Now, consider the values of these same variables expressing the position of the planet at a second point Q, and the speed with which it passes that point.
In all that precedes we have considered only two variables as determining the position of the planet, the latter being supposed to move in a plane.
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.
Functions of the variablespossessing this property of remaining constant are termed integrals.
In a word, although the position and speed of the planet and the direction of its motion are constantly changing, the values of the elements determined from these variables remain constant.
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.
We have supposed this to be done at a certain point P of the orbit, the direction and speed being expressed by the variables x, y, x' and y'.
Since the orbit is unchanged so long as no disturbing force acts, it follows that the elements determined by means of the two sets of values of the variables are in this case the same.
The number of known variables of the Algol type is, so far, small; not much indeed over thirty.
There may be two or more independent variables in an equation or problem.
A surface whose equation in three variables is of the second degree.
A function involving the coefficients and the variables of a quantic, and such that when the quantic is lineally transformed the same function of the new variables and coefficients shall be equal to the old function multiplied by a factor.
Dr Alexander Roberts, of Lovedale in Cape Colony, truly remarks that the study of Algol variables "brings us to the very threshold of the question of stellar evolution.
Such variables show regular or irregular periodic activity, and the independent actions as a whole result in the more-or-less variable annual schedule of breeding for any species at any one place.
This conclusion is warranted if we examine what would happen to frequency distributions if the variables or oscillators regulating timing were linked.
Let us assume that each of the environmental variablesis a nonlinear oscillator, as is probable.
This kind of response itself is evidence that most of the variables influencing the distribution are not mutually linked.
It would be useful at this point to examine how environmental variablesrelate to timing of breeding.
It is not hereby meant to ignore the fact that differential responses to dominant environmental variables occur within a species, indicating endogenous control over timing of breeding.
For some species in some situations major environmental variables are paramount in regulating timing of breeding, but in others the innate, regulatory "clock" is less closely tied to conspicuous exogenous stimuli.
This explanation it might have been difficult to receive, when the periods of the known variables were so markedly various in length.
The example of Mira Ceti and of other known variables makes this at least doubtful.
But as these Variables blow generally from the southward and westward, from a cause afterwards to be explained, it is obvious enough why this part of the homeward voyage is always more easily made than the outward passage.
Accordingly, analysts begin by dividing equations with one or more variables into two principal classes, according as they contain functions of only the first three couples (see the table in chapter i.
The integration of functions of several variables is much farther advanced in the case (infinitely more simple indeed) in which it has to do with only explicit differential formulas.
We evidently have to consider, for this purpose, only the functions of a single variable, since those relative to several independent variables are constantly, by their nature, more or less compound.
A catalogue of suspected variables has thus been prepared, doubtless containing many stars which are really important variables.
To observe all the long period variables once or twice every month throughout their variations according to such a system that all the observations may be reduced to the same absolute scale of magnitudes.
Doubtless many such so-called variables are really due to errors caused by moonlight, the proximity of brighter stars, varying position of the images on the retina of the observer, and other similar causes.
Awareness is not easily given to definition, having so many variables which shroud its very essence in obscurity.
The variables along the way would affect the resulting success or failure, but that, I knew, was simply a part of life's uncertainty.
This is particularly the case with those variables which are generally faint, but now and then flare up for a short time, after which temporary exaltation they again sink down to their original condition.
It was even possible that the star might be one of the large class of variables which alternate in brightness, and it might have been too faint to have been visible when the chart was made.
For example, in a one-dimensional system such as a string or a bar, we have one dependent variable, and two independent variables x and t.
These variables represent the whole assemblage of generalized co-ordinates qr; they are continuous functions of the independent variables x, y, z whose range of variation corresponds to that of the index r, and of t.
Let u be a function of several variables x1, x2, x3 .
The variables were our hope; without them the traverse would be maddeningly impossible.
In his passage between them in November, 1837, he had no variables near the line in coming south, and never could make easting on either tack, though he endeavoured by every means to do so.
The variables we encountered in 11° north latitude.
A more general problem of change of variables is presented when it is desired to express the partial differential coefficients of a function V with respect to x, y, .
New functions can be introduced also by means of the definite integrals of functions of two or more variables with respect to one of the variables, the limits of integration being fixed.
When there are more than two variables the multinomial theorem must be used instead of the binomial theorem.
Let u or [f](x, y) denote a function of two variables x and y.
The rule for a function of a function is not stated explicitly but is illustrated by examples in which new variables are introduced, in much the same way as in Newton's Methodus fluxionum.
Similar considerations are applicable to all cases in which n variables are connected by fewer than n equations.
Such variables as u, v are then described as "curvilinear coordinates" of the point.
It is necessary in the first place to determine the differential element expressed by the product of the differentials of the first set of variables in terms of the differentials of the second set of variables.
In the case of irrational functions, or rational functions which are not integral, new variables are introduced in such a way as to make the equations contain rational integral terms only.
In the case of a function of two variables x, y an abbreviated notation is often adopted for differential coefficients.
In other words, people have many utility functions running simultaneously - or, at best, one utility function with many variables and coefficients.
To isolate, observe and manipulate environmentalvariables and study human interactions.
A linear equation is a rational integral equation of the first degree in the dependent variable or variables and their derivatives.
Equations with several dependent variables occur in Elasticity, Electrodynamics, and Hydrodynamics.
It is difficult to withstand a suspicion that the three dimensions of space and the fourth dimension of time may be four independent variables of a system that is neither space nor time, but something else wholly unconceived by us.
There are too many variables in the environment to predict either incidence or severity of casualties.
Since there are many more possible attack variables than those considered, the guide presents a limited number of estimates and provisional guidance for estimating cases not modeled.
Since there are many more possible attack variables than those considered, the guide presents a limited number of estimates.
It will be recalled that the coefficient of correlation measures the resemblance between two variables on a scale between 0 and-1 or +1.
But a correlation is merely a statistical description of a particular case, and in some other population the same two variables might be correlated in a different way, other influences being at work on them.
Intelligence deals with the variables of life, leaving to instinct the basic reactions, but it is in these variables that intelligence meets situations that of themselves would end disastrously for the individual.
Native industry, the love of work arevariables of importance.
The capacity to enjoy music, especially the capacity to express it, is one of the great variables of life.
Out of this total number 509 were found to be variable; but the curious fact is, the extreme divergence in the proportion of variables to the whole number examined in the several clusters.
There are known at present twenty-two variables of the Algol type, that is, stars having each a dark companion very close to it which obscures it either wholly or partially during every revolution.
Roberts tells us that five out of these twenty-two variables revolve in absolute contact forming systems of the shape of a dumb-bell.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "variables" in a variety of sentences. We hope that you will now be able to make sentences using this word.
