In the second of these notices he gives the general formulae without demonstrations.
Though rejected by the Jesuits, who found peripatetic formulae a faithful weapon against the enemies of the church, Cartesianism was warmly adopted by the Oratory, which saw in Descartes something of St Augustine, by Port Royal, which discovered a connexion between the new system and Jansenism, and by some amongst the Benedictines and the order of Ste Genevieve.
Besides the logarithms and the calculating rods or bones, Napier's name is attached to certain rules and formulae in spherical trigonometry.
Constitutional formulae become of preponderating importance when we consider the more complicated inorganic and especially organic compounds.
The rules are curious and interesting, but of very doubtful utility, as the formulae are best remembered by the practical calculator in their unconnected form.
Is required for the successful application of definite formulae to the problem.
(16) All the above formulae refer to carriage stock.
He did not, however, confine himself to the consideration of forms involving only three indeterminates, but succeeded in establishing the principles on which the extension to the general case of n indeterminates depends, and obtained the general formulae, thus effecting what is probably the greatest advance made in the subject since the publication of Gauss's Disquisitiones arithmeticae.
It seems to have been common among the Jews, and the case of the witch of Endor is narrated in a way to suggest something beyond fraud; in the book of magic which bears the name of Dr Faustus may be found many of the formulae for raising demons; in England may be mentioned especially Dr Dee as one of the most famous of those who claimed before the days of modern spiritualism to have intercourse with the unseen world and to summon demons at his will.
Von Oppolzer's Lehrbuch zur Bahnbestimmung der Kometen and Planeten (2 vols.), which contains voluminous tables, formulae, and instructions for the computation of orbits in the many special cases that arise.
Its visible and religious forms then give way to abstract formulae, which in their turn are slowly replaced by the rational manifestation of the philosophic principles of law that gains the victory in the final stage of development, designated by Vico as that of civil and human law.
"Napier's rules of circular parts," which include the complete system of formulae for the solution of right-angled triangles, may be enunciated as follows.
The former contained 55, or, according to some formulae, 72 ingredients, and occurs in all the dispensatories, from that of Corvus Valerius up to the pharmacopoeias of the 19th century; and aromatic preparations of opium are still used, under the name of Theriaka in Persia.
The relative merits of the formulae of Kekule, Claus and Dewar were next investigated by means of the reduction products of benzene, it being Baeyer's intention to detect whether double linkages were or were not present in the benzene complex.
Thus the most prominent subdivision of the older school, the Taittiriyas, in their Samhita, have treated the main portion of the ceremonial in this promiscuous fashion, and to add to the confusion they have, by way of supplement, put forth a so-called Taittiriya-brahmana, which, so far from being a real Brahmana, merely deals with some additional rites in the same confused mixture of sacrificial formulae and dogmatic explanations.
The Pharmaceutical Society on the other hand has also published a Pharmaceutical Journal Formulary, including several hundred formulae of proprietary medicines sold by pharmacists, so that it is now possible for any medical man to ascertain what they contain.
The government accepts all the therein published formulae as " known, admitted and approved " remedies, and therefore not requiring a patent medicine stamp. In this way widely advertised secret remedies can be replaced by medicines of known composition and accepted value in any part of the world.
To these also belong the rite of wµoc¢ayta,and the communication of liturgical formulae for the guidance of the soul of the dead man on his way to the underworld, which also served as credentials to the gods below.
Formulae which merely express the relative number of atoms of the different elements present in a compound are termed empirical formulae, and the formulae of all compounds whose molecular weights are undetermined are necessarily empirical.
Before explaining these formulae it will be necessary, however, to consider the differences in combining power exhibited by the various elements.
The valency of an element is usually expressed by dashes or Roman numerals placed on the right of its symbol, thus: H', O", B"', C I ", P", mow; but in constructing graphic formulae the symbols of the elements are written with as many lines attached to each symbol as the element which it represents has units of affinity.
Thus acid sodium sulphate, normal sodium sulphate, and zinc sulphate have the formulae Na-0 O Na O, O O ¦ O H.o> S
Rational formulae of a much simpler description than these graphic formulae are generally employed.
(It will be noticed that Kolbe used the atomic weights H= 1, C=6, 0= 8, S = 16, &c.; his formulae, however, were molecular formulae, i.e.
For succinosuccinic ester, formed by the action of sodium on two molecules of succinic ester, has either of the formulae (I) or (II); oxidation of the free acid gives dioxyterephthalic acid in which the para-positions must remain substituted as in (I) and (II).
One of his earliest publications gave the complete theory and formulae of the phenomenon known as Brownian motion, which had puzzled physicists for nearly 80 years.
By combining the four symbols A, B, X, Y, according to their presence or absence, Garrod got a considerable number of formulae, each of which was overruled, so to speak, by the two categories of the presence or absence of the ambiens muscle.
1000 The Baldwin Locomotive Company give the formulae 0.565 r =3.36+ 3 and r z, = 1.68 +0.2245 for speeds from 47 to 77 m.
This paper of Thomson's, whose ideas Maxwell afterwards developed in an extraordinary manner, seems to have given the first hint that there are at least two perfectly distinct methods of arriving at the known formulae of statical electricity.
Ostwald has made the further proposal that the formulae of solids should be printed in heavy type (or within square brackets), of liquids (solutions, &c.) in ordinary type, and of gases in italics (or within curved brackets), so that the physical state of the substances 'might be indicated by the equation itself.
It is in fact one of the peculiarities of this theology, which professed to be at once churchly and philosophical, that most of its formulae could be interpreted and appreciated in utramque partem.
He admitted the possibility of the formulae of Kekule, Claus, Dewar and Ladenburg, although as to the last di-trimethylene derivatives should be possible reduction products, being formed by severing two of the prism edges; and he attempted to solve the problem by a systematic investigation of the reduced phthalic acids.
Simultaneously with the discussions of Kekule, Ladenburg, Claus, Baeyer and others as to the merits of various plane formulae of the benzene complex, there were published many suggestions with regard to the arrangement of the atoms in space, all of which attempted to explain the number of isomers and the equivalence of the hydrogen atoms. The development of stereo-isomerism at the hands of ' Victor Meyer and G.
Wislicenus, Le Bel and van 't Hoff has resulted in the introduction of another condition which formulae for the benzene complex must satisfy, viz.
Soc. Trans., p. 1013) considered in detail an octahedral form, and showed how by means of certain simple rotations of his system the formulae of Kekule and Claus could be obtained as projections.
Of the earlier suggestions for the constitution of naphthalene we notice the formulae of Wreden (1) and (2), Berthelot and Balls (3), R.
By continuing the introduction of methyl groups we obtain three series of homologous hydro carbons given by the general formulae CnH2,i 4.2, CnH2n, and CnH2n 2, each member differing from the preceding one of the same series by CH 2.
When chemical change is expressed with the aid of molecular formulae not only is the distribution of weight represented, but by the mere inspection of the symbols it is possible to deduce from the law of gaseous combination mentioned above, the relative volumes which the agents and resultants occupy in the state of gas if measured at the same temperature and under the same pressure.
But not only is the combining power or valency (atomicity) of the elements different, it is also observed that one element may combine with another in several proportions, or that its valency may vary; for example, phosphorus forms two chlorides represented by the formulae PC1 3 and PC1 51 nitrogen the series of oxides represented by the formulae N 2 0, NO, (N203), N 2 O 4, N205, molybdenum forms the chlorides MoC1 2, MoC1 3, MoC1 4, MoC1 5, MoCls(?), and tungsten the chlorides WC1 2, WCl 4, WC1 5, WC16.
It is not to be supposed that there are any actual bonds of union between the atoms; graphic formulae such as these merely express the hypothesis that certain of the atoms in a compound come directly within the sphere of attraction of certain other atoms, and only indirectly within the sphere of attraction of others, - an hypothesis to which chemists are led by observing that it is often possible to separate a group of elements from a compound, and to displace it by other elements or groups of elements.
This section treats of such subjects as nomenclature, formulae, chemical equations, chemical change and similar subjects.
In the development of the atomic theory and the deduction of the atomic weights of elements and the formulae of compounds, Dalton's arbitrary rules failed to find complete acceptance.