Let x, y, z be the co-ordinates of any particle of the medium in its natural state, and, 7 7, the displacements of the same particle at the end of time t, measured in the directions of the three axes respectively.
It remained a desideratum to express by equations the motion of a particle of the fluid in any assigned direction.
In starting the furnace, the bottom is prepared by ramming it with charcoal-powder that has been soaked in milk of lime and dried, so that each particle is coated with a film of lime, which serves to reduce the loss of current by conduction through the lining when the furnace becomes hot.
A particle of this mass is easily visible microscopically, and a velocity of 2 mm.
The word "alcohol" is of Arabic origin, being derived from the particle al and the word kohl, an impalpable powder used in the East for painting the eyebrows.
An intelligent creature, or "demon," possessed of unlimited powers of vision, is placed in charge of each door, with instructions to open the door whenever a particle in A comes towards it with more than a certain velocity V, and to keep it closed against all particles in A moving with less than this velocity, but, on the other hand, to open the door whenever a particle in B approaches it with less than a certain velocity v, which is not greater than V, and to keep it closed against all particles in B moving with a greater velocity than this.
On account of the smallness of the particles, the forces acting throughout the volume of any individual particle are all of the same intensity and direction, and may be considered as a whole.
When the fluids inside a particle were mixed together, the particle was neutral; when they were more or less completely separated, the particle became magnetized to an intensity depending upon the magnetic force applied; the whole body therefore consisted of a number of little spheres having north and south poles, each of which exerted an elementary action at a distance.
We may now investigate the mathematical expression for the disturbance propagated in any direction from a small particle upon which a beam of light strikes.
Molecula, the diminutive of moles, a mass), in chemistry and physics, the minutest particle of matter capable of separate existence.
Each bombardment will, however, change the motion of the particle, so that changes are too frequent for the separate motions to be individually visible.
The only circumstance which physics has to consider is the transference of movement from one particle to another, and the change of its direction.
The growth of an organic being is simply a process of enlargement, as a particle of dry gelatine may be swelled up by the intussusception of water; its death is a shrinkage, such as the swelled jelly might undergo on desiccation.
By his discovery that the attracting force in any direction of a mass upon a particle could be obtained by the direct process of differentiating a single function, Laplace laid the foundations of the mathematical sciences of heat, electricity and magnetism.
Within a quarter of an hour after a quantity of cinnabar has been injected into the blood of the frog nearly every particle will be found engulfed by the protoplasm of the leucocytes of the circulating blood.
Thrombosis is an accident of not dissimilar character, whereby a vessel is blocked not by a travelling particle, but by a clotting of the blood in situ, probably on the occasion of some harm to the epithelial lining of the vessel.
(5) (8) (I) The components of acceleration of a particle of fluid are consequently Du dudu du du dt = dt +u dx +v dy + wdz' Dr dv dv dv dv dt -dt+udx+vdy+wdz' dt v = dtJ+udx+vdy +w dx' leading to the equations of motion above.
2 = o, (8) so that a liquid particle remains always on a similar ellipsoid.
Two typical forms are in use; in one a liquid is prepared in which the crystal freely swims, the density of the liquid being ascertained by the pycnometer or other methods; in the other a liquid of variable density, the so-called "diffusion column," is prepared, and observation is made of the level at which the particle comes to rest.
Finally, in a celebrated memoir, Theorie des attractions des spheroides et de la figure des planetes, published in 1785 among the Paris Memoirs for the year 1782, although written after the treatise of 1784, Laplace treated exhaustively the general problem of the attraction of any spheroid upon a particle situated outside or upon its surface.
Of the former, the first, published in 1896, was on the dynamics of a particle; and afterwards there followed a number of concise treatises on thermodynamics, heat, light, properties of matter and dynamics, together with an admirably lucid volume of popular lectures on Recent Advances in Physical Science.
This, however, is not exactly accurate, if it be thereby implied that all living things have a visible organization, as there are numerous forms of living matter of which it cannot properly be said that they possess either a definite structure or permanently specialized organs: though, doubtless, the simplest particle of living matter must possess a highly complex molecular structure, which is far beyond the reach of vision.
In the Eulerian method the attention is fixed on a particular point of space, and the change is observed there of pressure, density and velocity, which takes place during the motion; but in the Lagrangian method we follow up a particle of fluid and observe how it changes.
- Nervous System of the Pond knob - like particle Snail, Limnaeus stagnalis, as a type of the (Neritina and Palu- short-looped euthyneurous condition.
Other writers have derived the word from the Arabic particle al (the definite article), and geber, meaning " man."
If the particle enveloped by the protoplasm be of an organic nature, such as a bacterium, it undergoes digestion, and ultimately becomes destroyed, and accordingly the term " phagocyte " is now in common use to indicate cells having the above properties.
(16) Along the path of a liquid particle 4)' is constant, and putting it equal to 2Uc2, (r 2 - a 3 /r) sin 2 0 = c 2, sin 2 0 = c2r/(r3 - a3), (17) the polar equation; or y 2 = c2r3/(r3 - a 3), r3 = a3y2 /(y2._ c2), (18) a curve of the 10th degree (C10).
But it can be shown that from the aggregation of these separate short motions the particle ought to have a resultant motion, described with an average velocity which, although much smaller than 2 mm.
Finally the word (confused not unnaturally with the particle usually attached to it) was borrowed by the West, and is the origin of the English "admiral."
The Dynamics of a Particle was written on the occasion of the contest between Gladstone and Mr Gathorne Hardy (afterwards earl of Cranbrook); and The New Belfry in ridicule of the erection put up at Christ Church for the bells that were removed from the Cathedral tower.
" Atom " has mainly a chemical import, being defined as the smallest particle of matter which can take part in a chemical reaction; a " molecule " is composed of atoms, generally two or more.
A magnetizable substance was supposed to consist of an indefinite number of spherical particles, each containing equivalent quantities of the two fluids, which could move freely within a particle, but could never pass from one particle to another.
D - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is irrotational H is a constant throughout the fluid.
Under such conditions each particle of soil is surrounded by a thin film of water and in the pore-space air can freely circulate.
The Arhab district, through which these two great wadis run, was formerly the centre of the Himyar kingdom; cultivation is now only to be found in the lower parts on the borders of the watercourses, all above being naked rock from which every particle of soil has been denuded.
When the wind rises above the snow-capped Andes, the last particle of moisture is wrung from it that a very low temperature can extract.
- If particles of matter attract one another according to the law of the inverse square the attraction of all sections of a cone for a particle at the vertex is the same.
Ii.) gave the first direct demonstration that no function of the distance except the inverse square can satisfy the condition that a uniform spherical shell exerts no force on a particle within it.
We must remember that the ocean is a continuous sheet of water of a certain depth, and the conditions of continuity which hold good for all fluids require that there should be no vacant space within it; hence if a single water particle is set in motion, the whole ocean must respond, as Varenius pointed out in 1650.
This deflecting force is directly proportional to the velocity and the mass of the particle and also to the sine of the latitude; hence it is zero at the equator and comes to a maximum at the poles.
The strongest direct evidence seems to be that the nuclear substances are the only parts of the cells which are always equivalent in quantity, and that in the higher plants and animals the male organ or spermatozoid is composed almost entirely of the nucleus, and that the male nucleus is carried into the female cell without a particle of cytoplasm.i Since, however, the nucleus of the female cell is always accompanied by a larger or smaller quantity of cytoplasm, and that in a large majority of the power plants and animals the male cell also contains cytoplasm, it cannot yet be definitely stated that the cytoplasm does not play some part in the process.
Along the path of a particle, defined by the of (3), _ c) sine 2e, - x 2 + y2 = y a 2 ' (Io) sin B' de' _ 2y-c dy 2 ds ds' on the radius of curvature is 4a 2 /(ylc), which shows that the curve is an Elastica or Lintearia.
The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.
With A' =0 over the surface of the paraboloid; and then' = ZU[y 2 - pJ (x2 + y2) + px ]; (9) =-2U p [1/ (x2 + y2)-x]; (io) 4, = - ZUp log [J(x2+y2)+x] (II) The relative path of a liquid particle is along a stream line 1,L'= 2Uc 2, a constant, (12) = /,2 3, 2 _ (y 2 _ C 2) 2 2 2 2' - C2 2 x 2p(y2 - c2) /' J(x2 +y 2)= py ` 2p(y2_c2)) (13) a C4; while the absolute path of a particle in space will be given by dy_ r - x _ y 2 - c2 dx_ - y - 2py y 2 - c 2 = a 2 e -x 1 46.
The solid angles subtended by all normal sections of a cone at the vertex are therefore equal, and since the attractions of these sections on a particle at the vertex are proportional to their distances from the vertex, they are numerically equal to one another and to the solid angle of the cone.
Well-known theorem in attractions that if a shell is made of gravitative matter whose inner and outer surfaces are similar ellipsoids, it exercises no attraction on a particle of matter in its interior.
The method of using these liquids is in all cases the same; a particle is dropped in; if it floats a diluent is added and the mixture well stirred.
Archimedes maintained that each particle of a fluid mass, when in equilibrium, is equally pressed in every direction; and he inquired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium.
As a rule these equations are established immediately by determining the component acceleration of the fluid particle which is passing through (x, y, z) at the instant t of time considered, and saying that the reversed acceleration or kinetic reaction, combined with the impressed force per unit of mass and pressure-gradient, will according to d'Alembert's principle form a system in equilibrium.