When it comes to this, I shall prefer emigrating to some country where they make no pretence of loving liberty -- to Russia, for instance, where despotism can be taken pure, without the base alloy of hypocrisy '' ( His emphasis )

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

When the writer uses material does he tamper with it to improve its commercial effect or does he leave it pure??

When heavy metals or radionuclides form their own pure colloids, the term " Eigencolloid " is used to designate pure phases, e. g., Tc ( OH )< sub > 4 </ sub >, U ( OH )< sub > 4 </ sub >, Am ( OH )< sub > 3 </ sub >.

When metal ions are reduced from ionic solution, they form a pure metal surface on the cathode.

When a user changes to pure darknet operation, Freenet becomes very difficult to detect from the outside.

When jewelry containing diamonds is heated ( for repairs ) the diamond should be protected with boracic acid ; otherwise the diamond ( which is pure carbon ) could be burned on the surface or even burned completely up.

" When I came to eleven years of age ", he said, " I knew pureness and righteousness ; for, while I was a child, I was taught how to walk to be kept pure.

When a metal ore is an ionic compound of that metal and a non-metal, the ore must usually be smelted — heated with a reducing agent — to extract the pure metal.

When pure Python code is not fast enough, time-critical functions can be rewritten in " closer to the metal " languages such as C, or by translating ( a dialect of ) Python code to C code using tools like Cython.

When a mixed state has rank 1, it therefore describes a pure ensemble.

When crystalline, tellurium is silvery-white and when it is in pure state it has a metallic luster.

When it is a water-based cell, a special isotopic composition called VSMOW is used because it is very pure and produces temperatures that are more comparable from lab to lab.

When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.

When the input is a pure sine wave, the measurement is most commonly the ratio of the sum of the powers of all higher harmonic frequencies to the power at the first harmonic, or fundamental, frequency:

When struck, the bars give a very pure, bell-like sound.

When the system S is prepared in a pure state, it is associated with a vector in H. Measurable quantities are associated with Hermitian operators acting on H: these are referred to as observables.

When it became clear that Azar's unrelenting hatred towards pure monotheism would never be fought, Abraham dissociated himself from him.

When working under practical, everyday conditions, high-energy-resolution settings will produce peak widths ( FWHM ) between 0. 4 – 0. 6 eV for various pure elements and some compounds.

When she is finished, her plaid is pure white and snow covers the land.

When declaring him the second-scariest character on television ( behind only Mr. Burns of The Simpsons ) in 2005, MSNBC's Brian Bellmont described Cartman as a " bundle of pure, unadulterated evil all wrapped up in a fat — er, big-boned — cartoony package " who " takes a feral delight in his evildoing ".

Barnett also gives the text of a document from 1769 in the records of the Gilead Lutheran Church " When it had pleased the Almighty and Merciful God in His goodness to plant the Evangelical Lutheran Church in this American part of the world also, and especially in the State of New York, during the reign of Queen Anna, and also in this neighborhood and district called Hosek Road, in Rensselaerwyck, Albany County, then more than twenty years ago, a small body of adherents of the above said Lutheran church, disposed to that end did build and erect a prayer and church House to the Honor of God, and for their convenience, upon that lot of ground which our most worthy Patroon generously gave to promote and perpetuate the service of God and for the better maintenance of our preacher, for which purpose he presented us with a Deed of Gift which We acknowledge with heartfelt thanks towards our Good Lord in Heaven, and that in addition He grants us all hereabouts by His grace that we through the permission of the Government are allowed to carry on our pure Lutheran Church service free and without hindrance.

When pure elements are sintered, the leftover powder is still pure, so it can be recycled.

When a low stratiform cloud contacts the ground, it is called fog, although radiation and advection types of fog do not form from stratus layers.

When solving an equation that involves division as well as other steps, do all the division steps first to reduce those parts of the equation to their numerical value.

When these forces are added, the equation of motion has the form:

When calculating the difference in voltage, one must first manipulate the half-cell reactions to obtain a balanced oxidation-reduction equation.

When the flow is everywhere irrotational and inviscid, Bernoulli's equation can be used throughout the flow field.

A number a is a root of P if and only if the polynomial x − a ( of degree one in x ) divides P. It may happen that x − a divides P more than once: if ( x − a )< sup > 2 </ sup > divides P then a is called a multiple root of P, and otherwise a is called a simple root of P. If P is a nonzero polynomial, there is a highest power m such that ( x − a )< sup > m </ sup > divides P, which is called the multiplicity of the root a in P. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots: with the above definitions every number would be a root of the zero polynomial, with undefined ( or infinite ) multiplicity.

When proper units are used for tangential speed v, rotational speed ω, and radial distance r, the direct proportion of v to both r and ω becomes the exact equation:

When v is larger than c, the denominator in the equation for the energy is " imaginary ", as the value inside the square root is negative.

When Dutch physicist J. D. van der Waals received the 1910 Nobel Prize " for his work on the equation of state for gases and liquids " he acknowledged the great influence of Gibbs's work on that subject.

When Λ is zero, this reduces to the original field equation of general relativity.

When T is zero, the field equation describes empty space ( the vacuum ).

When comparing the predicted expansion rate of the universe as given by the tracker solutions with cosmological data, a main feature of tracker solutions is that one needs four parameters to properly describe the behavior of their equation of state, whereas it has been shown that at most a two-parameter model can optimally be constrained by mid-term future data ( horizon 2015-2020 ).

When solved for the diffracted angle maxima, the equation is:

When this condition is expressed in terms of probability densities, the result is called the Chapman – Kolmogorov equation.

When reactive elements such as capacitors, inductors, or transmission lines are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation, so Ohm's law ( as defined above ) does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance (" C ") or inductance (" L ").

# When the balanced equation for a reaction is multiplied by an integer, the corresponding value of ΔH must be multiplied by that integer as well.

When the circles are of equal size, the equation is much simpler, but it still can be solved only approximately.

When this is true the equation is said to obey the superposition principle.

When c is very large and psi is slowly varying so that the lattice can be thought of as a line, this becomes the free Schrödinger equation:

When the domain is the real numbers, this is Cauchy's functional equation.

When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and summing the solutions.

When the wavelength of a gravity wave is less than twice the depth of the ocean or lake its behavior is governed by the nonlinear Schrodinger equation and its speed is proportional to.

When the color is represented as RGB values, as often is the case in computer graphics, this equation is typically modeled separately for R, G and B intensities, allowing different reflections constants and for the different color channels.