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.
In the latter case, which is the standard practice, mechanical vibration of the siphon is substituted in the place of electrification of the ink, so as to eliminate the effect of atmospheric conditions which frequently caused discontinuity in the flow of ink.
The association of algebra with arithmetic on the one hand, and with geometry on the other, presents difficulties, in that geometrical measurement is based essentially on the idea of continuity, while arithmetical measurement is based essentially on the idea of discontinuity; both ideas being equall
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
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