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Full text of "Scientific Papers - Vi"

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1915] THE PRINCIPLE OF SIMILITUDE 301 In order to entail the same strains, the force of gravity must be inversely as the linear dimension. Under a given gravity the larger structure is the weaker. The velocity of propagation of periodic waves on the surface of deep water is as the square root of the wave-length. The periodic time of liquid vibration under gravity in a deep cylindrical vessel of any section is as the square root of the linear dimension. . The periodic time of a tuning-fork, or of a Helmholtz resonator, is directly as the linear dimension. The intensity of light scattered in an otherwise uniform medium from a small particle of different refractive index is inversely as the fourth power of the wave-length. The resolving power of an object-glass, measured by the reciprocal of the angle with which it can deal, is directly as the diameter and inversely as the wave-length of the light. The frequency of vibration of a globe of liquid, vibrating in any of its modes under its own gravitation, is independent of the diameter and directly as the square root of the density. The frequency of vibration of a drop of liquid, vibrating under capillary force, is directly as the square root of the capillary tension and inversely as the square root of the density and as the 1|- power of the diameter. The time-constant (i.e. the time in which a current falls in the ratio e: 1) of a linear conducting electric circuit is directly as the inductance and inversely as the resistance, measured in electro-magnetic measure. The time-constant of circumferential electric currents in an infinite conducting cylinder is as the square of the diameter. In a gaseous medium, of which the particles repel one another with a force inversely as the nih power of the distance, the viscosity is as the (n + 3)/(2w — 2) power of the absolute temperature. Thus, if n = 5, the viscosity is proportional to temperature. Eiffel found that the resistance to a sphere moving through air changes its character somewhat suddenly at a certain velocity. The consideration of viscosity shows that the critical velocity is inversely proportional to the diameter of the sphere. If viscosity may be neglected, the mass (M) of a drop of liquid, delivered slowly from a tube of diameter (a), depends further upon (T) the capillary tension, the density (<r), and the acceleration of gravity (g). If these data suffice, it follows from similarity that -^.ri 9 The same order of magnitude as that calculated for a black body when its spectrum is cut down tq that of the flame, and we may infer that the light of a powerful soda flame is due much more to the widening of the spectrum lines than to an increased brightness of their central parts. wcnm t« rrinke rt<*