Archive image from page 580 of Darwin and modern science; essays. Darwin and modern science; essays in commemoration of the centenary of the birth of Charles Darwin and of the fiftieth anniversary of the publication of the Origin of species. Edited for the Cambridge Philosophical Society and the Syndics of the University press darwinmodernscie00cambuoft Year: 1910 Classification of modes of motion in 'families' 545 hereafter be density) which determines the motion exactly. In the particular case of the elliptic motion used for illustration the motion was stable, but other cases of motion migh
Archive image from page 580 of Darwin and modern science; essays. Darwin and modern science; essays in commemoration of the centenary of the birth of Charles Darwin and of the fiftieth anniversary of the publication of the Origin of species. Edited for the Cambridge Philosophical Society and the Syndics of the University press darwinmodernscie00cambuoft Year: 1910 Classification of modes of motion in 'families' 545 hereafter be density) which determines the motion exactly. In the particular case of the elliptic motion used for illustration the motion was stable, but other cases of motion might be adduced in which the motion would be unstable, and it \vould be found that classification in a family and specification by some measurable quantity would be equally applicable. A complex mechanical system may be capable of motion in several distinct modes or types, and the motions corresponding to each such type may be arranged as before in families. For the sake of simpli- city I will suppose that only two types are possible, so that there will Fig. 1. A 'family' of elliptic orbits with constant rotational momentum. only be two families ; and the rotational momentum is to be constant. The two types of motion will have certain features in common which we denote in a sort of shorthand by the letter A. Similarly the two types may be described as + rt and vl + ft, so that a and h denote the specific differences which discriminate the families from one another. Now following in imagination the family of the type + a, let us begin with the case where the specific difference a is well marked. As we cast our eyes along the series forming the family, we find the difference a becoming less conspicuous. It gradually dwindles until it disappears ; beyond this point it either becomes reversed, or else the type has ceased to be a possible one. In our shorthand we D. 35
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