His expression was bewildered for only a fraction of a second, and then he made a face.
Which is satisfied by every symmetric fraction whose partition contains no unit (called by Cayley non-unitary symmetric functions), is of particular importance in algebraic theories.
Trade was therefore still a mere fraction of what it was before the war.
This ingenious operation widens the track at the expense of an unimportant fraction of its length.
Only an insignificant fraction of these forests has ever been visited by human beings, the Malays and even the aboriginal tribe having their homes on the banks of the rivers, and never, even when travelling from one part of the country to another, leaving the banks of a stream except for a short time when passing from one river-system to another.
- Only a mere fraction of the enormous literature dealing with the skeleton of birds can here be mentioned.
With this assumption, 0.06 is the fraction of the heat energy of the coal which is utilized in the engine cylinders as mechanical work; that is to say, of the 15,000 B.Th.U.
Between 40,000 and 50,000 species of Diptera are at present known, but these are only a fraction of those actually in existence.
A known fraction of the current is then indicated and measured.
In the case of ammeters intended for very small currents, the whole current can be sent through the coil, but for larger currents it is necessary to provide in the instrument a shunt which carries the main current, the movable coil being connected to the ends of this shunt so that it takes a definite small fraction of the current passed through the instrument.
Very convenient and accurate instruments based on the above principles have been devised by Lord Kelvin, and a large variety of these ampere balances, as they are called, suitable for measuring currents from a fraction of an ampere up to many thousands of amperes, have been constructed by that illustrious inventor.
It is shown in the article on Combinatorial Analysis that (w; 0,n) is the coefficient of a e z w in the ascending expansion of the fraction 1-a.
PHENANTHRENE, C14H10, a hydrocarbon isomeric with anthracene, with which it occurs in the fraction of the coal tar distillate boiling between 270°-400° C. It may be separated from the anthracene oil by repeated fractional distillation, followed by fractional crystallization from alcohol (anthracene being the less soluble), and finally purified by oxidizing any residual anthracene with potassium bichromate and sulphuric acid (R.
When we know the mass of the earth in gravitational measure, its product by the denominator of the fraction just mentioned gives the mass of the sun in gravitational measure.
Equations (33) and (34) show that when, as is generally the case with ferromagnetic substances, the value of is considerable, the resultant magnetic force is only a small fraction of the external force, while the numerical value of the induction is approximately three times that of the external force, and nearly independent of the permeability.
(vii.) The only exception that may be made to the above rule is that an expression involving multiplication-dots only, or a simple fraction written with the solidus, may have the brackets omitted for additions or subtractions, provided the figures are so spaced as to prevent misunderstanding.
It should be observed that, by analogy with the definition of a fraction, a P l q mean (al/q)P, not (aP)llq.
We thus express P=Q in the form of a continued fraction, k+ + I, which is usually written,for conciseness, k+ s + t + &c., s t+&c.
It is usual to write this as a fraction, inverting the order of the factors in the numerator.
- An equation may involve a fraction of the form Q, where Q involves x.
Wars in that same period—the most destructive wars in all of history—took a fraction of that number.
By such a study in the ultra-violet region of a fraction prepared from crude yttria he detected a new element victorium, and subsequently by elaborate fractionation obtained the element itself.
And that thence every symbolic product is equal to a rational function of covariants in the form of a fraction whose denominator is a power of f x.
For a series of experiments made with the same coil this fraction is constant, and we may write SB = kD.
The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being R = P/M = (B 2 -H2)/87-M, where M is Young's modulus.
Algebraic Forms; Binomial; Combinatorial Analysis; Determin Ants; Equation; Continued Fraction; Function; Theory of groups; Logarithm; Number; Probability; Series.
The information at the disposal of dealers has steadily enlarged in volume and improved in trustworthiness, though some of it is not yet invariably above suspicion, and the time elapsing between an event and the knowledge of it becoming common property has been reduced to a fraction of what it used to be, in consequence chiefly of the telegraph and cables.
The resistance of the microphone can thus be made a large fraction of the total resistance of the circuit in which it is placed; hence by using considerable currents, small variations in its resistance can be made to induce somewhat powerful currents in the line wire.
The average acceleration in feet per second is measured by the fraction Change of speed in feet per sec. 60.07-58.6 64 tons; and to obtain the horse-power the boiler will be one of the largest that can be built to the construction gauge.
All these substances exist as only a fraction of one part or, at most, a few parts, per million of water.
Of the calls originated at an exchange are for subscribers connected to other exchanges, and in these cases the junction plant forms a considerable fraction of the whole equipment.
I killed over a hundred of Sasha's creatures at the Arch with only a fraction of my power.
In an experiment on 3500 grams of paraffin produced from shale (melting point 44'5° C.) they obtained nearly 4 litres of liquid hydrocarbons, which they subjected to fractional distillation, and on examining the fraction distilling below loo° C., they found it to consist mainly of olefines.
1-az2....1-azn' Hence (w; 0, n) - (w - I; 0, n) is given by the coefficient of aez'° in the fraction 1-z 1 -a.1-az.
Farming will be done on such a scale that thousands of experiments can be happening at any one time, putting a tiny fraction of the produce at risk.
We can so determine these n covariants that every other covariant is expressed in terms of them by a fraction whose denominator is a power of the binary form.
Long known as the ruins of Santi Quaranta, and probably an emporium (according to Meomartini, the portion preserved is only a fraction of the whole, which once measured 1791 ft.
With wireless telegraph transmitters, in which the oscillatory discharge of a condenser is used to create oscillations in an antenna, labours under the disadvantage that the time occupied by the oscillations is a very small fraction of the total time of actuation.
Its principal commercial source is the fraction of coal-tar which distils between i 50 and 200° C., in which it was discovered in 1834 by F.
K= (I +2a)/(I -a), or a=(K-I)/(K+2), where K is the dielectric constant and a the fraction of the total volume actually occupied by matter.