But Mayer did not adduce any fresh experimental evidence, and made no attempt to apply his theory to the fundamental equations of thermodynamics.
Helmholtz gives an admirable statement of the fundamental principle as applied to heat, but makes no attempt to formulate the correct equations of thermodynamics on the mechanical theory.
But he fails to notice that Holtzmann's equations are fundamentally inconsistent with the conservation of energy, because the heat equivalent of the external work done is supposed to remain in the gas.
His specimens are now in the Royal Scottish Museum at Edinburgh.
But he never forgot the while his Dutch origin or the models first presented to him by Schoreel and Mabuse.
Though insectivorous, the hedgehog is reported to have a liking for mice, while frogs and toads, as well as plants and fruits, all seem to be acceptable.
The day for a fuller investigation of this problem will partly depend upon the progress of the study of language in the direction marked out by W.
The upshot was that Hegel arrived at Jena in January 1801.
He was delighted with the varied play of the waterfalls, but no glamour blinded him to the squalor of Swiss peasant life.
In 1616 he collected his original Dutch poems into a volume.
But the characteristic feature of his studies was the copious extracts which from this time onward he unremittingly made and preserved.
After the countess's death the manor came to the hands of Edward I.
In any case the equations give a simple theoretical basis with which to compare experimental data in order to estimate the order of error involved in the assumptions.
Methods of obtaining such expansions for the solutions of linear differential equations of the second order were investigated by G.
The equations do this without expressing any conception, such as that of force, not associated with the actual phenomena.
In a case like the present one, where there are two differential equations of the second order, there will be four such constants.
Differential equations which express the changes of the co-ordinates are then constructed.
The theorems of motion just cited are expressed by seven integrals, or equations expressing a law that certain functions of the variables and of the time remain constant.
In the actual problems of celestial mechanics three co-ordinates necessarily enter, leading to three differential equations and six equations of solution.
Such equations can be formed for a system of any number of bodies, but the process of integration in a rigorous form is possible only to a limited extent or in special cases.
The general equations expressing the motion of a planet considered as a material particle round a centre of attraction lead to theorems the more interesting of which will now be enunciated.
This fact is fully expressed by the equations (4) where we have constants on one side of the equation equal to functions of the variables on the other.
The chaotic component captured and the necessity to visually display information as it changes over time are not reducible to equations or direct observation.
Meme mutation and spread of a reduced scale, such as the scale of finite artificial languages and limited logical rules, can be described in equations similar to those of genetics.
The equations of weather forecasting are obviously different from local observations of wind direction, precipitation, dew point, etc.
With Newton, equations started to replace words, and they became, almost to our time, the vocabulary of physics.
These equations show that the circles touch where they intersect the lines x squared + y squared = 0, i.
The equations to the chord, tangent and normal are readily derived by the ordinary methods.
In 1637, he invented analytic [Cartesian] geometry, in which lines and geometric shapes can be described by algebraic equations and vice-versa.
He used calculus and differential equations to determine centripetal forces of elliptical orbits, where the distance from the sun, the velocity, and the acceleration were variables.
For when, with respect to the equations of the centers, the moon shall be distant on the mechanism by a full semicircle from the sun (also in the heavens it will be truly in opposition to the sun) there will be a true full moon.
When the equations on the mechanism are examined, the sun and moon shall be found to be in the same degree of longitude, and in the same part of a degree.
Act of causing a quantity to disappear from an equation; especially, in the operation of deducing from several equations containing several unknown quantities a less number of equations containing a less number of unknown quantities.
From Poisson's equations Archibald Smith deduced the formulae given in the Admiralty Manual for Deviations of the Compass (1st ed.
If he tried to stand, the effort would surely interrupt his transmitting of equations and all the data he had not sent yet.
In the early stages of the work the equationsmay with advantage be memorized, but this can soon be discontinued.
The nomenclature, symbols, and writing ofequations are made prominent features.
The conclusion is true, but this is only because the equations are "homogeneous" (i.
In algebra he discovered the method of approximating to the real roots of an equation by means of continued fractions, and imagined a general process of solving algebraical equations of every degree.
The method indeed fails forequations of an order above the fourth, because it then involves the solution of an equation of higher dimensions than they proposed.
To Lagrange, perhaps more than to any other, the theory of differential equations is indebted for its position as a science, rather than a collection of ingenious artifices for the solution of particular problems.
Its scope may be briefly described as the reduction of the theory of mechanics to certain general formulae, from the simple development of which should be derived the equations necessary for the solution of each separate problem.
Laplace owned that he had despaired of effecting the integration of the differential equations relative to secular inequalities until Lagrange showed him the way.
Mr. Rooney, pander to the dull, conducted the class and smoked innumerable Pall Malls as he drew diagrams and worked equations from six in the morning until midnight.
He found it impossible to study conic sections; something in their calm and tantalizing respectability breathing defiantly through Mr. Rooney's fetid parlors distorted their equations into insoluble anagrams.
The equilibrium equations give us, thus, a comprehensive basis for the interpretation of the behavior of cyanide solutions containing silver.
The mathematical equationsgive us a measure of the extent to which water must decompose or ‹hydrolyze› the salt in question, as expressed in the chemical equations (p.
Similarly, the equations between the elements of phenomena express a universal, mathematically conceivable relation.
Instead of equations between the primitive variables, physics gives us, as much the easiest course, equations between functions of those variables.
The simple fact of change brings it about that the number of these equations must be smaller than the number of the [alpha beta gamma .
For the first, description by a system of differential equationsis sufficient; for the second, a gradual construction out of elementary laws is required.
The aim of research is the discovery of the equations which subsist between the elements of phenomena.
This kind of system can be represented crudely by an old-fashioned hourglass, as shown in the figure, which has the parameters of these equations marked.
It turns out to be a remarkable aspect of the Holmes-Houtermans calculation that the uranium-concentration terms cancel out in the equations and only the ratio of the isotopes and their decay constants need be considered.
In its ideal properties we find the means of determining the form of equations which are valid, and to the learned detached from all metaphysical prepossession this is the essential point.
Thus in all physical phenomena we should only have to regard the quantities of energy brought into play, and all the equations which link the phenomena to one another would have no meaning but when they apply to exchanges of energy.
It would not be impossible to link together all these phenomena without adopting the electronic hypothesis, by preserving the old optical equations as modified by the terms relating to the action of the magnetic field.
The coincidence of the formulas would thus be verified, for all the characteristic equations are symmetrical with regard to these two pressures.
You say Bobby knew all about these equations and diagrams and things.
Not to miss anything," he fumed and fretted over Maxwell's equations and made them part of the Dream and the Desire.
This motion is in exact accordance with the theoretical equations of the motion of a viscous fluid and constitutes almost a direct proof that the fundamental assumptions on which these equations are based are correct.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "equations" in a variety of sentences. We hope that you will now be able to make sentences using this word.
