I know the phase "in virtue of" means because or as a result of. But I also know the single word "virtue" is used to mean moral life and conduct. It comes to me so obscure to bind these two meanings together.
How to clarify "in virtue of" with regard to its etymology?
Virtue derives from a Latin word virtus. This originally meant "manliness"—the qualities which a man (vir) should have, such as courage, strength and honor. In classical Latin it came to designate the qualities themselves, and was gradually extended to the more general meaning "excellence" or "strength" or "worth". In this sense it was applied not only to people but to things. A particular herb, for instance, might have medicinal "virtue"—the ability to effect a cure of some disorder.
When applied to people it came in the Middle Ages to denote particularly the moral qualities which the Church values—the "excellences" or "strengths" such as faith and hope which enable a Christian to persevere on his heroic journey to heaven. It is that use which eventually developed into the primary modern sense of conformity to accepted standards of conduct.
But when applied to things it maintained the older sense. Chaucer, for instance, opens the Canterbury Tales (ca. 1380) in April, whose sweet showers have:
. . . bathed every veyne in swich licour
Of which vertu engendred is the flour
That is, the spring rain has the virtue of engendering flowers.
That sense of virtue as "efficacy" or "power" has largely disappeared in modern use; but it is still current in the fixed phrase by virtue of, which you may understand as "through the power of".
Excellent question! Looking into etymology is an excellent way to understand the connections across words and phrases within the English language.
"Virtue" comes from the Latin word vir, meaning "man" with connotations of strength and heroism, whence (also Latin) virtūs, meaning "manliness, courage, character, excellence." The English word "virile" also comes from vir, and is the Latinate synonym for the Anglo-Saxon "manly".
(Many English words come in Latinate and Germanic synonym-pairs like that. Other examples are: work/labor, often/frequently, find/locate, learning/education, smart/intelligent, and thousands more. The Germanic synonyms often have a different connotation and slightly different meaning from the Latinate synonyms.)
In later Latin, people also used virtūs to mean supernatural, miraculous, or even military or legal power. English absorbed the word "virtue" from medieval French to mean something like power or strength, especially power with a supernatural character, as well as courage, merit, a distinctive ability, or simply any specific quality at all, such as the power of a plant or chemical substance to produce an effect, especially a medicinal effect. The masculine connotation was lost in English, but the connotations of power and moral excellence have remained.
Today, "a virtue" usually means a desirable ability, a beneficial power, or a morally upright practice; "virtue" means beneficial quality or moral uprightness; and phrases like "in virtue of" still echo the meaning of power or quality. Usually when people say "in virtue of", they usually aren't describing any result of any cause, but a result that is explained by a distinctive or specific quality or power of something.
Here are some typical examples that I found by searching Google Books (slightly edited, trying to avoid books about "virtue"):
To the extent that a country survives in virtue of its having certain institutions, … those institutions are likely reliant on the significant loyalty of some of [their] members. [Source]
In virtue of his legislative power he fixed the rate of interest, and in virtue of his judicial [power] he inflicted the penalty of confiscation. [Source]
The Sthavira or ‘elder’ was merely superior to others in virtue of his age. The Upādhyāya and Āćārya were teachers of different kinds, who received honor in virtue of their knowledge. [Source]
While it's technically possible to say "in virtue of" in regard to anything, the phrase still evokes the word's meaning of a specific power or quality. As you can see in the third example, even the meaning of admirable personal character can still be echoed in "in virtue of".
Probably the most famous use of "virtue" in the sense of a specific power of something is the phrase "dormitive virtue" from Molière's play The Imaginary Invalid, in which a pompous doctor explains opium's power to cause sleep by saying (in Latin) that it has a "dormitive virtue". The phrase "dormitive virtue" has come to mean an empty expression, using more-abstract words to sound as if one is explaining something but really just restating the thing to be explained.
No, this is wrong. 'Vir' is the nominative of the stem 'viro-' — with the -tus suffix, it would give 'viritue', not virtue, just as the '-tudo' suffix gives the English word 'viritude' — masculinity.
Virtue is indeed from virtus, but virtus is from 'vires' — strength, itself from the same stem as 'vita' — life and 'vis' — force. Literally, 'virtus' means 'the source of vires', that is power. So 'by virtue of' means 'by power of', and virtue gained the additional sense of a moral rule because morality was regarded in the Renaissance as a source of power.
Nothing whatever to do with manliness or virility.
Others have discussed the 'virtus' etymology of virtue as good qualities - which I would agree relate to the good qualities in a man ('vires').
In relation to the the 'in', this is an archaic formulation that derives from classical usage of in (+ the appropriate case) to mean 'by', and mainly survives in legal and medical contexts.
So "in/by virtue of" means "in order to promote the virtue of" (illustrating the "in" derivation) or "because of the virtue of" (illustrating the "by" origins/authorship of the idea).
The preposition "in" is fundamentally spatial, but generalizes to spatiotemporal (imagine a trajectory mapped out spatially by an object over time) and hence also to process and in particular movement/change verbs, including in this case the process of reasoning, and the adjectives (and adverbs) one may apply to this process.
The word "by" is related to (and the most consistently workable translation for) the German "bis" where it has the idea of a goal or deadline that must be achieved, as well as the German "bei" which captures ideas that relate to spatial proximity but can relate by generalization to spatiotemporal proximity, boundary and trajectory as also reflected by "in" (and "near","at","on", etc.). This generalizes to abstract dimensions or qualities or belonging, and habitual spatiotemporal occurrence generalizes (sometimes superstitiously) to perceived causality (and overlap in sense with other prepositions): purpose/beneficiary ("for"), reason ("because"), means ("through") and causing/authoring/engendering/inseminating ("from").
