were held in Moscow on July 12, and in Washington on July 17.
Correct: Discussions were held in Moscow on July 12 and in Washington on July 17.

Do not use a comma to divide compound phrases of the type either … or, neither … nor, both … and, between … and, and from … to.

Incorrect: These reflectors are used both for measuring the lengths of the optical paths, and
for measuring the bare length.
Correct: These reflectors are used both for measuring the lengths of the optical paths and
for measuring the bare length.

3.4.8 In a series containing three or more items, use a comma before and and or. Note that translators sometimes incorrectly omit and in a series when it is not in the Russian original.

The reaction produced water, carbon dioxide, and hydrogen.
The equation for this system is F = pVT, where p is pressure, V is volume, and T is temperature.

3.4.9 Use commas to set off transitional adverbs and expressions (like however, therefore, consequently, thus, nevertheless, finally, on the contrary, on the other hand, in particular, in addition, as a rule) and expressions that introduce an illustration or example (like for example (e.g.), that is (i.e.), namely). When such words and phrases are used as conjunctive adverbs, connecting two independent clauses, they should be preceded by a semicolon (see Section 3.5.2).

This method fails, however, when the pressure drop is nonlinear.
He will travel through two countries, namely, France and England.
Many neural networks, for example, the Hopfield networks, tend to stabilize at the local energy minimum.

For transitional adverbs and expressions that are embedded in the sentence, the commas around them may be omitted if there is no distinct break in thought.

It is critical, therefore, that we reexamine these cost estimates. (distinct break in thought)
It is therefore critical that we reexamine these cost estimates. (spoken with rising voice)

When transitional adverbs and phrases precede the second part of a compound predicate, they are treated as interrupting expressions and are set off by two commas.

A mechanism should exist in the network that, on one hand, can control the competition of hypotheses and, on the other hand, can adaptively control the redistribution of the magnitudes of stimulation and retardation.

3.4.10 Use a comma to introduce direct questions or quotations, but if the quotation is used as a subject, predicate nominative, or predicate adjective, or if it is not being presented as actual dialogue, a comma is not used. Note that, if the quotation is a sentence, it ordinarily begins with a capital letter; if it is a fragment, it does not. However, a colon is used to introduce a formal statement, extract, or speech in dialogue (generally more than one sentence).

Mary said, “I am leaving.”
“The computer is down” was the reply he feared.
We quote from the address: “It now seems appropriate …

3.4.11 In order to avoid ambiguity, use a comma to indicate the omission of a word or words, and especially a word or words used earlier in the sentence. However, this construction is often difficult to read and should be avoided in the main text. If the meaning is clear without a comma, do not use one. Never use an em dash (as is done in Russian text) in this construction.

Correct
Common stocks are preferred by some investors; bonds, by others.
Better
Some investors preferred common stocks, and others preferred bonds.
Correct
One committee member was from Ohio, another from Pennsylvania, and a third from Oregon.

Incorrect: Hornblende is indicated by black triangles; mica—by white circles. [Russian punctuation carried over from translation.]

Correct: Hornblende is indicated by black triangles; mica, by white circles.

3.4.12 Do not use a comma to represent a decimal point (translators often make this mistake).

3.4.13 In names in text, use a comma before and after Jr. and Sr., but not II or III.

Martin Luther King, Jr. Nicholas II W.A. Goddard III

In references, such names are formatted as follows:

King, M.L., Jr., .... Goddard, W.A. III, ....

3.4.14 Set off etc. with commas when it is used in running text.

The trucks deliver milk, eggs, cheese, etc., fresh daily.

3.4.15 Dates should be written in the order month, day, year. If the day is not given, do not use a comma between the month and year. If the day is given, use a comma before the year, as well as after the year within a sentence. The month may be abbreviated for space considerations in tables and figures; see Section 5.10 for the correct abbreviations.

June 1984 (not June, 1984 or June of 1984)
June 15, 1984 (not 15 June 1984)
June 15 (not June 15th)
July 4, 1996 (not July 04, 1996)
The first litter appeared on March 5, 1995, in animals that had just started to darken.
In a table: Feb. 1–9 (not 1. II–9. II) If table space is insufficient, military style date
Sept. 20, 1992 (not 20.09.92) may be used: 20 Sep 92
(first three letters of month without period)

3.4.16 Use commas to set off individual elements in addresses and names of geographical locations or political divisions.

Meetings will take place in St. Louis, Missouri, and Atlanta, Georgia.
The Shirshov Institute of Oceanology, Russian Academy of Sciences, will host the next annual conference.

3.4.17 Generally, do not use a comma to set off symbols, formulas, or variables. However, if the variable is long or the sentence is complex, it may be necessary to set off the variable for clarity.

Incorrect
Consequently, the radiation with energy, x, was produced at the laser output.
Correct
Consequently, the radiation with energy x was produced at the laser output.
Also correct
The Gibbs free energy of formation of silicon dioxide under these conditions, fG, …

Note: For use of commas in chemical names, see Chemical Names and Symbols (Chapter 8).

3.4.18 A word, phrase, or clause that is in apposition to a noun is usually set off by commas, although dashes or parentheses are occasionally used instead.

Nelson, our commander, decided against the plan.

However, if the appositive is restrictive, it is not set off by commas.

Holly’s brother Jack was on time, but her brother Paul was late.