In existographies, Lady Professor (c.1830-c.1885) (SN:59), her characterized name, abbreviated LP, herein, or Girtham Girl, abbreviated GG, her used vicarious pen name (Ѻ), was an anonymous female science and or mathematics professor of Girtham College, whose lectures, essays, and other matter, as found in her desk, after her passing, were collected and published posthumously by Peter Hampson (1854-1930) (MA, Oriel College, Oxford) (Ѻ), and or Elliot Stock (pg. 131), one of her former students (possibly turned husband), in a book entitled The Romance of Mathematics: Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with Some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion. [1]

Social forces
In her “Social Forces” lecture (pgs. 72-77), LP stated the following:

“In this lecture I propose to examine some of the forces which exist in our social system, and shall endeavor to estimate them by methods of mathematical procedure and analogical reasoning. We will begin with the old definition of force as that which puts matter into motion, or which stops, or changes, a motion once commenced. When a mass is in motion, it has a capacity for doing work, which is called energy; and when this energy is caused by the motion of a body it is called kinetic energy, in mathematical language:

KE = ½ m

Another form of kinetic energy is called potential energy, which is in reality the capacity of a body for doing work owing to its position. For example, we may take an ordinary eight-day clock. When the weights are wound up, they have a certain amount of potential energy stored up, which will counteract the friction of the wheels and the resistance of the air on the pendulum. Or, again, we have the example of a water-wheel: first the water in the reservoir, being higher than the wheel, has an amount of potential energy. This is converted into kinetic energy in striking against the paddles, and after this we have potential energy again produced by the action of the fly-wheel.

By the principle of conservation of energy, if we consider the whole universe, not our planet alone (for its heat and energy are continually diminished to some slight degree), we find that no energy is lost. Force is recognized as acting in two ways: in statics, so as to compel rest, or to prevent change of motion; and in Kinetics, so as to produce or to change motion; and the whole science which investigates the action of force is called dynamics. All this is of course pure mathematics, and I have made these elementary observations for the benefit of my younger hearers, the students of this University. My grave and reverend seniors will pardon, I am sure, the repetition of facts well known to them for the sake of those who are less informed than themselves.

Now before I proceed further, I will endeavor to point out that these elementary truths of physical science hold good in our social system. Each individual is a mass, acted on by numerous forces, capable of 'doing work,' which work can be measured and his velocity calculated. Some individuals have a vast potential energy; that is to say, from their position and station in the social system, they have a power which is capable of producing work which a less exalted individual has not.”

Here, we recall the similar 1868 views expressed by Norman Lockyer and Balfour Stewart. [2]

Romance | Student
On Jun #, LP, in her diary notes (pg. 128), jotted her confusion on the matter of a student who was in love with her and her love for science, and being “forced” to choose between the two, per reason that married women couldn’t hold professorships in her day:

“It has come! and I half expected it. My eager pupil writes with all the energy and love of his noble nature to ask me to be his wife! He says that is all he cares for, and only values his Honors as a step to a higher honour and dignity, that of gaining my love and being my husband. All this is very nice to read; but a terribly difficult problem is placed before me for solution. I do indeed love this dear, good fellow—no one could help doing so, I am sure; but do I not love science more? There is a stringent regulation in this University that no one shall occupy the position of professor who is bound by any domestic ties or cares. All married women are excluded. If I say 'Yes,' I must resign my high position, leave this beloved college, give no more lectures to entranced audiences. In the interests of science, ought I to refuse, and sacrifice my heart's affections for the cause of mathematics? But if I say 'No,' I must give up—him; sacrifice his happiness too, and blight his life. Was ever anyone so perplexed? Science, aid thine obedient servant! May I not determine this vital question by thine all-pervading light? ....”

Reviews
In 1868, an anon book review, in Nature, edited by Norman Lockyer, dismisses Girtham Girl’s work as follows: [3]

“We ought to apologize for going into such detail, but our account will show our readers that the present work does not deal with mathematical discoveries. It is a ‘skit’, with the perusal of which a reader acquainted with mathematics may while away, not unpleasantly, an odd half-hour or two.”

Here we see a short-sighted mind, to say the least.

Quotes
The following are quotes by LP:

“I have been engaged, as you are doubtless aware, for some years in the pursuit of mathematical research, exploring the mines of science, which have of late been worked very persistently, but often, like the black diamond mines, at a loss. Concurrently with these researches, I have speculated on the great social problems which perplex the minds of men, both individually and collectively. And I have come to the conclusion that the same laws hold good in both spheres of work; that methods of mathematical procedure are applicable to the grand social problems of the day and to the regulation of the mutual relations which exist between man and man. Take, for example, the force of public opinion. Of what is it composed? It is the Resultant of all the forces which act upon that which is generally designated the 'social system.' Public opinion is a compromise between the many elements which make up human society; and compromise is a purely mechanical affair, based on the principle of the parallelogram of forces. Sometimes disturbing forces exert their influence upon the action of Public Opinion, causing the system to swerve from its original course, and precipitating society into a course of conduct inconsistent with its former behaviour ; and it is the duty of the governing body to eliminate as far as possible such disturbing forces, in order that society may pursue the even tenor of its way.”
— LP (c.1883), “Lecture on the Theory of Brain Waves and the Transmigration and Potentiality of Mental Forces”, in: The Romance of Mathematics (pg. 16-17)

“The application of mathematics to the study of social science and political government has curiously enough escaped the attention of those who ought to be most conversant with these matters. I shall endeavor to prove in the present lecture that the relations between individuals and the government are similar to those which mathematical knowledge would lead us to postulate, and to explain on scientific principles the various convulsions which sometimes agitate the social and political world. Indeed, by this method we shall be able to prophesy the future of states and nations, having given certain functions and peculiarities appertaining to them, just as easily as we can foretell the exact day and hour of an eclipse of the moon or sun. In order to do this, we must first determine the social properties of a conic section.
— LP (c.1885), “Lecture on the Social Properties of a Conic Section and the Theory of Polemical Mathematics”, in: The Romance of Mathematics (pg. 25-26)

References
1. (a) Girtham Girl. (1886). The Romance of Mathematics: Being the Original Researches of a Lady Professor of Girtham College in Polemical Science, with Some Account of the Social Properties of a Conic; Equations to Brain Waves; Social Forces; and the Laws of Political Motion (editor: Peter Hampson) (Arc). London: E. Stock.
(b) Norman Lockyer. (1888). “Book Review: The Romance of Mathematics” (Ѻ), Nature, 38:28-29.
2. Lockyer, Norman and Stewart, Balfour. (1868). “The Sun as a Type of the Material Universe”, MacMillan’s Magazine, 18: 319-; in: Contributions to Solar Physics (pgs. 63-84).
3. Norman Lockyer. (1888). “Book Review: The Romance of Mathematics” (Ѻ), Nature, 38:28-29.