moral science (Google Books Ngram)
A Google Books Ngram view (Ѻ) of the use of the term "moral science", whose usage peaked between 1840 and 1875, falling into disuse in the 20th century.
In science, moral science is the subject that considers and handles the will of man (Francis Bacon, c.1610); is quantified via the moral symbols of physical chemistry applied socially (Johann Goethe, 1809); a subject resembling physics, germane to agents whose operation involves the power of choice (Thomas Birks, 1873); the moral calculus of pleasure-intensity units, pleasure being the concomitant of energy of mathematical physics, postulated by distributive justice and utility maximization, the horizon in which every moral prospect terminates, on the most sacred and most trivial occasions (Francis Edgeworth, 1881).

Etymology
In 45BC, Roman scholar Cicero, in his "On Fate", introduced the terms “moral science” and “moral” concordantly, as follows: [8]

“That branch of philosophy which, because it relates to manners, the Greeks usually term ethics [from: ήθος or ‘ethos’], the Latins have hitherto called the philosophy of manners. But it may be well for one who designs to enrich the Latin language, to call it moral science. And here we have to explain the nature and force of certain propositions which the Greeks term ‘axioms’. When these propositions relate to the future, and speak of possibilities and impossibilities, it is difficult to determine their precise force. Such propositions necessarily refer to the amount of possibility, and are only resolvable by logic, which I call the art of reasoning.”

This would seem to define moral science, according to Cicero, as the study of actions of behaviors that lead to death (or the arrival of goddess Mor), and or the avoidance of such actions or behaviors, leading to the prolongation of life (accentuation of the stay of the goddess Vita).

In circa 1610, English thinker Francis Bacon, in his essay “On Moral Knowledge”, which he defines as the subject that considers and handles the will of man, according to which right reason governs will, good apparent seduces it; the spurs of will are the affections; her ministers, the organ and voluntary motions, employs the term moral science one time as follows:

“Philosophers in moral science have chosen to themselves a certain resplendent and illustrious mass of matter, to give glory either to the subtlety of their wit, or to the vigor of their eloquence. But such precepts as direct practice chiefly, (and life consists not in novelties or subtleties) they have for the most part omitted.”

Bacon, in his overall scheme, differentiates moral science from civil science, allotting priority to the latter over the former. [7]

Moral science (Wikipedia redirect)
The Wikipedia “moral science” page, which has been a redirect to “human science” since 2007, links to John Keynes, Alexander Bain, Stanley Jevons, George Magoun, Daniel Hausman, and to the talk page of “science of morality”, a discussion (Ѻ) on the difference between the two terms.

Into the 1710s, following, it seems, the English-translations of Bacon’s works, and over the next two centuries, the term “moral science” began to be increasingly employed in English in a variety of publications, albeit largely without explicit definition; the term largely falling off in usage into the 20th century.

Quotes
The following are related quotes:

Moral philosophy is nothing else but the science of what is good and evil, in the conversation, and society of mankind. Good and evil are names that signify our appetites, and aversions; which in different tempers, customs, and doctrines of men, are different: and diverse men, differ not only in their judgment, on the senses of what is pleasant and unpleasant to the taste, smell, hearing, touch, and sight; but also of what is conformable or disagreeable to reason, in the actions of common life.”
Thomas Hobbes (1651), Leviathan [5]

“You are right in speaking of the moral foundations of science, but you cannot speak of the scientific foundations of morality.”
Albert Einstein (1930), discussion on science and religion in Berlin [2]

“Even the greatest forces and abilities don’t seem to carry any clear instructions on how to use them. The sciences do not directly teach good or bad. Ethical values lie outside the scientific realm”
Richard Feynman (1963), “A Scientist Looks at Society” [3]

“Science does not have a moral dimension. It is like a knife. If you give it to a surgeon or a murder, each will use it differently.”
Wernher von Braun (c.1965), arose amid moral qualms surrounding WWII rocket science technology (Ѻ)

“The recurrence during the eighteenth century Enlightenment of the aspiration to be the ‘Newton of the moral sciences’ testifies to the prestige not just of celestial mechanics, but of the ‘experimental method’ more generally.”
— Stefan Collini (1993), ‘Introduction’ to C.P. Snow’s The Two Cultures [4]

References
1. (a) Birks, Thomas R. (1873). First Principles of Moral Science: a Course of Lectures Delivered in the University of Cambridge (pg. 127). MacMillan.
(b) Thomas Rawson Birks – Wikipedia.
(c) Edgeworth, Francis Y. (1881). Mathematical Psychics: an Essay on the Application of Mathematics to the Moral Sciences (moral calculus + energy, pgs. 7-9). C. Kegan Paul & Co.
2. Jammer, Max. (1999). Einstein and Religion: Physics and Theology (pg. 69). Princeton University Press, 2011; (Ѻ) (Ѻ).
3. (a) Feynman, Richard. (1963). “A Scientist Looks at Society”, John Danz Lecture Series, University of Washington, Seattle, Apr; published as: The Meaning of it All (pdf) (pgs. 32, 43). Addison-Wesley, 1998.
(b) The Meaning of It All – Wikipedia.
4. Collini, Stefan. (1993). “Introduction”, in: The Two Cultures (by Charles Snow) (pg. x). Canto.
5. Hobbes, Leviathan. (1651). Leviathan: or the Matter, Form, and Power of a Commonwealth, Ecclesiastical and Civil (pg. 78) (Ѻ). George Routledge and Sons.
6. (a) Bacon, Francis. (c.1620). “On Moral Knowledge”, in: Partitions of the Sciences (De Augmentis Scientiarum) (Lib. 7. Cap. I), in: Lord Bacon’s Essays: or Counsels Moral and Civil (§24: Of Moral Knowledge; moral science, pg. 322). H. Parson, J. Brotherton and W. Meadows, A. Bettesworth, S. Ballard, R. Gosling, and C. King, 1720.
(b) Works by Francis Bacon – Wikipedia.
7. Wormald, B.H.G. (1993). Francis Bacon: History, Politics and Science, 1561-1626 (§6: Morality and Policy I, pgs. 109-; moral science, 10+ pgs). Publisher.
8. Cicero, M.T. (45BC). “On Fate”. Publisher; in: The Treatises of M.T. Cicero: On the Nature of Gods; On Divination; On Fate; On the Republic on the Laws; and On Standing for the Consulship (translator: C.D. Yonge) (§3:264-82). George Bell & Sons, 1878.

External links
Science of morality – Wikipedia.

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