Locke, however, fails to " deduce " his categories.
This principle he endeavoured to deduce from his knowledge of geology, in contrast to Lorenz Oken, who developed the same theory on biological grounds.
From the former we deduce Ho, and from the latter the corresponding value of I, using the formulae Ho = 47rin/l and I - X s, (d (-- 11)2n7rr 2 i where s is the deflection in scale-divisions, n the distance in scaledivisions between the scale and the mirror, and r the radius of the wire.
Since the induction B is equal to H 47rI, it is easy from the results of experiments such as that just described to deduce the relation between B and H; a curve indicating such relation is called a curve of induction.
From this we can deduce successively X - 3s.= 26s., X= 29s.
Every orbit must clearly have a hodograph, and, conversely, every hodograph a corresponding orbit; and, theoretically speaking, it is possible to deduce the one from the other, having given the other circumstances of the motion.
Friar Odoric was despatched to the East, where a remarkable extension of missionary action was then taking place, about 1316-1318, and did not return till the end of 1329 or beginning of 1330; but, as regards intermediate dates, all that we can deduce from his narrative or other evidence is that he was in western India soon after 1321 (pretty certainly in 1322) and that he spent three years in China between the opening of 1323 and the close of 1328.
It is easy to deduce the modes of vibration from stationary waves as in the previous cases.
Hence if the readings of the verniers on the azimuth circle are made when the transit is observed we can deduce the reading corresponding to the geographical meridian.
The radical thought of this movement was voiced in the demand of Reinhold 2 that philosophy should " deduce " it all from a single principle and by a single method.
Coulomb, 2 however, by using long and thin steel rods, symmetrically magnetized, and so arranged that disturbing influences became negligibly small, was enabled to deduce from his experiments with reasonable certainty the law that the force of attraction or repulsion between two poles varies inversely as the square of the distance between them.
For instance, having found that (x+a)2=x2+2axda2, we can deduce that (x+b+c) 2 = }xd(b+c)}2=x2+2(b+c)x+ (b+c)2.
His principal discovery is concerned with equations, which he showed to be derived from the continued multiplication of as many simple factors as the highest power of the unknown, and he was thus enabled to deduce relations between the coefficients and various functions of the roots.
In the last resort, therefore, Spencer fails to deduce philosophically not only the necessity of progress, but also its compatibility with the evolution-dissolution oscillation, and even the general possibility of conceiving the world as a process.
We can deduce a remarkable expression for the energy stored up in an electric field containing electrified bodies as follows:' Let V denote the potential at any point in the field.
The value of the specific heat s at constant volume can also be measured in a few cases, but it is generally necessary to deduce it from that at constant pressure, by means of relation (6).
..) In order to deduce the complete variation of the specific heats from these equations, it is necessary to make some assumption with regard to the variation of the specific heats with temperature.
The height of the mercury in the wide tube and the top of f he narrow tube represents the pressure due to the mercury column, and this must be added to the barometric pressure in order to deduce the total pressure on the vapour.
He was a man of science - one who by the vigorous study of his subject matter sought from that subjectmatter itself to deduce laws.
But if complete, this Wissenschaftslehre must be able to deduce the whole organism of cognition from certain fundamental axioms, themselves unproved and incapable of proof; only thus can we have a system of reason.
The vibrations of certain sources of sound may be represented, at least as a first approximation, as consisting of stationary waves, and from a consideration of the rate of propagation of waves along these sources we can deduce their frequency when we know their length.
We shall deduce the modes of vibration of the air column in a cylindrical pipe from the consideration that the air in motion within the pipe forms some part of a system of stationary waves, one train being formed by the exciter of the disturbance, and the other being formed by the reflection of the train at the end of the pipe.
We shall then show that on certain limitations two trains of disturbance may be superposed so that stationary waves may be formed, and thence we shall deduce the modes of vibration as with pipes.
The historic frontiers of the Czechoslovak State it would indeed have been difficult, with justice, to deduce a right of self-determination, that is to say, the right, in this case, of retaining all the fruits of misused power.
From the formula for log e (p/q) we may deduce the following very convergent series for log e 2, log e 3 and log e 5, viz.: log e 2=2(7P +5Q +3R), log e 3 =2(11P+8Q +5R), log e 5=2(16P+12Q+7R), where P 1 +3?1) 3 5 s (31) &C.
Nor shall we stop here: but we shall further compare the readings of X and Y with each other and with those of A, and thus deduce the readings of a still more remote ancestor which we may call Z.
3), without pretending, like Plato, to deduce from any common principle the special principles of each science (Post.
Thus To Deduce The New Moon Of Tisri, For The Year Immediately Following Any Given Year (Y), When Y Is Ordinary, Subtract (1 1 °) Days 15 Hours Ii Min.
Before we deduce results from such abstract ideas as cause, substance, matter, we must ask what in reality do these mean - what is the actual content of consciousness which corresponds to these words?
Having thus confused contradiction and difference, independence and solitariness, experience and inference, Bradley is able to deduce finally that reality is not different substances, experienced and inferred, as Aristotle thought it, but is one absolute super-personal experience, to which the socalled plurality of things, including all bodies, all souls, and even a personal God, is appearance - an appearance, as ordinarily understood, self-contradictory, but, as appearing to one spiritual reality, somehow reconciled.
By the vibration experiment we obtain the value of the product of the magnetic moment (M) of the magnet into the horizontal component (H), while by the deflexion experiment we can deduce the value of the ratio of M to H, and hence the two combined give both M and H.
The more logical method of procedure is to determine the specific heat independently of the total heat, and then to deduce the variations of total heat by equation (52).
All this, however, must necessarily be of the nature of the purest speculation, and the only facts which we are able to deduce in the present state of our knowledge of the subject may be summed up as follows: (a) That the Malays ethnologically belong to a race which is allied to the Polynesians; (b) that the theory formerly current to the effect that the Sakai and other similar races of the peninsula and archipelago belonged to the Malayan stock cannot be maintained, since recent investigations tend to identify them with the Mon-Annam or Mon-Khmer family of races; (c) that the Malays are, comparatively speaking, newcomers in the lands which they now inhabit; (d) that it is almost certain that their emigration took place from the south; (e) and that, at some remote period of their history, they came into close contact with the Polynesian race, probably before its dispersion over the extensive area which it now occupies.
Whether we should deduce from its common occurrence in Babylonia the existence of an Elamite population there in early times, later displaced by the Sumerians, we do not know.
On the 2nd of February Loisy wrote to the archbishop: "I condemn, as a matter of course, all the errors which men have been able to deduce from my book, by placing themselves in interpreting it at a point of view entirely different from that which I had to occupy in composing it."
He attempts to grasp the national character as a whole, and thence to deduce practical conclusions.
Descartes's own attempts to deduce the different qualities and actions of bodies in this way are not of much value.
Finally, Schopenhauer's voluntarism has had a profound effect on psychology inside and outside Germany, and to a less degree produced attempts to deduce from voluntaristic psychology new systems of voluntaristic metaphysics, such as those of Paulsen and Wundt.
Both, however, used this influence freely; and, whereas Lotze used the Leibnitzian argument from indivisibility to deduce indivisible elements and souls, Fechner used the Leibnitzian hypotheses of universal perception and parallelism of motions and perceptions, in the light of the .Schellingian identification of physical and psychical, to evolve a world-view (Weltansicht) containing something which was neither Leibnitz nor Schelling.
By imagining that a dilute solution is put through a thermodynamic cycle we may deduce directly relations between its osmotic pressure and its freezing point.
The conceptions of osmotic pressure and ideal semi-permeable membranes enable us to deduce other thermodynamic relations between the different properties of solutions.
Recently Hermann Walther Nernst has been able to deduce the transitionpoint in the case of sulphur from the specific heat and the heat developed in the transition only.
After an analysis of the religious consciousness, which yields the doctrine of an absolute personal and spiritual God, Rothe proceeds to deduce from his idea of God the process and history of creative development, which is eternally proceeding and bringing forth, as its unending purpose, worlds of spirits, partially self-creative and sharing the absolute personality of the Creator.
Birkeland (19), who has made a special study of magnetic disturbances in the Arctic, proceeding on the hypothesis that they arise from electric currents in the atmosphere, and who has thence attempted to deduce the position and intensity of these currents, asserts that whilst in the case of many storms the data were insufficient, when it was possible to fix the position of the mean line of flow of the hypothetical current relatively to an auroral arc, he invariably found the directions coincident or nearly so.
It is not possible to deduce a more satisfactory value from the latent heat and the change of density, because these constants are very difficult to determine.
For only 88 of them has it been possible as yet to deduce a period, and at least half even of these periods are very doubtful.
Indeed, we often induce in order to deduce, ascending from particular to universal and descending from universal to particular in one act as it were; so that we may proceed either directly from particular to particular by analogical inference, or indirectly from particular through universal to particular by an inductivedeductive inference which might be called " perduction."
All M is P. Proceeding from one order to the other, by converting one of the premises, and substituting the conclusion as premise for the other premise, so as to deduce the latter as conclusion, is what he calls circular inference; and he remarked that the process is fallacious unless it contains propositions which are convertible, as in mathematical equations.
For example, as he says, the sphericity of the moon is the real ground of the fact of its light waxing; but we can deduce either from the other, as follows: - i.
Deduction is analysis when it is regressive from consequence to real ground, as when we start from the proposition that the angles of a triangle are equal to two right angles and deduce analytically that therefore (i) they are equal to equal angles made by a straight line standing on another straight line, and (2) such equal angles are two right angles.
Deduction is synthesis when it is progressive from real ground to consequence, as when we start from these two results of analysis as principles and deduce synthetically the proposition that therefore the angles of a triangle are equal to two right angles, in the order familiar to the student of Euclid.
Newton did indeed first show synthetically what kind of motions by mechanical laws have their ground in a centripetal force varying inversely as the square of the distance (all P is M); but his next step was, not to deduce synthetically the planetary motions, but to make a new start from the planetary motions as facts established by Kepler's laws and as examples of the kind of motions in question (all S is P); and then, by combining these two premises, one mechanical and the other astronomical, he analytically deduced that these facts of planetary motion have their ground in a centripetal force varying inversely as the squares of the distances of the planets from the sun (all S is M).
The result is that both Sigwart and Wundt transform the inductive process of adducing particular examples to induce a universal law into a deductive process of presupposing a universal law as a ground to deduce particular consequences.
Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.
Thus from P+Q - R+S=T we deduce P+(Q - R+S)=P+(T - P).