## O'Brien's *Researches in Symbolical Physics*

The Royal Society of London met on 5 June 1851 with the President, the Earl of Rosse, in the Chair. At this meeting George Gabriel Stokes was elected a fellow of the Royal Society. The first paper read to the Society at that meeting was

*Researches in Symbolical Physics. On the Translation of a Directed Magnitude as Symbolised by a Product. The Principles of Statics established symbolically*, by the Rev M O'Brien, M.A., late Fellow of Caius College, Cambridge, and Professor of Natural Philosophy and Astronomy in King's College, London. This paper, communicated by W A Miller, M.D., F.R.S. was received on 10 April 1851. The following is the abstract of this paper:**Abstract. Researches in Symbolical Physics.**

In this communication the author (starting from the well-known theorem, that two sides of a triangle are equivalent to the third, when

*direction*, as well as magnitude, is taken into account) proposes an elementary step in symbolization which consists in representing the

*Translation of a Directed Magnitude*by a

*Product*. Any magnitude which is drawn or points in a particular direction, such as a force, a velocity, a displacement, or any of those geometrical or physical quantities which we exhibit on paper by

*arrows*, he calls a

*directed magnitude*. By the

*translation*of such a magnitude he means the removal of it from one position in space to another

*without change of direction*.

**U**representing any directed magnitude and

**u**any distance, the translation of

**U**to any parallel position in space, in such wise that every point or element of

**U**is caused to describe the distance

**u**, is termed the

*translation of*

**U**

*along*

**u**.

This translation consists generally of two distinct changes, one the

*lateral*shifting of the line of direction of

**U**, and the other the motion of

**U**

*along*its line of direction. The former is called the

*transverse effect*, the latter the

*longitudinal effect*of the translation of

**U**along

**u**.

Both these effects are shown to be

*products*of

**U**and

**u**; the transverse effect is represented by

**uU**, and the longitudinal by

**u.U**, inserting a dot between the factors in the latter for the sake of distinction.

The author then goes on to apply the principles established to the proof of the

*Parallelogram of Forces*, and the determination of the effect of any set of forces on a rigid body. In doing this a remarkable symbolization of the

*point of application*, as well as the direction and magnitude of a force, is obtained, namely, that the expression

**(1 + u)U**represents a force

**U**acting at a distance

**u**from the origin.

The principles of statics are deduced with remarkable facility from the symbolical representation of the translation of a force along a given distance.