VI - END OF THE SUN ORIGIN OF NEBULA, continued …
The spectrum of this star is rather peculiar.
It belongs to the red stars with a band spectrum which is crossed by bright hydrogen lines.
The star is receding from us with a velocity of not less than 63 km. (39 miles) per second.
The bright hydrogen lines which correspond to the spectrum of the nebula may sometimes be resolved into three components, of which the middle one corresponds to a mean velocity of 60 km., and the two others have variable receding velocities of 35 and 82 km. that is to say, velocities of 25 or 22 km. less or more than the mean velocity.
Evidently the star is surrounded by three nebulae; one is concentrated about its centre; the two others lie on a ring the matter of which has been concentrated on two opposite sides.
The ring, which recalls the ring nebula in the Lyre, seems to move about the star with a velocity of 23.5 km. per second.
As this revolution is accomplished within eleven or, more correctly, within twenty-two months, since there must be two maxima and two minima during one revolution the total circumference of the ring will be 23.5 x 86,400 x 6701361 millions, and the radius of its orbit 217 million km., which is 1.45 times greater than the radius of the earth's orbit.
Now the velocity of the earth in its orbit is 29.5 km. (18.3 miles) per second.
A planet at 1.45 times that distance from the sun would have the (1.203 times smaller) velocity of 24.5 km. per second, which is approximately that of the hypothetical ring of Mira Ceti.
We conclude, therefore, that the mass of the central sun in Mira Ceti will nearly equal the mass of our sun.
The calculation really suggests that Mira would be about eight per cent smaller; but the difference lies within the range of the probable error.
Chandler has directed attention to a striking regularity in these stars.
The longer the period of their variation, the redder in general their color.
This is easily comprehended.
The denser the original atmosphere, the more widely the gases will have extended outward from the star, and the more dust will have been caught or secreted by it.
We have seen that the limb of the sun has a reddish light because of the quantities of dust in the solar atmosphere.
The effect is chiefly to be ascribed to the absorption of the blue rays by the dust; but it may partly be explained on the assumption that the solar radiations render the dust incandescent, though its temperature may be lower than that of the photosphere, because the dust lies outside the sun, and that it will therefore emit a relatively reddish light.
The more dust there is in a nebula, the redder will be its luminescence; and as the quantity of dust increases in general with the extension of the nebula, that star which is surrounded by wider rings of nebulae will in general be more red; but the greater the radius of the ring, the longer also will in general be its period.
TO BE CONTINUED ...
ARRHENIUS, WORLDS IN THE MAKING
Re: ARRHENIUS, WORLDS IN THE MAKING
VI - END OF THE SUN ORIGIN OF NEBULA, continued …
The so-called red stars show, in addition to the bright hydrogen lines, banded spectra which indicate the presence of chemical compounds.
On this account such stars were formerly credited with a lower temperature.
But the same peculiarity is also observed in sun-spots, although the latter, on account of their position, must have a higher temperature than the surrounding photosphere.
The presence of bands in the spectrum certainly suggests high pressure, however.
The red stars are evidently surrounded by a very extensive atmosphere of gases, in the inner portions of which the pressure is so high that the atoms enter into combination.
The spectra of the red stars display, on the whole, a striking resemblance to those of the sun-spots.
The violet portion of the spectrum is weakened, because the masses of dust have extinguished this light.
Owing to the large masses of dust which lie in our line of sight, the spectrum lines are in both cases markedly widened and sometimes accompanied by bright lines.
Another class of stars, distinguished by bright lines, comprises those studied by Wolf and Rayet, and named after them.
These stars are characterized by a hydrogen atmosphere of enormous extension, large enough in some cases, it has been calculated, to fill up the orbit of Neptune.
These stars are evidently either hotter and more strongly radiating than the red stars, or there is not so much dust in their neighborhood the dust may possibly have been expelled by the strong radiating pressure.
They are, therefore, classed with the yellow, and not with the red stars.
Although there is every reason to suppose that their central bodies are at least as hot as those of the white stars, the dust is yet able to reduce the color to yellow, owing to the vast extensions of their atmospheres.
TO BE CONTINUED ...
The so-called red stars show, in addition to the bright hydrogen lines, banded spectra which indicate the presence of chemical compounds.
On this account such stars were formerly credited with a lower temperature.
But the same peculiarity is also observed in sun-spots, although the latter, on account of their position, must have a higher temperature than the surrounding photosphere.
The presence of bands in the spectrum certainly suggests high pressure, however.
The red stars are evidently surrounded by a very extensive atmosphere of gases, in the inner portions of which the pressure is so high that the atoms enter into combination.
The spectra of the red stars display, on the whole, a striking resemblance to those of the sun-spots.
The violet portion of the spectrum is weakened, because the masses of dust have extinguished this light.
Owing to the large masses of dust which lie in our line of sight, the spectrum lines are in both cases markedly widened and sometimes accompanied by bright lines.
Another class of stars, distinguished by bright lines, comprises those studied by Wolf and Rayet, and named after them.
These stars are characterized by a hydrogen atmosphere of enormous extension, large enough in some cases, it has been calculated, to fill up the orbit of Neptune.
These stars are evidently either hotter and more strongly radiating than the red stars, or there is not so much dust in their neighborhood the dust may possibly have been expelled by the strong radiating pressure.
They are, therefore, classed with the yellow, and not with the red stars.
Although there is every reason to suppose that their central bodies are at least as hot as those of the white stars, the dust is yet able to reduce the color to yellow, owing to the vast extensions of their atmospheres.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VI - END OF THE SUN ORIGIN OF NEBULA, continued …
The unequal periods in stars like Mira may be explained by the supposition that there are several rings of dust moving about them, as in the case of the planet Saturn.
In the case of the inner rings which have a short period, there has probably been sufficient time during the uncounted number of revolutions to effect a uniform distribution of the dust.
Hence we do not discern any noteworthy nuclei in them, such as we observe in the tails of comets; the dust rings only help to impart to the star a uniform reddish hue.
In the outer rings the distribution of dust will, however, not be uniform.
One of the rings may be responsible for the chief proper period.
By the co-operation of other less important dust rings, the maximum or minimum, we shall easily understand, may be displaced, and thus the time interval between the maxima and minima be altered.
This alteration of the period is so strong for some stars that we have not yet succeeded in establishing any simple periodicity.
The best-known star of this type is the bright-red star Betelgeuse in the constellation of Orion.
The brightness of this star fluctuates irregularly between the magnitudes 1.0 and 1.4.
By far the largest number of variable stars belong to the type of Mira.
Others resemble the variable star Beta in the constellation of the Lyre, and thus belong to the Lyre type.
The variability of the spectra of a great many of these stars indicates that they must be moving about a dark star as companion, or rather that they both move about a common centre of gravity.
The change in the light intensity is, as a rule, explained by the supposition that the bright star is partially obscured at times by its dark companion.
Many irregularities, however, in their periods and other circumstances prove that this explanation is not sufficient.
The assumption of rings of dust circulating about the star and of larger condensation centres affords a better elucidation of the variability of these stars.
They are grouped with the white or yellow stars, in whose surroundings the dust does not play so large a part as in that of Mira Ceti.
The period of their variability is, as a rule, very short, moreover generally only a few days (the shortest known, only four hours) while the period of the Mira stars amounts to at least sixty-five days, and may attain two years.
There may be still longer periods so far not investigated.
TO BE CONTINUED ...
The unequal periods in stars like Mira may be explained by the supposition that there are several rings of dust moving about them, as in the case of the planet Saturn.
In the case of the inner rings which have a short period, there has probably been sufficient time during the uncounted number of revolutions to effect a uniform distribution of the dust.
Hence we do not discern any noteworthy nuclei in them, such as we observe in the tails of comets; the dust rings only help to impart to the star a uniform reddish hue.
In the outer rings the distribution of dust will, however, not be uniform.
One of the rings may be responsible for the chief proper period.
By the co-operation of other less important dust rings, the maximum or minimum, we shall easily understand, may be displaced, and thus the time interval between the maxima and minima be altered.
This alteration of the period is so strong for some stars that we have not yet succeeded in establishing any simple periodicity.
The best-known star of this type is the bright-red star Betelgeuse in the constellation of Orion.
The brightness of this star fluctuates irregularly between the magnitudes 1.0 and 1.4.
By far the largest number of variable stars belong to the type of Mira.
Others resemble the variable star Beta in the constellation of the Lyre, and thus belong to the Lyre type.
The variability of the spectra of a great many of these stars indicates that they must be moving about a dark star as companion, or rather that they both move about a common centre of gravity.
The change in the light intensity is, as a rule, explained by the supposition that the bright star is partially obscured at times by its dark companion.
Many irregularities, however, in their periods and other circumstances prove that this explanation is not sufficient.
The assumption of rings of dust circulating about the star and of larger condensation centres affords a better elucidation of the variability of these stars.
They are grouped with the white or yellow stars, in whose surroundings the dust does not play so large a part as in that of Mira Ceti.
The period of their variability is, as a rule, very short, moreover generally only a few days (the shortest known, only four hours) while the period of the Mira stars amounts to at least sixty-five days, and may attain two years.
There may be still longer periods so far not investigated.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VI - END OF THE SUN ORIGIN OF NEBULA, continued …
Nearly related to the Lyre stars are the Algol stars, whose variability can be explained bv the assumption that another bright or dark star is moving within their vicinity, partially cutting off their light.
There is no dust in these cases, and the spectrum characterizes these stars as stars of the first class that is, as white stars so far as they have been studied up to the present.
We must presume for all the variable stars that the line of sight from the observer to the star falls in the plane of their dust rings or of their companions.
If this were not so, they would appear to us like a nebula with a central condensation nucleus, or, so far as Algol stars are concerned, like the so-called spectroscopic doubles whose motion about each other is recognized from the displacement of their spectral lines.
The evolution of stars from the nebulous state has been depicted by the famous chief of the Lick Observatory, in California, W. W. Campbell, as follows (compare the spectra of the stars of the 2d, 3d, and 4th class, Figs. 59 and 60):
"It is not difficult to select a long list of well-known stars which cannot be far removed from nebular conditions."
"These are the stars containing both the Huggins and the Pickering series of bright hydrogen lines, the bright lines of helium, and a few others not yet identified."
Gamma Argus and Zeta Puppis are of this class.
Another is DM +30.3639, which is actually surrounded with a spherical atmosphere of hydrogen some five seconds of arc in diameter.
A little further removed from the nebular state are the stars containing both bright and dark hydrogen lines caught, so to speak, in the act of changing from bright-line to dark-line stars.
Gamma Cassiopeia, Pleione, and My Centauri are examples.
TO BE CONTINUED ...
Nearly related to the Lyre stars are the Algol stars, whose variability can be explained bv the assumption that another bright or dark star is moving within their vicinity, partially cutting off their light.
There is no dust in these cases, and the spectrum characterizes these stars as stars of the first class that is, as white stars so far as they have been studied up to the present.
We must presume for all the variable stars that the line of sight from the observer to the star falls in the plane of their dust rings or of their companions.
If this were not so, they would appear to us like a nebula with a central condensation nucleus, or, so far as Algol stars are concerned, like the so-called spectroscopic doubles whose motion about each other is recognized from the displacement of their spectral lines.
The evolution of stars from the nebulous state has been depicted by the famous chief of the Lick Observatory, in California, W. W. Campbell, as follows (compare the spectra of the stars of the 2d, 3d, and 4th class, Figs. 59 and 60):
"It is not difficult to select a long list of well-known stars which cannot be far removed from nebular conditions."
"These are the stars containing both the Huggins and the Pickering series of bright hydrogen lines, the bright lines of helium, and a few others not yet identified."
Gamma Argus and Zeta Puppis are of this class.
Another is DM +30.3639, which is actually surrounded with a spherical atmosphere of hydrogen some five seconds of arc in diameter.
A little further removed from the nebular state are the stars containing both bright and dark hydrogen lines caught, so to speak, in the act of changing from bright-line to dark-line stars.
Gamma Cassiopeia, Pleione, and My Centauri are examples.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VI - END OF THE SUN ORIGIN OF NEBULA, continued …
Closely related to the foregoing are the helium stars.
Their absorption lines include the Huggins hydrogen series complete, a score or more of the conspicuous helium lines, frequently a few of the Pickering series, and usually some inconspicuous metallic lines.
The white stars in Orion and in the Pleiades are typical of this age.
The assignment of the foregoing types to an early place in stellar life was first made upon the evidence of the spectroscope.
The photographic discovery of nebulous masses in the regions of a large proportion of the brightline and helium stars affords extremely strong confirmation of their youth.
Who that has seen the nebulous background of Orion (Fig. 51) or the remnants of nebulosity in which the individual stars of the Pleiades (Fig. 52) are immersed can doubt that the stars in these groups are of recent formation?
With the lapse of time, stellar heat radiates into space, and, so far as the individual star is concerned, is lost.
On the other hand, the force of gravity on the surface strata increases.
The inevitable contraction is accompanied by increasing average temperature.
Changes in the spectrum are the necessary consequence.
The second hydrogen series vanishes, the ordinary hydrogen absorption is intensified, the helium lines become indistinct, and calcium and iron absorptions begin to assert themselves.
Vega and Sirius are conspicuous examples of this period.
Increasing age gradually robs the hydrogen lines of their importance, the H and K lines broaden, the metallic lines develop, the bluish-white color fades in the direction of the yellow, and, after passing through types exemplified by many well-known stars, the solar stage is reached.
The reversing layer in solar stars represents but four or five hydrogen lines of moderate intensity; the calcium lines are commandingly permanent, and some twenty thousand metallic lines are visible.
The solar type seems to be near the summit of stellar life.
The average temperature of the mass must be nearly a maximum; for the low density indicates a constitution that is still gaseous [compare Chapter VII.].
Passing time brings a lowering of the average temperature.
The color passes from yellow to red, in consequence of lower radiation, temperature, and increasing general absorption by the atmosphere.
The hydrogen lines become indistinct, metallic absorption remains permanent, and broad absorption bands are introduced.
In one type (Secchi's Type III.), of which Alpha Herculis is an example, these bands are of unknown origin.
In another class (Secchi's Type IV.), illustrated by the star 19 Piscium, they have been definitely identified as of carbon origin.
There is scarcely room for doubt that these types of stars (Type IV.) are approaching the last stages of stellar development.
Surface temperatures have been lowered to the point of permitting more complex chemical combinations than those in the sun.
Secchi's Type III. includes the several numbered long-period variable stars of the Mira Ceti class, whose spectra at maximum brilliancy show several bright lines of hydrogen and other chemical elements.
It is significant that the dull-red stars are all very faint; there are none brighter than magnitude 5.5.
Their effective radiative power is undoubtedly very low.
NOTE: This circumstance indicates that the red color of these stars, as we have already remarked with regard to Mira Ceti, is not to be traced back to a low temperature, but rather to the dust surrounding them. The most extraordinary brightness of some stars, like Arcturus and Betelgeuse, which are redder than the sun, and whose spectra, according to Hale, resemble those of the sun-spots, presuppose a very high temperature. The characteristic lines of their spectra are produced by the relatively cool vapors of their outer portions.
TO BE CONTINUED ...
Closely related to the foregoing are the helium stars.
Their absorption lines include the Huggins hydrogen series complete, a score or more of the conspicuous helium lines, frequently a few of the Pickering series, and usually some inconspicuous metallic lines.
The white stars in Orion and in the Pleiades are typical of this age.
The assignment of the foregoing types to an early place in stellar life was first made upon the evidence of the spectroscope.
The photographic discovery of nebulous masses in the regions of a large proportion of the brightline and helium stars affords extremely strong confirmation of their youth.
Who that has seen the nebulous background of Orion (Fig. 51) or the remnants of nebulosity in which the individual stars of the Pleiades (Fig. 52) are immersed can doubt that the stars in these groups are of recent formation?
With the lapse of time, stellar heat radiates into space, and, so far as the individual star is concerned, is lost.
On the other hand, the force of gravity on the surface strata increases.
The inevitable contraction is accompanied by increasing average temperature.
Changes in the spectrum are the necessary consequence.
The second hydrogen series vanishes, the ordinary hydrogen absorption is intensified, the helium lines become indistinct, and calcium and iron absorptions begin to assert themselves.
Vega and Sirius are conspicuous examples of this period.
Increasing age gradually robs the hydrogen lines of their importance, the H and K lines broaden, the metallic lines develop, the bluish-white color fades in the direction of the yellow, and, after passing through types exemplified by many well-known stars, the solar stage is reached.
The reversing layer in solar stars represents but four or five hydrogen lines of moderate intensity; the calcium lines are commandingly permanent, and some twenty thousand metallic lines are visible.
The solar type seems to be near the summit of stellar life.
The average temperature of the mass must be nearly a maximum; for the low density indicates a constitution that is still gaseous [compare Chapter VII.].
Passing time brings a lowering of the average temperature.
The color passes from yellow to red, in consequence of lower radiation, temperature, and increasing general absorption by the atmosphere.
The hydrogen lines become indistinct, metallic absorption remains permanent, and broad absorption bands are introduced.
In one type (Secchi's Type III.), of which Alpha Herculis is an example, these bands are of unknown origin.
In another class (Secchi's Type IV.), illustrated by the star 19 Piscium, they have been definitely identified as of carbon origin.
There is scarcely room for doubt that these types of stars (Type IV.) are approaching the last stages of stellar development.
Surface temperatures have been lowered to the point of permitting more complex chemical combinations than those in the sun.
Secchi's Type III. includes the several numbered long-period variable stars of the Mira Ceti class, whose spectra at maximum brilliancy show several bright lines of hydrogen and other chemical elements.
It is significant that the dull-red stars are all very faint; there are none brighter than magnitude 5.5.
Their effective radiative power is undoubtedly very low.
NOTE: This circumstance indicates that the red color of these stars, as we have already remarked with regard to Mira Ceti, is not to be traced back to a low temperature, but rather to the dust surrounding them. The most extraordinary brightness of some stars, like Arcturus and Betelgeuse, which are redder than the sun, and whose spectra, according to Hale, resemble those of the sun-spots, presuppose a very high temperature. The characteristic lines of their spectra are produced by the relatively cool vapors of their outer portions.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VI - END OF THE SUN ORIGIN OF NEBULA, continued …
The state of evolution, which succeeds that characterized as the Secchi Type IV., may be elucidated with the aid of the examples of Jupiter and the earth, with which we are more familiar.
These planets would be invisible if they were not shining in borrowed light.
Jupiter has not advanced so far as the earth.
The specific gravity of Jupiter is somewhat lower than that of the sun (1.27 against 1.38), and, apart from the clouds in its atmosphere, this planet is probably altogether in a gaseous condition, while the earth, with its mean density of 5.52, possesses a solid cold crust, enclosing its incandescent interior.
This state of the earth corresponds to the last stage in the evolution of the stars.
Of the streams of gaseous matter which are ejected when stars collide with one another, the metallic vapors are rapidly condensed by cooling; only helium and hydrogen will remain in the gaseous condition and form nebular masses about the central body.
These nebula yield bright lights.
Their luminosity is clue to the negative particles which are sent to them by the radiation pressure of near stars, and especially by the central bodies of the nebula.
With the new stars which have so far been observed, this pressure of radiation soon diminishes, and the nebular light likewise decreases in such cases.
In other instances, as with the stars characterized by bright hydrogen and helium lines, the radiation of the central body or stars in their vicinity seems to be maintained at full force for long periods.
TO BE CONTINUED ...
The state of evolution, which succeeds that characterized as the Secchi Type IV., may be elucidated with the aid of the examples of Jupiter and the earth, with which we are more familiar.
These planets would be invisible if they were not shining in borrowed light.
Jupiter has not advanced so far as the earth.
The specific gravity of Jupiter is somewhat lower than that of the sun (1.27 against 1.38), and, apart from the clouds in its atmosphere, this planet is probably altogether in a gaseous condition, while the earth, with its mean density of 5.52, possesses a solid cold crust, enclosing its incandescent interior.
This state of the earth corresponds to the last stage in the evolution of the stars.
Of the streams of gaseous matter which are ejected when stars collide with one another, the metallic vapors are rapidly condensed by cooling; only helium and hydrogen will remain in the gaseous condition and form nebular masses about the central body.
These nebula yield bright lights.
Their luminosity is clue to the negative particles which are sent to them by the radiation pressure of near stars, and especially by the central bodies of the nebula.
With the new stars which have so far been observed, this pressure of radiation soon diminishes, and the nebular light likewise decreases in such cases.
In other instances, as with the stars characterized by bright hydrogen and helium lines, the radiation of the central body or stars in their vicinity seems to be maintained at full force for long periods.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VI - END OF THE SUN ORIGIN OF NEBULA, concluded …
The nebulous accumulations of helium and hydrogen will gradually escape and be condensed in near-by stars under the formation of "explosive" compounds.
The tendency to enter into combination seems to be strongest in the case of helium; it disappears first from the stellar atmosphere.
That helium enters into compounds at high temperatures seems to follow from the researches of Ramsay, Cooke, and Kohlschiitter.
Hydrogen will afterwards be absorbed, and the light of the central body will then show the predominating occurrence of the vapors of calcium and of other metals in its atmosphere.
Simultaneously with these, chemical compounds will be noticed, among which the carbon compounds will play an important part in the outer portions of the sun-spots, in the stars of the Secchi Type IV., as well as in the gaseous envelopes of the comets.
Finally a crust will form.
The star is extinct.
NOTE: The presence of carbon bands in the spectrum need not be taken as a mark of low temperature. Crew and Hale have observed that these bands gradually vanished from an arc spectrum as the temperature was lowered by decreasing the current intensity.
TO BE CONTINUED ...
The nebulous accumulations of helium and hydrogen will gradually escape and be condensed in near-by stars under the formation of "explosive" compounds.
The tendency to enter into combination seems to be strongest in the case of helium; it disappears first from the stellar atmosphere.
That helium enters into compounds at high temperatures seems to follow from the researches of Ramsay, Cooke, and Kohlschiitter.
Hydrogen will afterwards be absorbed, and the light of the central body will then show the predominating occurrence of the vapors of calcium and of other metals in its atmosphere.
Simultaneously with these, chemical compounds will be noticed, among which the carbon compounds will play an important part in the outer portions of the sun-spots, in the stars of the Secchi Type IV., as well as in the gaseous envelopes of the comets.
Finally a crust will form.
The star is extinct.
NOTE: The presence of carbon bands in the spectrum need not be taken as a mark of low temperature. Crew and Hale have observed that these bands gradually vanished from an arc spectrum as the temperature was lowered by decreasing the current intensity.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VII - THE NEBULAR AND THE SOLAR STATES
WE will now proceed to a more intimate consideration of the chemical and physical conditions which probably characterize the nebula in distinction from the suns.
These properties differ in many respects essentially from those which we are accustomed to associate with matter as investigated by us, which may, from this point of view, be styled relatively concentrated.
The differences must be fundamental.
For the motto of Clausius, which comprises the sum of our knowledge of the nature of heat, cannot apply to nebulse.
This motto reads:
"The energy of the universe is constant."
"The entropy of the universe tends to a maximum."
Everybody understands what is meant by energy.
We know energy in many forms.
The most important are: energy of position (a heavy body has larger energy by virtue of its having been raised to a certain height above the surface of the earth than when it is lying on the surface); energy of motion (a discharged rifle-bullet has an energy which is proportional to the mass of the bullet and to the square of its velocity); energy of heat, which is regarded as the energy of the motion of the smallest particles of a body; electrical energy, such as can, for instance, be stored in an accumulator battery, and which, like all other modifications of energy, may be converted into energy of heat; and chemical energy, such as is displayed by a mixture of eight grammes of oxygen with one gramme of hydrogen, which can be transformed into water under a strong evolution of heat.
When we say that the energy of a system to which energy is not imparted from outside is constant, we merely mean that the different forms of energy of the separate parts of this system may be transformed into other forms of energy, but that the sum total of all the energies must always remain unchanged.
According to Clausius this law is valid throughout the infinite space of the universe.
By entropy we understand the quantity of heat of a body divided by its absolute temperature.
If a quantity of heat, of Q calories, of a body at a temperature of 100 (absolute temperature, 373) passes over to another body of (absolute temperature, 273), the total entropy of the two will have been decreased by yf, and increased by TS.
As the latter quantity is the greater, the entropy of the whole will have increased.
By itself, we know, heat always passes, either by radiation or by conduction, from bodies of higher temperature to bodies of lower temperature.
That evidently implies an increase in entropy, and it is in agreement with the law of Clausius that entropy tends to increase.
TO BE CONTINUED ...
WE will now proceed to a more intimate consideration of the chemical and physical conditions which probably characterize the nebula in distinction from the suns.
These properties differ in many respects essentially from those which we are accustomed to associate with matter as investigated by us, which may, from this point of view, be styled relatively concentrated.
The differences must be fundamental.
For the motto of Clausius, which comprises the sum of our knowledge of the nature of heat, cannot apply to nebulse.
This motto reads:
"The energy of the universe is constant."
"The entropy of the universe tends to a maximum."
Everybody understands what is meant by energy.
We know energy in many forms.
The most important are: energy of position (a heavy body has larger energy by virtue of its having been raised to a certain height above the surface of the earth than when it is lying on the surface); energy of motion (a discharged rifle-bullet has an energy which is proportional to the mass of the bullet and to the square of its velocity); energy of heat, which is regarded as the energy of the motion of the smallest particles of a body; electrical energy, such as can, for instance, be stored in an accumulator battery, and which, like all other modifications of energy, may be converted into energy of heat; and chemical energy, such as is displayed by a mixture of eight grammes of oxygen with one gramme of hydrogen, which can be transformed into water under a strong evolution of heat.
When we say that the energy of a system to which energy is not imparted from outside is constant, we merely mean that the different forms of energy of the separate parts of this system may be transformed into other forms of energy, but that the sum total of all the energies must always remain unchanged.
According to Clausius this law is valid throughout the infinite space of the universe.
By entropy we understand the quantity of heat of a body divided by its absolute temperature.
If a quantity of heat, of Q calories, of a body at a temperature of 100 (absolute temperature, 373) passes over to another body of (absolute temperature, 273), the total entropy of the two will have been decreased by yf, and increased by TS.
As the latter quantity is the greater, the entropy of the whole will have increased.
By itself, we know, heat always passes, either by radiation or by conduction, from bodies of higher temperature to bodies of lower temperature.
That evidently implies an increase in entropy, and it is in agreement with the law of Clausius that entropy tends to increase.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VII - THE NEBULAR AND THE SOLAR STATES, continued ...
The most simple case of heat equilibrium is that in which we place a number of bodies of unequal temperatures in an enclosure which neither receives heat from outside nor communicates heat to the outside.
In some way or other, usually by conduction or radiation, the heat will pass from the warmer to the colder bodies, until at last equilibrium ensues and all the bodies have the same temperature.
According to Clausius, the universe tends to that thermal equilibrium.
If it be ever attained, all sources of motion, and hence of light, will have been exhausted.
The so-called "heat-death" (Warmetod) will have come.
If Clausius were right, however, this heat-death, we may object, should already have occurred in the infinitely long space of time that the universe has been in existence.
Or we might argue that the world has not yet been in existence sufficiently long, but that, anyhow, it had a beginning.
That would contradict the first part of the law of Clausius, that the energy of the universe is constant; for in that case all the energy would have originated in the moment of creation.
That is quite inconceivable, and we must hence look for conditions for which the entropy law of Clausius does not hold.
TO BE CONTINUED ...
The most simple case of heat equilibrium is that in which we place a number of bodies of unequal temperatures in an enclosure which neither receives heat from outside nor communicates heat to the outside.
In some way or other, usually by conduction or radiation, the heat will pass from the warmer to the colder bodies, until at last equilibrium ensues and all the bodies have the same temperature.
According to Clausius, the universe tends to that thermal equilibrium.
If it be ever attained, all sources of motion, and hence of light, will have been exhausted.
The so-called "heat-death" (Warmetod) will have come.
If Clausius were right, however, this heat-death, we may object, should already have occurred in the infinitely long space of time that the universe has been in existence.
Or we might argue that the world has not yet been in existence sufficiently long, but that, anyhow, it had a beginning.
That would contradict the first part of the law of Clausius, that the energy of the universe is constant; for in that case all the energy would have originated in the moment of creation.
That is quite inconceivable, and we must hence look for conditions for which the entropy law of Clausius does not hold.
TO BE CONTINUED ...
Re: ARRHENIUS, WORLDS IN THE MAKING
VII - THE NEBULAR AND THE SOLAR STATES, continued ...
The famous Scotch physicist Clerk-Maxwell has conceived of such a case.
Imagine a vessel which is divided by a partition into two halves, both charged with a gas of perfectly uniform temperature.
Let the partition be provided with a number of small holes which would not allow more than one gas molecule to pass at a time.
In each hole Maxwell places a small, intelligent being (one of his "demons"), which directs all the molecules which enter into the hole, and which have a greater velocity than the mean velocity of all the molecules, to the one side, and which sends to the other side all the molecules of a smaller velocity than the average.
All the undesirable molecules the demon bars by means of a little flap.
In this way all the molecules of a velocity greater than the average may be collected in the one compartment, and all the molecules of a lesser velocity in the other compartment.
In other words, heat, for heat consists in the movements of molecules, will pass from the one constantly cooling side to the other, which is constantly raising its temperature, and which must therefore become warmer than the former.
In this instance heat would therefore pass from a colder to a warmer body, and the entropy would diminish.
Nature, of course, does not know any such intelligent beings.
Nevertheless, similar conditions may occur in celestial bodies in the gaseous state.
When the molecules of gas in the atmosphere of a celestial body have a sufficient velocity which in the case of the earth would be 11 km. (7 miles) per second and when they travel outward into the most extreme strata, they may pass from the range of attraction out into infinite space, after the manner of a comet, which, if endowed with sufficient velocity when near the sun, must escape from the solar system.
According to Stoney, it is in this way that the moon has lost its original atmosphere.
This loss of gas is certainly imperceptible in the case of our sun and of large planets like the earth.
But it may play an important part in the household of the nebulae, where all the radiation from the hot celestial bodies is stored up, and where, owing to the enormous distances, the restraining force of gravity is exceedingly feeble.
Thus the nebulae will lose their most rapid molecules from their outer portions, and they will therefore be cooling in these outer strata.
This loss of heat is compensated by the radiation from the stars.
If, now, there were only nebulae of one kind in the whole universe, those escaped molecules would finally land on some other nebula, heat equilibrium would thus be established between the different nebulae, and the "heat-death" be realized.
But we have already remarked that the nebulae enclose many immigrated celestial bodies, which are able to condense the gases from their neighborhood, and which thereby assume a higher temperature.
The lost molecules of gases may also stray into the vast atmosphere of these growing stars, and the condensation will then be hastened under a continuous lowering of the entropy.
By such processes the clock-work of the universe may be maintained in motion without running down.
TO BE CONTINUED ...
The famous Scotch physicist Clerk-Maxwell has conceived of such a case.
Imagine a vessel which is divided by a partition into two halves, both charged with a gas of perfectly uniform temperature.
Let the partition be provided with a number of small holes which would not allow more than one gas molecule to pass at a time.
In each hole Maxwell places a small, intelligent being (one of his "demons"), which directs all the molecules which enter into the hole, and which have a greater velocity than the mean velocity of all the molecules, to the one side, and which sends to the other side all the molecules of a smaller velocity than the average.
All the undesirable molecules the demon bars by means of a little flap.
In this way all the molecules of a velocity greater than the average may be collected in the one compartment, and all the molecules of a lesser velocity in the other compartment.
In other words, heat, for heat consists in the movements of molecules, will pass from the one constantly cooling side to the other, which is constantly raising its temperature, and which must therefore become warmer than the former.
In this instance heat would therefore pass from a colder to a warmer body, and the entropy would diminish.
Nature, of course, does not know any such intelligent beings.
Nevertheless, similar conditions may occur in celestial bodies in the gaseous state.
When the molecules of gas in the atmosphere of a celestial body have a sufficient velocity which in the case of the earth would be 11 km. (7 miles) per second and when they travel outward into the most extreme strata, they may pass from the range of attraction out into infinite space, after the manner of a comet, which, if endowed with sufficient velocity when near the sun, must escape from the solar system.
According to Stoney, it is in this way that the moon has lost its original atmosphere.
This loss of gas is certainly imperceptible in the case of our sun and of large planets like the earth.
But it may play an important part in the household of the nebulae, where all the radiation from the hot celestial bodies is stored up, and where, owing to the enormous distances, the restraining force of gravity is exceedingly feeble.
Thus the nebulae will lose their most rapid molecules from their outer portions, and they will therefore be cooling in these outer strata.
This loss of heat is compensated by the radiation from the stars.
If, now, there were only nebulae of one kind in the whole universe, those escaped molecules would finally land on some other nebula, heat equilibrium would thus be established between the different nebulae, and the "heat-death" be realized.
But we have already remarked that the nebulae enclose many immigrated celestial bodies, which are able to condense the gases from their neighborhood, and which thereby assume a higher temperature.
The lost molecules of gases may also stray into the vast atmosphere of these growing stars, and the condensation will then be hastened under a continuous lowering of the entropy.
By such processes the clock-work of the universe may be maintained in motion without running down.
TO BE CONTINUED ...