The theorem that any coplanar system of forces can be reduced to a force acting through any assigned point, together with a couple, has an important illustration in the theory of the distribution of shearing stress and bending moment in a horizontal beam, or other structure, subject to vertical extraneous forces.
It is evident that the normal blue is more or less diluted with extraneous white light, having its origin in reflections from the grosser particles of foreign matter with which the air is usually charged.
A number of particles attached at various points of a string are acted on by given extraneous forces Pi, P, P3.
The reason of this is apparently that the negative pressure of the pleural, and partly of the peritoneal, cavity tends to aspirate a liquid relatively thicker, so to speak, than that effused where no such extraneous mechanism is at work (James).
It appears then that this sum is a measure of the total capacity for doing work against extraneous resistances which the particle possesses in virtue of its motion and its position; this is in fact the origin of the term energy.
If the extraneous forces are n equilibrium the total work which they would perform in any such displacement would be zero, since they reduce to a zero force and a zero couple.
Brimstone is easily burned without any extraneous help; indeed the only precaution required is to take care lest the heat produced by the burning sulphur should not volatilize part of it in the unburned state.
She received a rather desultory education, and mastered algebra and Euclid in secret after she had left school, and without any extraneous help. In 1804 she married her cousin, Captain Samuel Greig, who died in 1806; and in 1812 she married another cousin, Dr William Somerville (1771-1860), inspector of the army medical board, who encouraged and greatly aided her in the study of the physical sciences.
This discussion, though strictly speaking extraneous to the scheme, has always been looked upon as a most important part of his philosophy, and his name is perhaps as much associated with the doctrine of Idols (Idola) as with the theory of induction or the classification of the sciences.
We will suppose that the extraneous forces consist of a known force (X, Y, Z) at the centre, and of the reactions (Fi, Ff, R) at the point of contact.