We can now calculate when our nebula will pass through this critical stage, to which a lowering of the temperature must succeed. Accepting the above figures, we find that half the mass of the nebula will fill a sphere of a radius 0.53 of that of the nebula. If the mass were everywhere of the same density, half of it would fill a sphere of 0.84 of this radius. When will the interior mass cross the boundary of the above stage, while the exterior portions still remain below this stage? That will be at about the time when the nebula in its totality will pass through its maximum temperature. We will now base our calculations on the temperatures which apply to iron in the gaseous state; for in the interior of the nebula the mean molecular weight will at least be 56 (that of iron). We shall find that the pressure at the distance 0.53 will be about 177,000 atmospheres, and the temperature approximately 71 million degrees—_i.e._, 245,000 times higher than the absolute temperature in the experiments of Amagat. The specified stage will then be reached when the pressure will be 245,000 times as large as 250 atmospheres—viz., 61 million atmospheres. As, now, the pressure is only 177,000 atmospheres, our nebula will yet be far removed from that stage at which cooling will set in. We can easily calculate that this will take place when the nebula has contracted to a volume about three times that of our sun. The assertion which is so often made that the sun might possibly attain higher temperatures in the future is unwarranted. This celestial body has long since passed through the culminating-point of its thermal evolution, and is now cooling. As the temperatures which Schuster deduced were no doubt much too high, the cooling must, indeed, have set in already in an earlier stage. But stars like Sirius, whose density is probably not more than one per cent, of the solar density, are probably still in a rising-temperature stage. Their condition approximates that of the mass of gas of our example. The planetary nebulæ are vastly more voluminous. The immense space which these celestial bodies may occupy will be understood from the fact that the largest among them, No. 5 in Herschel’s catalogue, situated near the star B in the Great Bear, has a diameter of 2.67 seconds of arc. If it were as near to us as our nearest star neighbor, its diameter would yet be more than three times that of the orbit of Neptune; doubtless it is many hundreds of times larger. This consideration furnishes us with an idea of the infinite attenuation in such structures. In their very densest portions the density cannot be more than one-billionth of the density of the air. In the outer portions of such nebulæ the temperature must also be exceedingly low; else the particles of the nebula could not be kept together, and only hydrogen and helium can occur in them in the gaseous state.