Example sentences for "equations"

equate; equated; equates; equating; equation; equator; equatorial; eque; equerries; equerry

- 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. - He also detected singular solutions in differential
**equations**of the first order, and of the second and higher degrees. - 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
**equations**may with advantage be memorized, but this can soon be discontinued. - The nomenclature, symbols, and writing of
**equations**are made prominent features. - Compare these
**equations**with those for HNO3. - 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 for
**equations**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. - See the
**equations**for K{Base} and K{Acid}, on p. - The equilibrium
**equations**give us, thus, a comprehensive basis for the interpretation of the behavior of cyanide solutions containing silver. - The mathematical
**equations**give 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
**equations**is 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.