These numbers constitute an arithmetical progression of the rth order.
The equivalent volumes and topic parameters are tabulated: From these figures it is obvious that the first three compounds form a morphotropic series; the equivalent volumes exhibit a regular progression; the values of x and t,t, corresponding to the a axes, are regularly increased, while the value of w, corresponding to the c axis, remains practically unchanged.
Of course there may be single taxes which are progressive in form, such as the licence tax in France, or the income tax in Great Britain, where progression is established by abatements, or the death duties, where progression by scale is very common.
It was early perceived by Huxley, Cope and many others that Cuvier's broad belief in a universal progression was erroneous, and there developed the distinction between " persistent primitive types " (Huxley) and " progressive types."
Every "line" of its build is designed and eminently adapted for rapid progression through the water; the muscles massed along the vertebral column are enormously developed, especially on the back and the sides of the tail, and impart to the body a certain rigidity which interferes with abruptly sideward motions of the fish.
" Now for the interpolation of the rest, I considered that the denominators I, 3, 5, &c., were in arithmetical progression; and that therefore only the numerical coefficients of the numerators were to be investigated.
Here the ordinary processes of nature and progression of the seasons were symbolized under the figure of the death and resuscitation of the god.
A 7; and from this we easily pass to the general formula for the sum of a geometrical progression having a given number of terms.
B = 2 (a+c); the geometrical mean b places a, b, c in geometrical progression, i.e.
The formula of Dalton would make the pressure increase in geometrical progression for equal increments of temperature.
Sombart (Der moderne Kapitalismus, 2 vols., Leipzig, 1902), have propounded the doctrine of one gradual progression from an agricultural state to modern capitalistic conditions.
If we wish the successive divisions of the scale to correspond to equal increments in the density of the corresponding liquids, then the volumes of the instrument, measured up to the successive divisions of the scale, must form a series in harmonical progression, the lengths of the divisions increasing as we go up the stem.
In the polypetalous forms progression from hypogyny to epigyny is generally recognized, and where dorsiventrality with insect-pollination has been established, a dominant group has been developed as in the Leguminosae.
A more detailed investigation of all the characters of the Ferns will be needed before the course of evolution thus broadly indicated can be traced, but the results obtained afford a deeper insight into the general method of progression and the selective factors in the process.
The sequence of orders in the polypetalous subdivision of Dicotyledons undoubtedly represents a progression from simpler to more elaborate forms, but a great drawback to the value of the system is the inclusion among the Monochlamydeae of a number of orders which are closely allied with orders of Polypetalae though differing in absence of a corolla.
By the waves of contraction executed by the proboscis accompanied by inflation of the collar, progression is effected, sometimes with marvellous rapidity.
The most famous outcome of his inquiries is the law known as Weber's or Fechner's law which may be expressed as follows:- "In order that the intensity of a sensation may increase in arithmetical progression, the stimulus must increase in geometrical progression."
On a long journey a horse should have occasional short drinks, and near the end a long drink with a slower rate of progression with the object of cooling off.
The teaching of history, during the three to four thousand years of which contemporary chronicles have been preserved, is that civilization is gradually developed in the course of ages by enlargement and increased precision of knowledge, invention and improvement of arts, and the progression of social and political habits and institutions towards general well-being.
The successive conjunctions following will be along CR 2, CS2, CQ3, &c., the law of progression being obvious.
14), and the presence of an anterior and posterior sucker, produce a looping mode of progression similar to that of a Geometrid larva.
In mathematics, he was the first to draw up a methodical treatment of mechanics with the aid of geometry; he first distinguished harmonic progression from arithmetical and geometrical progressions.
ï¿½ ï¿½ x0 yn ï¿½ This must not be confused with the use of suffixes to denote particular terms of a series or a progression (as in ï¿½ 41 (viii.) and (ix.)).
With slight powers of progression on the ground; the patagium or "flying-membrane" of some squirrels and of Galeopithecus probably indicates the way in which the modification was effected.
His universal process of Evolution seems to give Spencer a criterion of" higher "and" lower " progression "and" degeneration,"independent of the accidents of actual history, and unattainable by strictly Darwinian methods.
Now in order to [do] this, it appeared that in all the series the first term was x; that the second terms R- x 3 3x 3, 3x 3, &c., were in arithmetical progression; and consequently that the first two terms of all the series to be interpolated would be x-- 3, x- `3, x-- 3, &c.
These epistles took their form at once from a natural progression of thought and from a new phase of controversy, a sort of Gnosticizing theory, or theories, which perverted Christian practice and impaired the supremacy of Christ by placing other beings or entities by His side.
This table distinctly involves the principle of logarithms and may be described as a modified table of antilogarithms. It consists of two series of numbers, the one being an arithmetical and the other a geometrical progression: thus 0, 1,0000 0000 10, I,0001 0000 20, 1,0002 000 I 9 90, 1,0099 4967 In the arithmetical column the numbers increase by io, in the geometrical column each number is derived from its predecessor by multiplication by i 0001.
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.
As a matter of fact, as far as modern Europe is concerned, there has twice been a progression, separated by a period of retrogression, and it is to the latter that Bucher's picture of the agricultural and strictly protectionist town (the geschlossene Stadtwirtschaft) of the 14th and r 5th centuries belongs, while Sombart's notion of an entire absence of a spirit of capitalistic enterprise before the middle of the 15th century in Europe north of the Alps, or the 14th.
Rapid progression is, however, performed only by the powerful hind-limbs, the animals covering the ground by a series of immense bounds, during which the fore part of the body is inclined forwards, and balanced by the long, strong and tapering tail, which is carried horizontally backwards.
The two modes of progression overlap in human life, but the child's tendency when learning is to rest on the soles of the feet and the palms of the hands, unlike the apes, which support themselves on the sides of the feet and the bent knuckles of the hands.
But such progression may arise in a different way and on different principles from those proposed in defence of a general system of progressive taxation.
Oedogonium, Coleochaete), the Bryophyta, and the simpler Pteridophyta, such as Phylloglossum, have been regarded as illustrating the method of progression, though there is no reason to regard the existing forms as constituting an actual series.
Added to this the spiders commonly copy to the life the mode of progression and the restless activities of their models.
The anatomy of the stele in the stem exhibits on the whole a progression from a solid protostele through a tubular solenostele to one or more circles of separate steles derived by the breaking up of the solenostele.
This ring serves both for progression and for bringing up food.
For, if the members of a natural kind had no common idea to unite them, scientific research, having nothing objective in view, could at best afford a Aoyos or definition of the appropriate particulars; and, as the discrimination of the One and the Good implied the progression of particulars towards perfection, such a Xbyos or definition could have only a temporary value.
As a believer in the progression of the human race, he placed the principle of moral approbation in the attainment of perfection.
The rhythm of his strokes felt good too, an order, a progression, a logical sequence, straight and definite.
Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem.