If there be but one of these uncovered by the generalization, this cannot be sound.
It may be added that we have here no generalization imported from a higher level of culture, but an idea or blend of ideas familiar to primitive thought.
The earliest generalization in this direction is associated with F.
At the beginning is the well-known generalization of Eucl.
Granting this is a general truth, it must yet be acknowledged as a special fact, that in fossil birds we have as yet but scanty means of arriving at any precise results which will justify bold generalization in the matter of avine distribution.
The Treaty of Algeciras is essentially a generalization of the Franco-German agreement of the 28th of September 1905.
This generalization was of great value inasmuch as it permitted the deduction of the atomic weight of a non-gasifiable element from a study of the densities of its gasifiable compounds.
We will briefly notice the case of two degrees, which involves an interesting generalization of the method (already explained) of compounding rotations about intersecting axes.
No biological generalization rests on a wider series of observations, or has been subjected to a more critical scrutiny than that every living organism has come into existence from a living portion or portions of a pre-existing organism.
Relief maps on a small scale necessitate a generalization of the features of the ground, as in the case of ordinary maps, as likewise an exaggeration of the heights.
All are contained in the broad generalization that every part of an animal, however minute, has its separate and independent basis in the hereditary substance of the germ cells from which it is derived and may enjoy consequently a separate and independent history.
A generalization of Galileo's results takes the form that under constant conditions of this kind, force (defined in terms of motion) is constant, and that the superposition of two sets of conditions, if their independence can be secured, results in superposition of the forces associated with them separately.
He founded his generalization to a large extent upon the observation that in Gloeosiphonia capillaris two cells completely fuse, and that only one nucleus can be detected in the fused mass.
Soon after his time, however, this conception was clearly established, and with so large a generalization the mental horizon was widened to conceive of a geography which was a science.
Its striated plumage also favours this view, as an evidence of permanent immaturity or generalization of form, since striped feathers are so often the earliest clothing of many of these birds, which only get rid of them at their first moult.
Of economic students, many are unaware of the fact that he wrote any other book than the Essay on the Principle of Population, and what is of permanent importance in that work is contained in the generalization which it suggested to Darwin.
A further generalization was effected by August Kekule, who rejected the hydrochloric acid type as unnecessary, and introduced the methane type and condensed mixed types.
A Similar Theorem Holds In The Case Of Any Number Of Binary Forms, The Mixed Seminvariants Being Derived From The Jacobians Of The Several Pairs Of Forms. If The Seminvariant Be Of Degree 0, 0' In The Coefficients, The Forms Of Orders P, Q Respectively, And The Weight W, The Degree Of The Covariant In The Variables Will Be P0 Qo' 2W =E, An Easy Generalization Of The Theorem Connected With A Single Form.
It was a favourite idea of his that chemical affinity and capillary attraction would eventually be included under the same law, and it was perhaps because of its recalcitrance to this cherished generalization that the undulatory theory of light was distasteful to him.
Noticed in their immediate connexion with literary results; but Hallam had little taste for the spacious generalization which such subjects suggest.
Their generalization is given by the Euler-Maclaurin formula = I, = 0, = 0, = 0 .
Materials accumulated far more rapidly, however, than the power of generalization and classification.
The greatest generalization of this second period, however, was that partly prepared for by d'Orbigny, as will be more fully explained later in this article, and clearly expressed by Agassiz - namely, the law of repetition of ancestral stages of life in the course of the successive stages of individual development.
Such a generalization will become sounder, if, as is now generally done by anthropologists, the Eskimo with their pyramidal skulls, dull complexion and flat noses are removed into a division by themselves.
Various chemists had traced numerical sequences among the atomic weights of some of the elements and noted connexions between them and the properties of the different substances; but it was left to him to give a full expression to the generalization, and to treat it not merely as a system of classifying the elements according to certan observed facts, but as a "law of nature" which could be relied upon to predict new facts and to disclose errors in what were supposed to be old facts.
Bradley had already perceived, in the case of the two stars previously scrutinized, that the apparent difference of declination from the maximum positions was nearly proportional to the sun's distance from the equinoctial points; and he realized the necessity for more observations before any generalization could be attempted.
Next, he supposes that mind obeys the same law of evolution, and exemplifies integration by generalization, differentiation by the development of the five senses, and determination by the development of the order of consciousness.
It must, however, be remembered that so important a generalization is as yet supported upon a somewhat narrow base of observation.
In such a consideration we have to make use not only of the fact just mentioned, but of three important generalizations which serve as it were as implements for the proper estimation of the relationships of any series of organic forms. First of all there is the generalization that the relationships of the various forms of animals (or of plants) to one another is that of the ultimate twigs of a much-branching genealogical tree.
Amongst the brilliant group of mathematicians whose magnanimous rivalry contributed to accomplish the task of generalization and deduction reserved for the 18th century, Lagrange occupies an eminent place.
His genius was one of generalization and abstraction; and the aspirations of the time towards unity and perfection received, by his serene labours, an embodiment denied to them in the troubled world of politics.
Holding that chemistry had not attained the rank of a science - his lectures dealt with the "effects of heat and mixture" - he had an almost morbid horror of hasty generalization or of anything that had the pretensions of a fully fledged system.
Apart from that, the chief source of our error in this matter is due to the fact that in the historical accounts a whole series of innumerable, diverse, and petty events, such for instance as all those which led the French armies to Russia, is generalized into one event in accord with the result produced by that series of events.
He was wanting in mathematical ability, and never displayed in any remarkable degree the still more important power of scientific generalization, which, whether accompanied by mathematical skill or not, never fails to mark the highest genius in physical science.
Legendre, in 1783, extended Maclaurin's theorem concerning ellipsoids of revolution to the case of any spheroid of revolution where the attracted point, instead of being limited to the axis or equator, occupied any position in space; and Laplace, in his treatise Theorie du mouvement et de la figure elliptique des planetes (published in 1784), effected a still further generalization by proving, what had been suspected by Legendre, that the theorem was equally true for any confocal ellipsoids.
On the ether hand, a survey of the facts of cellular embryology which were accumulated in regard to a variety of classes within a few years of Kovalevsky's work led to a generalization, independently arrived at by Haeckel and Lankester, to the effect that a lower grade of animals may be distinguished, the Protozoa or Plastidozoa, which consist either of single cells or colonies of equiformal cells, and a higher grade, the Metazoa or Enterozoa, in which the egg-cell by " cell division " gives rise to two layers of cells, the endoderm and the ectoderm, surrounding a primitive digestive chamber, the archenteron.
Their observations on the solid elements led to a remarkable generalization, now known as Dulong and Petit's law.