Square-root Sentence Examples

When the compass is far from the magnet, the vibrations will be comparatively slow; when it is near a pole, they will be exceedingly rapid, the frequency of the vibrations varying as the square root of the magnetic force at the spot.

The equation then becomes a 2 /V = k, or a = A / Vk, so that the molecular conductivity is proportional to the square root of the dilution.

In the case of the determinant of order 4 the square root is Al2A34 - A 13 A 24 +A14A23.

He then by means of a simple proportion deduced that log (I 00000 00000 00000 I)=o 00000 00000 00000 0 434 2 944 81 90325 1804, so that, a quantity 1.00000 00000 00000 x (where x consists of not more than seventeen figures) having been obtained by repeated extraction of the square root of a given number, the logarithm of I 00000 00000 00000 x could then be found by multiplying x by 00000 00000 00000 04342 To find the logarithm of 2, Briggs raised it to the tenth power, viz.

The quadratic mean of n quantities is the square root of the arithmetical mean of their squares.

If the effects depended merely on the velocity of translation of the molecules, both conductivity and viscosity should increase directly as the square root of the absolute temperature; but the mean free path also varies in a manner which cannot be predicted by theory and which appears to be different for different gases (Rayleigh, Proc. R.S., January 1896).

Snow-Harris found that this charge varied as the square root of the weight in the opposite pan, thus showing that the 1 It is probable that an experiment of this kind had been made as far back as 1746 by Daniel Gralath, of Danzig, who has some claims to have suggested the word " electrometer " in connexion with it.

For a given fluid and a given orifice the length is approximately proportional to the square root of the head.

The pitch of the note, though not absolutely definite, cannot differ much from that which corresponds to the division of the jet into wave-lengths of maximum instability; and, in fact, Savart found that the frequency was directly as the square root of the head, inversely as the diameter of the orifice, and independent of the nature of the fluid - laws which follow immediately from Plateau's theory.

The interval from one swelling to the next is the space described by the drop during one complete vibration,and is therefore (as Plateau shows) proportional ceteris paribus to the square root of the head.

The time of vibration is of course itself a function of the nature of the fluid and of the size of the drop. By the method of dimensions alone it may be seen that the time of infinitely small vibrations varies directly as the square root of the mass of the sphere and inversely as the square root of the capillary tension; and it may be proved that its expression is - V C?

In open places that height is seldom more than about one and a half times the square root of the " fetch " or greatest distance in nautical miles from which the wave has travelled to the point in question; but in narrow reaches or lakes it is relatively higher.

A number of this kind is called a surd; the surd which is the pth root of N is written ¦JN, but if the index is 2 it is usually omitted, so that the square root of N is written, /N.

Calculation of Square Root.-The calculation of the square root of a number depends on the formula (iii) of § 60.

If the complete square root is a+b, the remainder after subtracting a 2 is (2a+b)b.

If this is equal to the remainder, we have found the square root.

If the product is less than the remainder, we get a new remainder, which is N-(a+b) 2; we then assume the full square root to be c, so that the new remainder is equal to (2a+ 2b+c) c, and try to find c in the same way as we tried to find b.

To find a root other than a square root we can use logarithms, as explained in § 113.

Logarithms.-Multiplication, division, involution and evolution, when the results cannot be exact, are usually most simply performed, at any rate to a first approximation, by means of a table of logarithms. Thus, to find the square root of 2, we have log A /2 = log (21)=1 log 2.

And so if D =2, then the transformed curve is a nodal quartic; 4 can be expressed as the square root of a sextic function of 0 and the theorem is, that the co-ordinates x, y, z of a point of the tricursal curve can be expressed as proportional to rational and integral functions of 0, and of the square root of a sextic function of 0.

Observe that the radical, square root of a quartic function, is connected with the theory of elliptic functions, and the radical, square root of a sextic function, with that of the first kind of Abelian functions, but that the next kind of Abelian functions does not depend on the radical, square root of an octic function.

The singular value decomposition is given by where the columns of are orthonormal and is a diagonal square-root matrix.

The refractive index, n, is given by the square root of the relative dielectric permittivity, i.e. .

I'll have the square root of 2, then, please.

If EXPR is omitted, returns square root of $ _ .

The difference relates to the difference between average whole body SAR and peak spatial SAR (which involves the square root of 2 ).

And didn't they also have a great acronym that used great typography, including the signs for square root and the colon?

Torricelli, observing that in a jet where the water rushed through a small ajutage it rose to nearly the same height with the reservoir from which it was supplied, imagined that it ought to move with the same velocity as if it had fallen through that height by the force of gravity, and hence he deduced the proposition that the velocities of liquids are as the square root of the head, apart from the resistance of the air and the friction of the orifice.

If EXPR is omitted, returns square root of $ _.

The difference relates to the difference between average whole body SAR and peak spatial SAR (which involves the square root of 2).

The thermal G G detectors are especially useful for the purpose of quantitative measurements, because they indicate the true effective or square root of mean square value of the current or train of oscillations passing through the hot wire.

It is sometimes assumed that this is measured perfectly by the standard deviation,' which is obtained by taking the squares of the differences between the average and the individual prices, summing them and extracting the square root.

Since the current passing through the balance when equilibrium is obtained with a given weight is proportional to the square root of the couple due to this weight, it follows that the current strength when equilibrium is obtained is proportional to the product of the square root of the weight used and the square root of the displacement distance of this weight from its zero position.

Each instrument is accompanied by a pair of weights and by a square root table, so that the product of the square root of the number corresponding to the position of the sliding weight and the ascertained constant for each weight, gives at once the value of the current in amperes.

In the case of an axial moment, the square root of the resulting mean square is called the radius of gyration of the system about the axis in question.

If we imagine the current in the conductor to be instantaneously reversed in direction, the magnetic force surrounding it would not be instantly reversed everywhere in direction, but the reversal would be propagated outwards through space with a certain velocity which Maxwell showed was inversely as the square root of the product of the magnetic permeability and the dielectric constant or specific inductive capacity of the medium.