In 1860 he was appointed to the professorship of higher geometry at the university of Bologna, and in 1866 to that of higher geometry and graphical statics at the higher technical college of Milan.
His manual on Graphical Statics and his Elements of Projective Geometry (translated by C. Leudesdorf), have been published in English by the Clarendon Press.
These headings are: "Geometry and Kinematics of Particles and Solid Bodies"; "Principles of Rational Mechanics"; "Statics of Particles, Rigid Bodies, &c."; "Kinetics of Particles, Rigid Bodies, &c."; "General Analytical Mechanics"; "Statics and Dynamics of Fluids"; "Hydraulics and Fluid Resistances"; "Elasticity."
He also published two larger works, Social Statics in 1850, and Principles of Psychology in 1855.
In Social Statics (1850) he still regards the process teleologically, and argues after the fashion of Paley that "the greatest happiness is the purpose of creation" (ch.
C. Turner, Graphics applied to Arithmetic, Mensuration and Statics (1907).
The external forces on a frame or bridge in equilibrium under those forces may, by a well-known proposition in statics, be represented by a closed polygon, each side of which is parallel to one force, and represents the force in magnitude as well as in direction.
In its account of the concept, it brings the statics of knowledge, so to speak, into integral relation with the dynamics.
Presence of what is at least an important half-truth, which intellectuallism with its statics of the rational order viewed as a completely articulate system has tended to ignore.
The subject is usually expounded under the two divisions of statics and kinetics, the former dealing with the conditions of rest or equilibrium and the latter with the phenomena of motion as affected by force.
We follow als the traditional practice of dealing first with statics and thel with kinetics.
Statics of a particle.
Statics of a system of particles.
Statics of inextensible chains.
Statics of a Particle.By a particle is meant a body whose position can for the purpose in hand be sufficiently specified by a mathematical point.
In most questions of pure statics we are concerned only with the ratios of the various forces which enter into the problem, so that it is indifferent what unit of force is adopted.
Statics of a System of ParticlesWe assume that the mutual forces between the pairs of particles, whatever their nature, are subject to the Law of Action and Reaction (Newtons Third Law); i.e.
Plane Stalics.The statics of a rigid body rests on the following two assumptions:
Three-dimensional Statics.A system of, parallel forces can be combined two and two until they are replaced by a single resultant equal to their sum, acting in a certain line.
Statics of Inextensible Chains.The theory of bodies or structures which are deformable in their smallest parts belongs properly to elasticity.
The question remains, of course, as to how far the measurement of force here implied is practically consistent with the gravitational method usually adopted in statics; this will be referred to presently.
Kinetics of a System of Discrete Particles.The momenta of the several particles constitute a system of localized vectors which, for purposes of resolving and taking moments, may be reduced like a system of forces in statics (~ 8).
This is subject tc the same relations as a couple in statics; it may be represented by a vector which will, however, in general vary with the position of 0.
Routh, Analytical Statics (2nd.
Minchin, Statics (4th ed., oxford, 1888); A.
The literature of graphical statics and its technical applications is very extensive.
This principle of least resistance renders determinate many problems in the statics of structures which were formerly considered indeterminate.
Relations between Polygons of Loads and of Resistances.In a structure in which each piece is supported at two joints only, the well-known laws of statics show that the directions of the gross load on each piece and of the two resistances by which it is supported must lie in one plane, must either be parallel or meet in one point, and must bear to each other, if not parallel, the proportions of the sides of a triangle respectively parallel to their directions, and, if parallel, such proportions that each of the three forces shall be proportional to the distance between the other two,all the three distances being measured along one direction.
According to a well-known principle of statics, because the loads or external pressures P1L~, &c., balance each other, they must be proportional to the sides of a closed polygon drawn respectively parallel to their directions.
In the polygon of loads the direction of a load sustained by parallel resistances traverses the point O-i i Since the relation discussed in 7 was enunciated by Rankine, an enormous development has taken place in the subject of Graphic Statics, the first comprehensive textbook on the subject being Die Graphische Statik by K.
Joint; then, by the principles of statics, - - the component of the resistance normal to the joint is CP=CR.cos PCR;
The mode of distribution of a force applied to a solid body requires to be considered when its stiffness and strength are treated of; but, in questions respecting the action of a force upon a rigid body considered as a whole, the resultant of the distributed force, determined according to the principles of statics, and considered as acting in a single line and applied at a single point, may, for the occasion, be substituted for the force as really distributed.
Forces applied to Mechanism Classed.If 0 be the obliquity of a force F applied to a piece of a machinethat is, the angle made by the direction of the force with the direction of motion of its point of applicationthen by the principles of statics, F may be resolved into two rectangular components, viz.
Now from the laws of statics it is known that, in order that a system of forces applied to a system of connected points may be in equilibrium, it is necessary that the sum formed by putting together the products of the forces by the respective distances through which their points of application are capable of moving simultaneously, each along the direction of the force applied to it, shall be zero, products being considered positive or negative according as, the direction of the forces and the possible motions of their points of application are the same or opposite.
Let the useful resistance and the weight of the piece be compounded by the principles of statics into one force, and let this be called the given force.
Then, according to a well-known principle in statics, the normal pressure at the elementary arc do is TdO, T being the mean tension of the band at that elementary arc; consequently the friction on that arc is dF =JTdo.
According to the principles of statics, the resultant of the force P, applied at G perpendicular to the plane OG, and the couple M is a force equal and parallel to P, but applied at a distance GC from G, in the prolongation of the perpendicular OG, whose value is GC = M/P = R2/OG.
He made considerable contributions to scientific literature, and among his publications were: An Analytical View of Newton's Principia, with Lord Brougham (1855); an Essay on the Stability of a given State of Motion, which won the Adams' prize in 1877; and treatises on the Dynamics of Rigid Bodies, on Analytical Statics, and on the Dynamics of a Particle.
Meanwhile he was filling his note-books as busily as ever with the results of his studies in statics and dynamics, in human anatomy, geometry and the phenomena of light and shade.
STATICS (from Gr.