CHAPTER V.Analysis of the Process of Induction.AphorismXXXIV.The Process of Induction may be resolved into three steps; theSelection of the Idea,theConstruction of the Conception,and theDetermination of the Magnitudes.AphorismXXXV.These three steps correspond to the determination of theIndependent Variable,theFormula,and theCoefficients,in mathematical investigations; or to theArgument,theLaw,and theNumerical Data,in a Table of an astronomical or otherInequality.AphorismXXXVI.The Selection of the Idea depends mainly upon inventive sagacity: which operates by suggesting and trying various hypotheses. Some inquirers try erroneous hypotheses; and thus, exhausting the forms of errour, form the Prelude to Discovery.AphorismXXXVII.The following Rules may be given, in order to the selection of the Idea for purposes of Induction:—the Idea and the Facts must behomogeneous;and the Rule must betested by the Facts.Sect. I.—The Three Steps of Induction.1.WHEN facts have been decomposed and phenomena measured, the philosopher endeavours to combine them into general laws, by the aid of187Ideas and Conceptions; these being illustrated and regulated by such means as we have spoken of in the last two chapters. In this task, of gathering laws of nature from observed facts, as we have already said24, the natural sagacity of gifted minds is the power by which the greater part of the successful results have been obtained; and this power will probably always be more efficacious than any Method can be. Still there are certain methods of procedure which may, in such investigations, give us no inconsiderable aid, and these I shall endeavour to expound.24B. ii. c. vi.2. For this purpose, I remark that the Colligation of ascertained Facts into general Propositions may be considered as containing three steps, which I shall term theSelection of the Idea,the Construction of the Conception, andthe Determination of the Magnitudes. It will be recollected that by the wordIdea, (or Fundamental Idea,) used in a peculiar sense, I mean certain wide and general fields of intelligible relation, such as Space, Number, Cause, Likeness; while byConceptionI denote more special modifications of these ideas, as acircle, asquare number, auniform force, alike formof flower. Now in order to establish any law by reference to facts, we must select thetrue Ideaand thetrue Conception. For example; when Hipparchus found25that the distance of the bright star Spica Virginis from the equinoxial point had increased by two degrees in about two hundred years, and desired to reduce this change to a law, he had first to assign, if possible, theideaon which it depended;—whether it was regulated for instance, byspace, or bytime; whether it was determined by the positions of other stars at each moment, or went on progressively with the lapse of ages. And when there was found reason to selecttimeas the regulativeideaof this change, it was then to be determined how the change went on with the time;—whether uniformly, or in some other manner: theconception, or the rule of the progression, was to be188rightly constructed. Finally, it being ascertained that the change did go on uniformly, the question then occurred what was itsamount:—whether exactly a degree in a century, or more, or less, and how much: and thus the determination of themagnitudecompleted the discovery of the law of phenomena respecting this star.25Hist. Ind. Sc.b. iii. c. iv. sect. 3.3. Steps similar to these three may be discerned in all other discoveries of laws of nature. Thus, in investigating the laws of the motions of the sun, moon or planets, we find that these motions may be resolved, besides a uniform motion, into a series of partial motions, or Inequalities; and for each of these Inequalities, we have to learn upon what it directly depends, whether upon the progress of time only, or upon some configuration of the heavenly bodies in space; then, we have to ascertain its law; and finally, we have to determine what is its amount. In the case of such Inequalities, the fundamental element on which the Inequality depends, is called by mathematicians theArgument. And when the Inequality has been fully reduced to known rules, and expressed in the form of a Table, the Argument is the fundamental Series of Numbers which stands in the margin of the Table, and by means of which we refer to the other Numbers which express the Inequality. Thus, in order to obtain from a Solar Table the Inequality of the sun’s annual motion, the Argument is the Number which expresses the day of the year; the Inequalities for each day being (in the Table) ranged in a line corresponding to the days. Moreover, the Argument of an Inequality being assumed to be known, we must, in order to calculate the Table, that is, in order to exhibit the law of nature, know also theLawof the Inequality, and itsAmount. And the investigation of these three things, the Argument, the Law, and the Amount of the Inequality, represents the three steps above described, the Selection of the Idea, the Construction of the Conception, and the Determination of the Magnitude.4. In a great body of cases,mathematicallanguage and calculation are used to express the connexion189between the general law and the special facts. And when this is done, the three steps above described may be spoken of as the Selection of theIndependent Variable, the Construction of theFormula, and the Determination of theCoefficients. It may be worth our while to attend to an exemplification of this. Suppose then, that, in such observations as we have just spoken of, namely, the shifting of a star from its place in the heavens by an unknown law, astronomers had, at the end of three successive years, found that the star had removed by 3, by 8, and by 15 minutes from its original place. Suppose it to be ascertained also, by methods of which we shall hereafter treat, that this change depends upon the time; we must then take thetime, (which we may denote by the symbolt,) for theindependent variable. But though the star changes its placewiththe time, the change is notproportionalto the time; for its motion which is only 3 minutes in the first year, is 5 minutes in the second year, and 7 in the third. But it is not difficult for a person a little versed in mathematics to perceive that the series 3, 8, 15, may be obtained by means of two terms, one of which is proportional to the time, and the other to the square of the time; that is, it is expressed by theformula at + btt. The question then occurs, what are the values of thecoefficientsaandb; and a little examination of the case shows us thatamust be 2, andb, 1: so that the formula is 2t+tt. Indeed if we add together the series 2, 4, 6, which expresses a change proportional to the time, and 1, 4, 9, which is proportional to the square of the time, we obtain the series 3, 8, 15, which is the series of numbers given by observation. And thus the three steps which give us the Idea, the Conception, and the Magnitudes; or the Argument, the Law, and the Amount, of the change; give us the Independent Variable, the Formula, and the Coefficients, respectively.We now proceed to offer some suggestions of methods by which each of these steps may be in some degree promoted.190Sect. II.—Of the Selection of the Fundamental Idea.5. When we turn our thoughts upon any assemblage of facts, with a view of collecting from them some connexion or law, the most important step, and at the same time that in which rules can least aid us, is the Selection of the Idea by which they are to be collected. So long as this idea has not been detected, all seems to be hopeless confusion or insulated facts; when the connecting idea has been caught sight of, we constantly regard the facts with reference to their connexion, and wonder that it should be possible for any one to consider them in any other point of view.Thus the different seasons, and the various aspects of the heavenly bodies, might at first appear to be direct manifestations from some superior power, which man could not even understand: but it was soon found that the ideas of time and space, of motion and recurrence, would give coherency to many of the phenomena. Yet this took place by successive steps. Eclipses, for a long period, seemed to follow no law; and being very remarkable events, continued to be deemed the indications of a supernatural will, after the common motions of the heavens were seen to be governed by relations of time and space. At length, however, the Chaldeans discovered that, after a period of eighteen years, similar sets of eclipses recur; and, thus selecting the idea oftime, simply, as that to which these events were to be referred, they were able to reduce them to rule; and from that time, eclipses were recognized as parts of a regular order of things. We may, in the same manner, consider any other course of events, and may enquire by what idea they are bound together. For example, if we take the weather, years peculiarly wet or dry, hot and cold, productive and unproductive, follow each other in a manner which, at first sight at least, seems utterly lawless and irregular. Now can we in any way discover some rule and order in these occurrences? Is there, for example, in these events, as in eclipses, a certain cycle of years, after which like191seasons come round again? or does the weather depend upon the force of some extraneous body—for instance, the moon—and follow in some way her aspects? or would the most proper way of investigating this subject be to consider the effect of the moisture and heat of various tracts of the earth’s surface upon the ambient air? It is at our choice totrythese and other modes of obtaining a science of the weather: that is, we may refer the phenomena to the idea oftime, introducing the conception of a cycle;—or to the idea of externalforce, by the conception of the moon’s action;—or to the idea ofmutual action, introducing the conceptions of thermotical and atmological agencies, operating between different regions of earth, water, and air.6. It may be asked, How are we to decide in such alternatives? How are we to select the one right idea out of several conceivable ones? To which we can only reply, that this must be done bytryingwhich will succeed. If there really exist a cycle of the weather, as well as of eclipses, this must be established by comparing the asserted cycle with a good register of the seasons, of sufficient extent. Or if the moon really influence the meteorological conditions of the air, the asserted influence must be compared with the observed facts, and so accepted or rejected. When Hipparchus had observed the increase of longitude of the stars, the idea of a motion of the celestial sphere suggested itself as the explanation of the change; but this thought wasverifiedonly by observing several stars. It was conceivable that each star should have an independent motion, governed by time only, or by other circumstances, instead of being regulated by its place in the sphere; and this possibility could be rejected by trial alone. In like manner, the original opinion of the composition of bodies supposed the compounds to derive their properties from the elements according to the law oflikeness; but this opinion was overturned by a thousand facts; and thus the really applicable Idea of Chemical Composition was introduced in modern times. In what has already been said on the History of Ideas, we have seen how each science was in a state192of confusion and darkness till the right idea was introduced.7. No general method of evolving such ideas can be given. Such events appear to result from a peculiar sagacity and felicity of mind;—never without labour, never without preparation;—yet with no constant dependence upon preparation, or upon labour, or even entirely upon personal endowments. Newton explained the colours which refraction produces, by referring each colour to a peculiarangle of refraction, thus introducing the right idea. But when the same philosopher tried to explain the colours produced by diffraction, he erred, by attempting to apply the same idea, (the course of a single ray,) instead of applying the truer idea, of theinterference of two rays. Newton gave a wrong rule for the double refraction of Iceland spar, by making the refraction depend on theedgesof the rhombohedron: Huyghens, more happy, introduced the idea of theaxis of symmetryof the solid, and thus was able to give the true law of the phenomena.8. Although the selected idea is proved to be the right one, only when the true law of nature is established by means of it, yet it often happens that there prevails a settled conviction respecting the relation which must afford the key to the phenomena, before the selection has been confirmed by the laws to which it leads. Even before the empirical laws of the tides were made out, it was not doubtful that these laws depended upon the places and motions of the sun and moon. We know that the crystalline form of a body must depend upon its chemical composition, though we are as yet unable to assign the law of this dependence.Indeed in most cases of great discoveries, the right idea to which the facts were to be referred, was selected by many philosophers, before the decisive demonstration that it was the right idea, was given by the discoverer. Thus Newton showed that the motions of the planets might be explained by means of a central force in the sun: but though he established, he did not first select the idea involved in the conception of a193central force. The idea had already been sufficiently pointed out, dimly by Kepler, more clearly by Borelli, Huyghens, Wren, and Hooke. Indeed this anticipation of the true idea is always a principal part of that which, in theHistory of the Sciences, we have termed thePreludeof a Discovery. The two steps ofproposinga philosophical problem, and ofsolvingit, are, as we have elsewhere said, both important, and are often performed by different persons. The former step is, in fact, the Selection of the Idea. In explaining any change, we have to discover first theArgument, and then theLawof the change. The selection of the Argument is the step of which we here speak; and is that in which inventiveness of mind and justness of thought are mainly shown.9. Although, as we have said, we can give few precise directions for this cardinal process, the Selection of the Idea, in speculating on phenomena, yet there is one Rule which may have its use: it is this:—The idea and the facts must be homogeneous: the elementary Conceptions, into which the facts have been decomposed, must be of the same nature as the Idea by which we attempt to collect them into laws. Thus, if facts have been observed and measured by reference to space, they must be bound together by the idea of space: if we would obtain a knowledge of mechanical forces in the solar system, we must observe mechanical phenomena. Kepler erred against this rule in his attempts at obtaining physical laws of the system; for the facts which he took were thevelocities, not thechanges of velocity, which are really the mechanical facts. Again, there has been a transgression of this Rule committed by all chemical philosophers who have attempted to assign the relative position of the elementary particles of bodies in their component molecules. For their purpose has been to discover therelationsof the particles inspace; and yet they have neglected the only facts in the constitution of bodies which have a reference to space—namely,crystalline form, andoptical properties. No progress can be made in the theory of the elementary structure of bodies,194without making these classes of facts the main basis of our speculations.10. The only other Rule which I have to offer on this subject, is that which I have already given:—the Idea must be tested by the facts. It must be tried by applying to the facts the conceptions which are derived from the idea, and not accepted till some of these succeed in giving the law of the phenomena. The justice of the suggestion cannot be known otherwise than by making the trial. If we can discover atrue lawby employing any conceptions, the idea from which these conceptions are derived is therightone; nor can there be any proof of its rightness so complete and satisfactory, as that we are by it led to a solid and permanent truth.This, however, can hardly be termed a Rule; for when we would know, to conjecture and to try the truth of our conjecture by a comparison with the facts, is the natural and obvious dictate of common sense.Supposing the Idea which we adopt, or which we would try, to be now fixed upon, we still have before us the range of many Conceptions derived from it; many Formulæ may be devised depending on the same Independent Variable, and we must now consider how our selection among these is to be made.
CHAPTER V.Analysis of the Process of Induction.
AphorismXXXIV.
The Process of Induction may be resolved into three steps; theSelection of the Idea,theConstruction of the Conception,and theDetermination of the Magnitudes.
AphorismXXXV.
These three steps correspond to the determination of theIndependent Variable,theFormula,and theCoefficients,in mathematical investigations; or to theArgument,theLaw,and theNumerical Data,in a Table of an astronomical or otherInequality.
AphorismXXXVI.
The Selection of the Idea depends mainly upon inventive sagacity: which operates by suggesting and trying various hypotheses. Some inquirers try erroneous hypotheses; and thus, exhausting the forms of errour, form the Prelude to Discovery.
AphorismXXXVII.
The following Rules may be given, in order to the selection of the Idea for purposes of Induction:—the Idea and the Facts must behomogeneous;and the Rule must betested by the Facts.
Sect. I.—The Three Steps of Induction.
1.WHEN facts have been decomposed and phenomena measured, the philosopher endeavours to combine them into general laws, by the aid of187Ideas and Conceptions; these being illustrated and regulated by such means as we have spoken of in the last two chapters. In this task, of gathering laws of nature from observed facts, as we have already said24, the natural sagacity of gifted minds is the power by which the greater part of the successful results have been obtained; and this power will probably always be more efficacious than any Method can be. Still there are certain methods of procedure which may, in such investigations, give us no inconsiderable aid, and these I shall endeavour to expound.
24B. ii. c. vi.
2. For this purpose, I remark that the Colligation of ascertained Facts into general Propositions may be considered as containing three steps, which I shall term theSelection of the Idea,the Construction of the Conception, andthe Determination of the Magnitudes. It will be recollected that by the wordIdea, (or Fundamental Idea,) used in a peculiar sense, I mean certain wide and general fields of intelligible relation, such as Space, Number, Cause, Likeness; while byConceptionI denote more special modifications of these ideas, as acircle, asquare number, auniform force, alike formof flower. Now in order to establish any law by reference to facts, we must select thetrue Ideaand thetrue Conception. For example; when Hipparchus found25that the distance of the bright star Spica Virginis from the equinoxial point had increased by two degrees in about two hundred years, and desired to reduce this change to a law, he had first to assign, if possible, theideaon which it depended;—whether it was regulated for instance, byspace, or bytime; whether it was determined by the positions of other stars at each moment, or went on progressively with the lapse of ages. And when there was found reason to selecttimeas the regulativeideaof this change, it was then to be determined how the change went on with the time;—whether uniformly, or in some other manner: theconception, or the rule of the progression, was to be188rightly constructed. Finally, it being ascertained that the change did go on uniformly, the question then occurred what was itsamount:—whether exactly a degree in a century, or more, or less, and how much: and thus the determination of themagnitudecompleted the discovery of the law of phenomena respecting this star.
25Hist. Ind. Sc.b. iii. c. iv. sect. 3.
3. Steps similar to these three may be discerned in all other discoveries of laws of nature. Thus, in investigating the laws of the motions of the sun, moon or planets, we find that these motions may be resolved, besides a uniform motion, into a series of partial motions, or Inequalities; and for each of these Inequalities, we have to learn upon what it directly depends, whether upon the progress of time only, or upon some configuration of the heavenly bodies in space; then, we have to ascertain its law; and finally, we have to determine what is its amount. In the case of such Inequalities, the fundamental element on which the Inequality depends, is called by mathematicians theArgument. And when the Inequality has been fully reduced to known rules, and expressed in the form of a Table, the Argument is the fundamental Series of Numbers which stands in the margin of the Table, and by means of which we refer to the other Numbers which express the Inequality. Thus, in order to obtain from a Solar Table the Inequality of the sun’s annual motion, the Argument is the Number which expresses the day of the year; the Inequalities for each day being (in the Table) ranged in a line corresponding to the days. Moreover, the Argument of an Inequality being assumed to be known, we must, in order to calculate the Table, that is, in order to exhibit the law of nature, know also theLawof the Inequality, and itsAmount. And the investigation of these three things, the Argument, the Law, and the Amount of the Inequality, represents the three steps above described, the Selection of the Idea, the Construction of the Conception, and the Determination of the Magnitude.
4. In a great body of cases,mathematicallanguage and calculation are used to express the connexion189between the general law and the special facts. And when this is done, the three steps above described may be spoken of as the Selection of theIndependent Variable, the Construction of theFormula, and the Determination of theCoefficients. It may be worth our while to attend to an exemplification of this. Suppose then, that, in such observations as we have just spoken of, namely, the shifting of a star from its place in the heavens by an unknown law, astronomers had, at the end of three successive years, found that the star had removed by 3, by 8, and by 15 minutes from its original place. Suppose it to be ascertained also, by methods of which we shall hereafter treat, that this change depends upon the time; we must then take thetime, (which we may denote by the symbolt,) for theindependent variable. But though the star changes its placewiththe time, the change is notproportionalto the time; for its motion which is only 3 minutes in the first year, is 5 minutes in the second year, and 7 in the third. But it is not difficult for a person a little versed in mathematics to perceive that the series 3, 8, 15, may be obtained by means of two terms, one of which is proportional to the time, and the other to the square of the time; that is, it is expressed by theformula at + btt. The question then occurs, what are the values of thecoefficientsaandb; and a little examination of the case shows us thatamust be 2, andb, 1: so that the formula is 2t+tt. Indeed if we add together the series 2, 4, 6, which expresses a change proportional to the time, and 1, 4, 9, which is proportional to the square of the time, we obtain the series 3, 8, 15, which is the series of numbers given by observation. And thus the three steps which give us the Idea, the Conception, and the Magnitudes; or the Argument, the Law, and the Amount, of the change; give us the Independent Variable, the Formula, and the Coefficients, respectively.
We now proceed to offer some suggestions of methods by which each of these steps may be in some degree promoted.190
Sect. II.—Of the Selection of the Fundamental Idea.
5. When we turn our thoughts upon any assemblage of facts, with a view of collecting from them some connexion or law, the most important step, and at the same time that in which rules can least aid us, is the Selection of the Idea by which they are to be collected. So long as this idea has not been detected, all seems to be hopeless confusion or insulated facts; when the connecting idea has been caught sight of, we constantly regard the facts with reference to their connexion, and wonder that it should be possible for any one to consider them in any other point of view.
Thus the different seasons, and the various aspects of the heavenly bodies, might at first appear to be direct manifestations from some superior power, which man could not even understand: but it was soon found that the ideas of time and space, of motion and recurrence, would give coherency to many of the phenomena. Yet this took place by successive steps. Eclipses, for a long period, seemed to follow no law; and being very remarkable events, continued to be deemed the indications of a supernatural will, after the common motions of the heavens were seen to be governed by relations of time and space. At length, however, the Chaldeans discovered that, after a period of eighteen years, similar sets of eclipses recur; and, thus selecting the idea oftime, simply, as that to which these events were to be referred, they were able to reduce them to rule; and from that time, eclipses were recognized as parts of a regular order of things. We may, in the same manner, consider any other course of events, and may enquire by what idea they are bound together. For example, if we take the weather, years peculiarly wet or dry, hot and cold, productive and unproductive, follow each other in a manner which, at first sight at least, seems utterly lawless and irregular. Now can we in any way discover some rule and order in these occurrences? Is there, for example, in these events, as in eclipses, a certain cycle of years, after which like191seasons come round again? or does the weather depend upon the force of some extraneous body—for instance, the moon—and follow in some way her aspects? or would the most proper way of investigating this subject be to consider the effect of the moisture and heat of various tracts of the earth’s surface upon the ambient air? It is at our choice totrythese and other modes of obtaining a science of the weather: that is, we may refer the phenomena to the idea oftime, introducing the conception of a cycle;—or to the idea of externalforce, by the conception of the moon’s action;—or to the idea ofmutual action, introducing the conceptions of thermotical and atmological agencies, operating between different regions of earth, water, and air.
6. It may be asked, How are we to decide in such alternatives? How are we to select the one right idea out of several conceivable ones? To which we can only reply, that this must be done bytryingwhich will succeed. If there really exist a cycle of the weather, as well as of eclipses, this must be established by comparing the asserted cycle with a good register of the seasons, of sufficient extent. Or if the moon really influence the meteorological conditions of the air, the asserted influence must be compared with the observed facts, and so accepted or rejected. When Hipparchus had observed the increase of longitude of the stars, the idea of a motion of the celestial sphere suggested itself as the explanation of the change; but this thought wasverifiedonly by observing several stars. It was conceivable that each star should have an independent motion, governed by time only, or by other circumstances, instead of being regulated by its place in the sphere; and this possibility could be rejected by trial alone. In like manner, the original opinion of the composition of bodies supposed the compounds to derive their properties from the elements according to the law oflikeness; but this opinion was overturned by a thousand facts; and thus the really applicable Idea of Chemical Composition was introduced in modern times. In what has already been said on the History of Ideas, we have seen how each science was in a state192of confusion and darkness till the right idea was introduced.
7. No general method of evolving such ideas can be given. Such events appear to result from a peculiar sagacity and felicity of mind;—never without labour, never without preparation;—yet with no constant dependence upon preparation, or upon labour, or even entirely upon personal endowments. Newton explained the colours which refraction produces, by referring each colour to a peculiarangle of refraction, thus introducing the right idea. But when the same philosopher tried to explain the colours produced by diffraction, he erred, by attempting to apply the same idea, (the course of a single ray,) instead of applying the truer idea, of theinterference of two rays. Newton gave a wrong rule for the double refraction of Iceland spar, by making the refraction depend on theedgesof the rhombohedron: Huyghens, more happy, introduced the idea of theaxis of symmetryof the solid, and thus was able to give the true law of the phenomena.
8. Although the selected idea is proved to be the right one, only when the true law of nature is established by means of it, yet it often happens that there prevails a settled conviction respecting the relation which must afford the key to the phenomena, before the selection has been confirmed by the laws to which it leads. Even before the empirical laws of the tides were made out, it was not doubtful that these laws depended upon the places and motions of the sun and moon. We know that the crystalline form of a body must depend upon its chemical composition, though we are as yet unable to assign the law of this dependence.
Indeed in most cases of great discoveries, the right idea to which the facts were to be referred, was selected by many philosophers, before the decisive demonstration that it was the right idea, was given by the discoverer. Thus Newton showed that the motions of the planets might be explained by means of a central force in the sun: but though he established, he did not first select the idea involved in the conception of a193central force. The idea had already been sufficiently pointed out, dimly by Kepler, more clearly by Borelli, Huyghens, Wren, and Hooke. Indeed this anticipation of the true idea is always a principal part of that which, in theHistory of the Sciences, we have termed thePreludeof a Discovery. The two steps ofproposinga philosophical problem, and ofsolvingit, are, as we have elsewhere said, both important, and are often performed by different persons. The former step is, in fact, the Selection of the Idea. In explaining any change, we have to discover first theArgument, and then theLawof the change. The selection of the Argument is the step of which we here speak; and is that in which inventiveness of mind and justness of thought are mainly shown.
9. Although, as we have said, we can give few precise directions for this cardinal process, the Selection of the Idea, in speculating on phenomena, yet there is one Rule which may have its use: it is this:—The idea and the facts must be homogeneous: the elementary Conceptions, into which the facts have been decomposed, must be of the same nature as the Idea by which we attempt to collect them into laws. Thus, if facts have been observed and measured by reference to space, they must be bound together by the idea of space: if we would obtain a knowledge of mechanical forces in the solar system, we must observe mechanical phenomena. Kepler erred against this rule in his attempts at obtaining physical laws of the system; for the facts which he took were thevelocities, not thechanges of velocity, which are really the mechanical facts. Again, there has been a transgression of this Rule committed by all chemical philosophers who have attempted to assign the relative position of the elementary particles of bodies in their component molecules. For their purpose has been to discover therelationsof the particles inspace; and yet they have neglected the only facts in the constitution of bodies which have a reference to space—namely,crystalline form, andoptical properties. No progress can be made in the theory of the elementary structure of bodies,194without making these classes of facts the main basis of our speculations.
10. The only other Rule which I have to offer on this subject, is that which I have already given:—the Idea must be tested by the facts. It must be tried by applying to the facts the conceptions which are derived from the idea, and not accepted till some of these succeed in giving the law of the phenomena. The justice of the suggestion cannot be known otherwise than by making the trial. If we can discover atrue lawby employing any conceptions, the idea from which these conceptions are derived is therightone; nor can there be any proof of its rightness so complete and satisfactory, as that we are by it led to a solid and permanent truth.
This, however, can hardly be termed a Rule; for when we would know, to conjecture and to try the truth of our conjecture by a comparison with the facts, is the natural and obvious dictate of common sense.
Supposing the Idea which we adopt, or which we would try, to be now fixed upon, we still have before us the range of many Conceptions derived from it; many Formulæ may be devised depending on the same Independent Variable, and we must now consider how our selection among these is to be made.