An argument for discontinuity of race is found in the fact that whereas the Sumerians are never represented as using the bow, their predecessors certainly made flint arrowheads.
Thus, for example, with = 4Uy 2 (r 2 a 2 -I), r2 = x2 +y 2, (13) for the space inside the sphere r=a, compared with the value of, i' in § 34 (13) for the space outside, there is no discontinuity of the velocity in crossing the surface.
These conditions cannot be consistent with sensible convection of the aether near the earth without involving discontinuity in its motion at some intermediate distance, so that we are thrown back on the previous theory.
Noll adopts mercury because it is easily purified, and its physical condition in the liquid state is determinate; there is, however, a discontinuity involved in passing from the liquid to the solid state at a temperature of -40° C., and it cannot be used at all with some metals, such as lead, on account of the rapidity with which it dissolves them.
If the pressure alters as the water tank empties, a discontinuity occurs in the trace when the tank is refilled, and a fictitious element may be introduced into the diurnal variation.
It must always be remembered that we are liable (especially in the case of fossilized integuments) to attach an unwarranted interpretation to the mere discontinuity or continuity of the thickened plates of chitinous cuticle on the back of an Arthropod.
The concept is accounted for in Kantian terms. There is no discontinuity between the pre-logical or sub-logical ' See Ueberweg, System of Logic and History of Logical Doctrines, § 34.
These experiments distinctly point to the conclusion, although without absolutely proving it, that in such cases the coefficient of kinetic friction gradually increases as the velocity becomes extremely small, and passes without discontinuity into that of static friction.
Discontinuity happens, but it is not unpredictable.
To prevent discontinuity of results at this stage, recapitulation from an analytical point of view is desirable.
With reference to all such further refinements of theory, it is to be borne in mind that the perfect fluid of hydrodynamic analysis is not a merely passive inert plenum; it is also a continuum with the property that no finite internal slip or discontinuity of motion can ever arise in it through any kind of disturbance; and this property must be postulated, as it cannot be explained.
Hence, as with the progressive transfer of the carbon from the graphitic to the cementite state in our imaginary series of cast irons, the combined carbon present in the matrix increases, so does the tensile strength of the mass as a whole for two reasons; first, because the strength of the matrix itself is increasing (DE), and second, because the discontinuity is decreasing with the decreasing proportion of graphite.
With further transfer of the carbon from the graphitic to the combined state, the matrix itself grows weaker (EF); but this weakening is offset in a measure by the continuing decrease of discontinuity due to the decreasing proportion of graphite.