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.
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.
Thomsen and Berthelot independently enunciated a generalization (commonly known as Berthelot's Third Principle, or Principle of Maximum Work), which may be stated in brief as follows: - Every pure chemical reaction is accompanied by evolution of heat.
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.
The earliest generalization in this direction is associated with F.
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.
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.
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.
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.
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 generalization is given by the Euler-Maclaurin formula = I, = 0, = 0, = 0 .
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.
The Treaty of Algeciras is essentially a generalization of the Franco-German agreement of the 28th of September 1905.
At the beginning is the well-known generalization of Eucl.
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.
This is a deeper generalization than that which says, "A man is born to trouble as the sparks fly upward."
Yet they are alike in requiring the generalization of the universal and the belief that there are classes which are whole numbers of similars.
The generalization of a class is not, as the conceptual logic assumes, the abstraction of a general idea, but an inference from the analogy of a whole individual thing, e.g.
Universal inference thus requires particular and universal conceptions as its condition; but, so far as it arises from sense, memory, experience, and involves generalization, it consists of judgments which do not consist of conceptions, but are beliefs in things existing beyond conception.
If there be but one of these uncovered by the generalization, this cannot be sound.
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.
The details of the logical method on which its author laid the greatest stress have not been found of practical service; 5 yet the fundamental ideas on which the theory rested, the need for rejecting rash generalization, and the necessity for a critical analysis of experience, are as true and valuable now as they were then.
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.
"Jethart or Jeddart justice," according to which a man was hanged first and tried afterwards, seems to have been a hasty generalization from a solitary fact - the summary execution in James VI.'s reign of a gang of rogues at the instance of Sir George Home, but has nevertheless passed into a proverb.
Postulating some generalization as the goal of the movement of humanity, the historians study the men of whom the greatest number of monuments have remained: kings, ministers, generals, authors, reformers, popes, and journalists, to the extent to which in their opinion these persons have promoted or hindered that abstraction.
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, and corresponding with this generalization the whole series of commands is also generalized into a single expression of will.