We begin by deducing every well-known historical situation from the series of its antecedents.
(-) 5 + &c., in which the series is always convergent, so that the formula affords a method of deducing the logarithm of one number from that of another.
Deducing from the figures of production since 1859 an equation of increase, one finds that in each nine years as much oil has been produced as in all preceding years together, and in recent years the factor of increase has been higher.
The second question he answered from his parallelistic metaphysics by deducing that even within the organism there is only a constant dependency of sensation on nervous process without causation, because the nervous process is physical but the sensation psychical.
Green, on the other hand, in deducing his own conclusion that the world is, or is a system of, one eternal intelligence, incautiously put it forward as " what may be called broadly the Kantian view " (Prolegomena, § 36), and added that he follows Kant " in maintaining that a single active conscious principle, by whatever name it be called, is necessary to constitute such a world, as the condition under which alone phenomena, i.e.
Hall proposed to overcome this difficulty by coating the plate thickly with copper on both sides, and deducing the difference of temperature between the two surfaces of junction of the iron and the copper from the thermo-electric force observed by means of a number of fine copper wires attached to the copper coatings at different points of the disk.
The method of deducing the diffusivity from these curves is as follows: - The total quantity of heat absorbed by the soil per unit area of surface between any two dates, and any two depths, x' and x", is equal to c times the area included between the corresponding curves.
The gas current is simultaneously observed by a suitable meter, which, with subsidiary corrections for pressure, temperature, &c., gives the necessary data for deducing calorific value.
He re-defines analysis in the very opposite way to the ancients; whereas they defined it as a regressive process from consequence to ground, according to Wundt it is a progressive process of taking for granted a proposition and deducing a consequence, which being true verifies the proposition.
The method of deducing the specific heat from Regnault's formula for the variation of the total heat is evidently liable in a greater degree to the objections which have been urged against his method of determining the specific heat, since it makes the value of the specific heat depend on small differences of total heat observed under conditions of greater difficulty at various pressures.
Regnault's formula for the total heat is here again seen to be inadmissible, as it would make the latent heat of steam vanish at about 870° C. instead of at 365° C. It should be observed, however, that the assumptions made in deducing the above formulae apply only for moderate pressures, and that the formulae cannot be employed up to the critical point owing to the uncertainty of the variation of the specific heats and the cooling effect Q at high pressures beyond the experimental range.
Since it is much easier to measure p than either L or v, the relation has generally been employed for deducing either L or v from observations of p. For instance, it is usual to calculate the specific volumes of saturated steam by assuming Regnault's formulae for p and L.
Foster's pendulum-experiments, deducing from them an ellipticity for the earth of 2 9 (Memoirs R.
The true explanation of things was to be found, according to Strato, in the forces which produced their attributes, and he followed Aristotle in deducing all phenomena from the fundamental attributes or elements of heat and cold.
It is usually the case that the secondary caustic is easier to determine than the caustic, and hence, when determined, it affords a ready means for deducing, the primary caustic. It may be shown by geometrical considerations that the secondary caustic is a curve similar to the first positive pedal of the reflecting curve, of twice the linear dimensions, with respect to the luminous point.
Cauchy, and succeeded in deducing laws of double refraction closely resembling those of A.
The Arab astronomers measured a degree on the plains of Mesopotamia, thereby deducing a fair approximation to the size of the earth.
The best way of deducing r„ is to select portions of the dynamometer record where the speed is constant.
Ramus also set the modern fashion of deducing the figures from the position of the middle term in the premises, instead of basing them, as Aristotle does, upon the different relation of the middle to the so-called major and minor term.
It is not necessary to suppose that c varies inversely as the nth power of the temperature, and that b is constant, as assumed in deducing the expressions for cp, E, and F.
It is the first example in Italian literature of a national biography, the first attempt in any literature to trace the vicissitudes of a people's life in their logical sequence, deducing each successive phase from passions or necessities inherent in preceding circumstances, reasoning upon them from general principles, and inferring corollaries for the conduct of the future.
A good many years later he was entrusted by the committee of the British Association on standards of electric resist ance with the task of deducing the mechanical equivalent of heat from the thermal effects of electric currents.
It is curious, however, to find that an ancient nation of the East, so wise in geometrical proportions, should have followed what by modern experience may be regarded as an inverse method, that of obtaining a unit of length by deducing it through weights and cubic measure, rather than by deriving cubic measure through the unit of length.
De Chimie et de Physique, 1866-1868) applied the principles of thermodynamics to capillary phenomena, and the experiments of his son Paul were exceedingly ingenious and well devised, tracing the influence of surfacetension in a great number of very different circumstances, and deducing from independent methods the numerical value of the surface-tension.
There is no difficulty in deducing the highly differentiated asterids and ophiurids of a later day from these simpler types.
It was inevitable that, in proportion as this casuistry assumed the character of a systematic penal jurisprudence, its precise determination of the limits between the prohibited and the allowable, with all doubtful points closely scrutinized and illustrated by fictitious cases, would have a tendency to weaken the moral sensibilities of ordinary minds; the greater the industry spent in deducing conclusions from the diverse authorities, the greater necessarily became the number of points on which doctors disagreed; and the central authority that might have repressed serious divergences was wanting in the period of moral weakness'- that the church went through after the death of Boniface Viii.
Their art (disciplina) consisted especially in deducing the will of the gods from the appearance presented by the entrails of the slain victim.
To please the god, the victim must be without spot or blemish, and the practice of observing whether the entrails presented any abnormal appearance, and thence deducing the will of heaven, was also very important in Greek religion.
In his Discorso intorno alle cose the stanno su l'acqua, published in 1612, he used the principle of virtual velocities to demonstrate the more important theorems of hydrostatics, deducing from it the equilibrium of fluid in a siphon, and proved against the Aristotelians that the floating of solid bodies in a liquid depends not upon their form, but upon their specific gravities relative to such liquid.
His treatment is synthetic, and he follows his tutor and Pascal in deducing the properties of conics by projection from a circle.