3io 



SCIENCE. 



law, and we conclude finally that, although in the com- 

 mon phrase there may be something in it, yet our 

 assumed law is in fact no law at all. 



Again I examine my table of squares, and I find a 

 rule of this kind : The second differences of the squares 

 are constant, and equal to 2. I make many trials of 

 this rule and never find an exception. Others do the 

 same and always the same result is found. We con- 

 clude therefore that we have at length discovered a 

 real law that exists in the formation of squares ; but 

 at the same time we invite every one to make the ex- 

 amination for himself, and if possible to find an ex- 

 ception. A. Hall. 



Washington, D. C, December 17, 1880. 



PROFESSOR TAIT AND MR. 

 SPENCER. 



HERBERT 



In another column we have referred to the controversy 

 between Professor Tait and Mr. Spencer. Since this 

 was put in form we have received a copy of Mr. Spen- 

 cer's reply and, with pleasure, give his own explanation, 

 which appears in Nature of the 2d instant : 



" I pass now to his implied judgment on the formula, 

 or definition, of Evolution. And here I have first to ask 

 him some questions. He says that because he has used 

 the word ' definition ' instead of ' formula,' he has in- 

 curred my ' sore displeasure and grave censure.' In 

 what place have I expressed or implied displeasure or 

 censure in relation to this substitution of terms ? Al- 

 leging that I have an obvious motive for calling it a 

 'formula,' he says I am ' indignant at its being called a 

 definition.' I wish to see the words in which I have ex- 

 pressed my indignation ; and shall be glad if Prof. Tait 

 will quote them. He says — ' It seems I should have 

 called him the discoverer of the formula /' instead of 

 ' the inventor of the definition. Will he oblige me by 

 pointing out where I have used eiiher the one phrase or 

 the other ? These assertions of Prof. Tait are to me 

 utterly incomprehensible. I have nowhere either said or 

 implied any of the things which he here specifies. So 

 far am 1 from consciously preferring one of these words 

 to the other, that, until I read this passage in Prof. Tait's 

 lecture, I did not even know that 1 was in the habit of 

 saying ' formula ' rather than ' definition.' The whole of 

 these statements are fictions, pure and absolute. 



" My intentional use of the one word rather than the 

 other, is alleged by him apropos of an incidental compar- 

 ison I have made. To a critic who had said that the 

 formula or definition of Evolution ' seems at best rather 

 the blank form for a universe than anything correspond- 

 ing to the actual world about us,' I had replied that it 

 might similarly be ' remarked that the formula — " bodies 

 attract one another directly as their masses and inversely 

 as the squares of their distances," was at best but a 

 blank form for solar systems and sidereal clusters. 

 Whereupon Prof. Tait assumes that I put the ' Formula 

 of Evolution alongside of the Law of Gravitation,' in 

 1 t to the definiteness of the piovisions they sever- 

 ally enable us to make ; and he proceeds to twit me with 

 inability to predict what will be the condition of Europe 

 tour years hence, as astronomers ' predict the positions 

 of known celestial bodies four years beforehand.' Here 

 we have another example of Prof. Tait's peculiarity of 

 thought Because two abstract generalizations are com- 

 pared as both being utterly unlike the groups of concrete 

 facis interpreted by them, therefore they are compared 

 ; • 1.1 to their other chaiacters. 



" Bui now I am not unwilling to deal with the contrast 

 Prof. Tait rlraws ; and am prepared to show that when 



the conditions are analogous, the contrast disappears. 

 It seems strange that 1 should have to point out to a sci- 

 entific man in his position, that an alleged law may be 

 perfectly true, and that yet, where the elements of a 

 problem to be dealt with under it are numerous, no spe- 

 cific deduction can be drawn. Does not Prof. Tait from 

 time to time teach his students that in proportion as the 

 number of factors concerned in the production of any 

 phenomenon becomes great, and also in proportion as 

 those factors admit of less exact measurement, any pre- 

 diction made concerning the phenomenon becomes less 

 definite ; and that where the factors are multitudinous 

 and not measurable, nothing but some general result can 

 be foreseen, and often not even, that ? Prof. Tait ignores 

 the fact that the positions of planets and satellites admit 

 of definite prevision, only because the forces which ap- 

 preciably affect them are few ; and he ignores the fact 

 that where further such forces, not easily measured, 

 come into play, the previsions are imperfect and often 

 wholly wrong, as in the case of comets ; and he ignores 

 the fact that where the number of bodies, affecting one 

 another by mutual gravitation, is great, no definite previ- 

 sion of their positions is possible. If Prof. Tait were 

 living in one of the globular star-clusters, does he think 

 that after observations duly taken, calculations based on 

 the law of gravitation would enable him to predict the 

 positions of the component stars four years hence ? By 

 an intelligence immeasurably transcending the human, 

 with a mathematics to match, such prevision would 

 doubtless be possible ; but considered from the human 

 standpoint, the law of gravitation, even when uncompli- 

 cated by other laws, can yield under such conditions only 

 general and not special results. And if Prof. Tait will 

 deign to look into ' First Principles,' which he apparently 

 prides himself on not having done, he will there find a 

 sufficient number of illustrations showing that not only 

 other orders of changes, but even social changes, are 

 predictable in respect to their general, if not in respect 

 to their special characters." 



REVERSION IN FLORAL PARTS. 



By William A. Buckhout. 



One of the best plants for showing the reversion of 

 floral parts to the form of leaves is the common red field- 

 clover {Trifoliuni pralense.) 



It is always easily obtained, and during the fall of the 

 year these heads of reverted flowers are quite common. 

 The pedicels of the flowers are much elongated, and 

 somewhat reduced in number; hence the heads have 

 a loose appearance, which, with their very leafy look 

 and absence of color, makes them conspicuous among 



Fig. 



Fig. 2. 



hose having well developed flowers. Fig. 1 gives at 

 fair idea of one of these heads. A dissection of a 



