Various

“ She will brood with complacency the egg of a redbreast (Erithacus rubecula) , so unlike her own, and for aught we know to the contrary may even be colour-blind. In the case of such a species there would be no need of anything further to ensure success—the terror of the nest-owner at seeing her home invaded by a hawk-like giant, and some of her treasures tossed out, would be enough to stir her motherly feelings so deeply that she would without misgiving, if not with joy that something had been spared to her, resume the duty of incubation so soon as the danger was past. ”

“ Developing from this is a new point of practical importance to the hedonism of the Cyrenaics. Aristippus, both in theory and in practice, insisted that true pleasure belongs only to him who is self-controlled and master of himself. The truly happy man must have φρόνησις (prudence) , which alone can save him from falling a prey to mere passion. Thus, in the end, Aristippus, the founder of the purest hedonism in the history of thought, comes very near not only to the Cynics, but to the more cultured hedonism of Epicurus and modern thinkers. ”

“ Even by night they are not silent; but as the season advances the song is less frequently heard, and the cuckoo seems rather to avoid observation as much as possible, the more so since whenever it shows itself it is a signal for all the small birds of the neighbourhood to be up in its pursuit, just as though it were a hawk, to which indeed its mode of flight and general appearance give it an undoubted resemblance—a resemblance that misleads some into confounding it with the birds of prey, instead of recognizing it as a harmless if not a beneficial destroyer of hairy caterpillars. ”

“ The prawns support themselves on their long slender legs on convenient points of the rockwork, and the Sepia stalks them with great caution and determination, the rapid play of its chromatophores giving evidence of its excitement. When it has arrived within striking distance, the two tentacular arms are shot out with great rapidity, and the prawn is seized between the two expanded ends, drawn within the circle of short arms, and devoured; unless, as sometimes happens, the prawn springs away and the Sepia misses its aim. ”

“ The principle of correspondence, or say rather the theorem of united points, is a most powerful instrument of investigation, which may be used in place of analysis for the determination of the number of solutions of almost every geometrical problem. We can by means of it investigate the class of a curve, number of inflections, &c.—in fact, Plücker’s equations; but it is necessary to take account of special solutions: thus, in one of the most simple instances, in finding the class of a curve, the cusps present themselves as special solutions. ”

“ In this memoir by Gergonne, the theory of duality is very clearly and explicitly stated; for instance, we find “dans la géométrie plane, à chaque théorème il en répond nécessairement un autre qui s’en déduit en échangeant simplement entre eux les deux mots points et droites; tandis que dans la géométrie de l’espace ce sont les mots points et plans qu’il faut échanger entre eux pour passer d’un théorème à son corrélatif” ”

“ By a cleverly imparted twist a stone may be made to curve round a guard and either drive away an opposing winner or find a favourable lie for itself. This, the equivalent of “bias” in the game of bowls, is the height of scientific play. If the situation seems desperate a very hard throw, a “thunderin’ cast,” may succeed in clearing away the opponents’ stones from the neighbourhood of the tee. ”

“ It is indeed usually assumed that the mitotic mechanism is not merely for the distribution, but for the equal distribution, of the sister granules to the two daughter nuclei. The conspicuous part the chromatin is seen to play in the whole mechanism of heredity—in maturation, fertilization and development—indicating as it does that the chromatin is the chief, if not the only, bearer of the specific qualities of the organism, sufficiently clearly emphasizes the importance of the equal distribution of this substance between the daughter cells at successive cell-divisions. ”

“ We may consider in relation to a curve, not only the line infinity, but also the circular points at infinity; assuming the curve to be real, these present themselves always conjointly; thus a circle is a conic passing through the two circular points, and is thereby distinguished from other conics. Similarly a cubic through the two circular points is termed a circular cubic; a quartic through the two points is termed a circular quartic, and if it passes twice through each of them, that is, has each of them for a node, it is termed a bicircular quartic. ”

“ The ordinary pleasures of life were for them not merely negligible but positively harmful inasmuch as they interrupted the operation of the will. Wealth, popularity and power tend to dethrone the authority of reason and to pervert the soul from the natural to the artificial. Man exists for and in himself alone ”

“ They had sought to prove that there were universal truths, entitled to be called laws of nature, from the concurrence of the testimonies of many men, peoples and ages, and through generalizing the operations of certain active principles. Cumberland admits this method to be valid, but he prefers the other, that from causes to effects, as showing more convincingly that the laws of nature carry with them a divine obligation. It shows not only that these laws are universal, but that they were intended as such; that man has been constituted as he is in order that they might be. ”

“ That the colour of an egg-shell can be in some mysterious way affected by the action of external objects on the perceptive faculties of the mother is a notion too wild to be seriously entertained. Consequently, only one explanation of the facts can here be suggested. Every one who has sufficiently studied the habits of animals will admit the influence of heredity. That there is a reasonable probability of each cuckoo most commonly putting her eggs in the nest of the same species of bird, and of this habit being transmitted to her posterity, does not seem to be a very violent supposition. ”

“ A curve is a line, or continuous singly infinite system of points. We consider in the first instance, and chiefly, a plane curve described according to a law. Such a curve may be regarded geometrically as actually described, or kinematically as in the course of description by the motion of a point; in the former point of view, it is the locus of all the points which satisfy a given condition ”

“ He may be regarded as the founder of English utilitarianism, but his utilitarianism is distinct from what is known as the selfish system; it goes to the contrary extreme, by almost absorbing individual in universal good. Nor does it look merely to the lower pleasures, the pleasures of sense, for the constituents of good, but rises above them to include especially what tends to perfect, strengthen and expand our true nature. ”

“ In all cases, however, whether the cell-unit lives freely as a unicellular organism or forms an integral part of a multicellular individual, it exhibits in itself all the phenomena characteristic of living things. Each cell assimilates food material, whether this is obtained by its own activity, as in the majority of the protozoa, or is brought, as it were, to its own door by the blood stream, as in the higher Metazoa, and builds this food material into its own substance, a process accompanied by respiration and excretion and resulting in growth. ”

“ Plücker first gave a scientific dual definition of a curve, viz.; “A curve is a locus generated by a point, and enveloped by a line—the point moving continuously along the line, while the line rotates continuously about the point”; the point is a point (ineunt.) of the curve, the line is a tangent of the curve. And, assuming the above theory of geometrical imaginaries, a curve such that m of its points are situate in an arbitrary line is said to be of the order m; a curve such that n of its tangents pass through an arbitrary point is said to be of the class n ”

“ It is especially desirable to point out that there is not the slightest ground for imagining that the cuckoo, or any other bird, can voluntarily influence the colour of the egg she is about to lay. Over that she can have no control, but its destination she can determine. It would seem also impossible that a cuckoo, having laid an egg, should look at it, and then decide from its appearance in what bird’s nest she should put it. ”

“ Bishop Cumberland was distinguished by his gentleness and humility. He could not be roused to anger, and spent his days in unbroken serenity. The basis of his ethical theory is Benevolence, and is the natural outcome of his temperament. He was a man of a sound understanding, improved by extensive learning, and left behind him several monuments of his talents and industry. His favourite motto was that a man had better “wear out than rust out.”
The philosophy of Cumberland is expounded in the treatise De legibus naturae. The merits of the work are almost confined to its speculative theories ”

“ Individuality of the Chromosomes.—The most striking feature in the behaviour of the chromatin in mitosis is its resolution, at each division, into a—for any particular species—constant number of chromosomes. This constant recurrence of the specific number of chromosomes at every cell-division is capable of explanation in two radically different ways. ”

“ The introduction of pacing by multicycles and motors next took from cycle racing what interest was left. A motor race, in which the machines are run at top speed, is more exciting than the spectacle of a motor being driven at a rate which the cyclist can follow with the protection of a wind-shield. In America this system of proving what cyclists can do with racing machines was carried so far that in 1899 a board track was laid down on the Long Island railway for about 2 m. ”

“ The leg of an infinite branch may have at the extremity a tangent; this is an asymptote of the curve, and the leg is then hyperbolic; or the leg may tend to a fixed direction, but so that the tangent goes further and further off to infinity, and the leg is then parabolic; a branch may thus be hyperbolic or parabolic as to its two legs; or it may be hyperbolic as to one leg and parabolic as to the other. The epithets hyperbolic and parabolic are of course derived from the conic hyperbola and parabola respectively. ”

“ Socrates had spoken of the higher pleasures of the intellect; the Cyrenaics denied the validity of this distinction and said that bodily pleasures as being more simple and more intense are to be preferred. Momentary pleasure (μονόχρονος ἡδόνη) , preferably of a carnal kind, is the only good for man. Yet Aristippus was compelled to admit that some actions which give immediate pleasure entail more than their equivalent of pain. This fact was to him the basis of the conventional distinction of right and wrong, and in this sense he held that regard should be paid to law and custom. ”

“ He thinks it ill-advised to build the doctrines of natural religion and morality on a hypothesis which many philosophers, both Gentile and Christian, had rejected, and which could not be proved against Epicureans, the principal impugners of the existence of laws of nature. He cannot assume, he says, that such ideas existed from eternity in the divine mind, but must start from the data of sense and experience, and thence by search into the nature of things discover their laws. It is only through nature that we can rise to nature’s God. ”

“ And we then say that a curve consists of one or more circuits; thus the right line, or curve of the first order, consists of one circuit; a curve of the second order consists of one circuit; a cubic curve consists of one circuit or else of two circuits.
A circuit is met by any right line always in an even number, or always in an odd number, of points, and it is said to be an even circuit or an odd circuit accordingly; the right line is an odd circuit, the conic an even circuit. And we have then the theorem, two odd circuits intersect in an odd number of points ”

“ It is remarkable that Cyprus was celebrated in antiquity for its forests, which not only clothed the whole of its mountain ranges, but covered the entire central plain with a dense mass, so that it was with difficulty that the land could be cleared for cultivation. At the present day the whole plain of the Mesaoria is naturally bare and treeless, and it is only the loftiest and central summits of Mount Olympus that still retain their covering of pine woods. ”

“ Feeling that the most forcible method of attacking Hobbes was to assert the opposite in the same form, he maintained that the whole-hearted pursuit of the good of all contributes to the good of each and brings personal happiness; that the opposite process involves misery to individuals including the self. If, then, Hobbes went to the one extreme of postulating selfishness as the sole motive of human action, Cumberland was equally extravagant as regards Benevolence. ”

“ There have always been a few amateurs who have raced for the love of the sport, but the greater number of prominent racing men have raced for the benefit of a firm, so much so that, at one time, an entire section of racing men were classed as “makers’ amateurs.” They did not confine themselves to the race track, but appropriated the public roads until they became a danger and a nuisance, and road-racing finally was abolished, though record rides, as they are called, are still indulged in, being winked at by the police and by the cycling authorities. ”

“ But although we thus arrive by projection at the notion of a circuit, it is not necessary to go out of the plane, and we may (with Zeuthen, using the shorter term circuit for his complete branch) define a circuit as any portion (of a curve) capable of description by the continuous motion of a point, it being understood that a passage through infinity is permitted. ”

“ The important part played by the centrosome in fertilization,26 first described by van Beneden and Theodor Boveri in their papers of 1887-1888, together with the behaviour of this structure in mitosis, led these authors to regard the centrosome not only as the dynamic centre of the cell but as a permanent cell-organ, which, like the nucleus, passed by division from one cell-generation to the next. ”

“ It is possible to suggest a mechanico-physical explanation of multicellular structure which will deprive the cell of much of its assumed significance as a unit of organization. The fact that surface area becomes relatively less extensive as bulk increases would alone set a limit to the size of “unicellular” organisms; for not only is there a constant reaction between nucleus and cytoplasm through the nuclear membrane, but the surface of the cell serves both for the intake of food and the elimination of waste material. ”

“ First, if the three intersections by the line infinity are all distinct, we have the hyperbolas; if the points are real, the redundant hyperbolas, with three hyperbolic branches; but if only one of them is real, the defective hyperbolas, with one hyperbolic branch. Secondly, if two of the intersections coincide, say if the line infinity meets the curve in a onefold point and a twofold point, both of them real, then there is always one asymptote: the line infinity may at the twofold point touch the curve, and we have the parabolic hyperbolas ”