Equations of motion in generalized co-ordinates.
They may be called (in a generalized sense) the co-ordinates of the lamina.
Though considered fantastic by many, it had secured fairly general acceptance in Germany in 1912, and was followed by the generalized theory in 1915.
Linete and Linet-wige, whence seems to have been corrupted the old Scottish "Lintquhit," and the modern northern English "Lintwhite" - originally a somewhat generalized bird's name, but latterly specialized for the Fringilla cannabina of Linnaeus, the Linota cannabina of recent ornithologists.
The idea_can be generalized so as to have regard to ternary and higher forms each of the same order and of the same number of variables.
Little is known of the form of the appendages in the lowest archaic Arachnida, but the tendency of those of the prosomatic somites has been (as in the Crustacea) to pass from a generalized bi-ramose or multi-ramose form to, that of uni-ramose antennae, chelae and walking legs.
The method of "generalized coordinates," as it is now called, by which he attained this result, is the most brilliant achievement of the analytical method.
This led to the idea of algebra as generalized arithmetic.
It is true that we obtain this result by subtracting 3 from io by means of a subtractiontable (concrete or ideal); but this table merely gives the generalized results of a number of operations of addition or subtraction performed with concrete units.
On the other hand, if laws of social phenomena, empirically generalized from history, can, when once suggested, be affiliated to the known laws of human nature; if the direction actually taken by the developments and changes of human society, can be seen to be such as the properties of man and of his dwelling-place made antecedently probable, the empirical generalizations are raised into positive laws, and sociology becomes a science."
Maximus), has retained the slightly more generalized characters of the mammoth's contemporaries of more southern climes, E.
The most generalized type is Coryphodon, representing the family Goryphodontidae, from the lower Eocene of Europe and North America, in which there were 44 teeth, and no horn-like excrescences on the long skull, while the femur had a third trochanter.
They agree, for instance, with that family in the presence of a descending flange at the hinder end of each side of the lower jaw; but their dentition is of a more generalized type, comprising the full series of 44 teeth, among which the incisors and canines are of normal form, but specially enlarged, and developing roots in the usual manner.
Qr,, be the generalized coordinates of any dynamical system, and let pi, P2,
The generalized formula is fxo u¢ (x)dx = Aq(xm) - where 0, A 2, ...
Wittich in 1584 made known at Cassel the calculation of one case by this prosthaphaeresis; and Justus Byrgius proved it in such a manner that from his proof the extension to the solution of all triangles could be deduced.3 Clavius generalized the method in his treatise De astrolabio (1593), lib.
Thus Huxley, with true prophetic instinct, found that the sum of primitive characters of all the higher placental mammals points to a stem form of a generalized insectivore type, a prophecy which has been fully confirmed by the latest research.
More or less independently, Huxley, Kowalevsky and Cope restored the stem ancestor of the hoofed animals, or ungulates, a restoration which has been nearly fulfilled by the discovery, in 1873, of the generalized type Phenacodus of northern Wyoming.
Thus the analysis of George Baur of the ancestral form of the lizards, mosasaurs, dinosaurs, crocodiles and phytosaurs led both to the generalized Palaeohatteria of the Permian and indirectly to the surviving Tuatera lizard of New Zealand.
In mammals Sir William Flower pointed out that a generalized type of liver exists, from which that of any mammal may be derived by suppression or fusion of lobes.
In tracing the lobulation of man's liver back to this generalized type, it is evident at once that his quadrate lobe does not correspond to any one generalized lobe, but is merely that part of the right central which lies between the gall bladder and the umbilical fissure.
Pology, Cambridge, 1904, p. 98), it is fairly clear that the human liver is formed, not by a suppression of any of the lobes of the generalized type, but by a fusion of those lobes and obliteration of certain fissures.
5) shows an abnormal human liver in the Anatomical Department of St Thomas's Hospital which reproduces the generalized type.
- Human Liver showing a the primate liver, and among reversion to the generalized mamother things suggests the remalian type.
The first figure is the generalized type, the second the male and the third the female specialized arrangements.
C. Pickering, generalized by T.
He generalized Weber's law in the form that sensation generally increases in intensity as the stimulus increases by a constant function of the previous stimulus; or increases in an arithmetical progression as the stimulus increases in a geometrical ratio; or increases by addition of the same amount as the stimulus increases by the same multiple; or increases as the logarithm of the stimulus.
But the question of knowledge was never generalized by them, and their reply to Hume, therefore, remains partial and inadequate, while its effect is weakened by the uncritical assumption of principles which is a characteristic feature of their writings.
Already before Alexander pan-hellenic feeling had in various ways overridden the internal divisions of the Greek race, but now, with the vast mingling of Greeks of all sorts in the newlyconquered lands, a generalized Greek culture in which the old local characteristics were merged, came to overspread the world.
In the order of human knowledge the particular facts of experience come first and are the basis of generalized laws or causes (the Scholastic notiora nobis); but in the order of nature the latter rank first as the self-existent, fundamental truths of existence (notiora naturae).
The result may be generalized into the statement that a frame has a critical form whenever a frame of the same structure can be designed with corresponding bars parallel, but without complete geometric similarity.
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.
In all, there is a wonderful amount of specialization, though perhaps in a very straight line from generalized forms; but the affinity to Australian or Polynesian types is in many cases clearly traceable, and it cannot be supposed but that these last are of cognate origin with those of New Zealand.
The generalized arrangement of the wing-nervure and the nature of the larva, which is less unlike the adult than in other beetles, distinguish this tribe as primitive, although the perfect insects are, in the more dominant families, distinctly specialized.
Many forms of animal sacrifice were found; the generalized account given above for Greece is true also for the Romans.
In the more generalized insects the abdomen evidently consists of ten segments, the hindmost of which often carries a pair of tail-feelers, (cerci or cercopods) and a terminal anal segment.
In generalized biting insects, such as cockroaches and locusts (Orthoptera), the parts of a typical maxilla can be easily recognized in the labium.
The head is usually connected with the thorax by a distinct membranous neck, strengthened in the more generalized orders with small chitinous plates (cervical sclerites).
Taken in connexion with the likeness of the young among the more generalized orders to the adults, it indicates clearly a thysanuroid starting-point for the evolution of the hexapod orders.
They could even discern dimly some generalized stock whence had descended whole groups that now differed strangely in habits and appearance - their discernment aided, may be, by some isolated form which yet retained undeniable traces of a primitive structure.
In the author's concluding summary he remarks on the fact that, while the Odontolcae, as exhibited in Hesperornis, had teeth inserted in a continuous groove - a low and generalized character as shown by reptiles, they had, however, the strongly differentiated saddle-shaped vertebrae such as all modern birds possess.
These observations were generalized by J.
In the case of general maps on a smaller scale, the orographic features must be generalized by a skilful draughtsman and artist.
The generalized view of angles and their measurement is treated in the article Trigonometry.
Thus the condition in the Dermaptera is more primitive than in any other Pterygote order except the Ephemeroptera (Mayflies) which are still more generalized, the primitive mesodermal ducts (oviducts and vasa deferentia) opening by paired apertures as in the Crustacea.
The groups of organisms utilized for zoning and correlation by different workers include brachiopods, pelecypods, cephalopods, corals, fishes and plants; and the results of the comparison of the faunas and floras of different areas where Carboniferous rocks occur are generalized in the table below.
Schlosser has described remains of a large camel-like animal from China, with apparently generalized affinities, for which the name of Paracamelus is proposed.
It should be added that this generalized animal is not unfrequently classed among the ancestral pigs, but its cameline affinities are strongly emphasized by Professor Scott.