In the _Philosophical Magazine_ (January 1902) is a remarkable article by Lord Kelvin, in which he discusses the very same problem as that which Professor Newcomb had discussed at a much earlier date, but, starting from different assumptions, equally based on ascertained facts and probabilities deduced from them, brings out a very different result. Lord Kelvin postulates a sphere of such a radius that a star at its confines would have a parallax of one-thousandth part of a second (0".001), equivalent to 3215 light-years. Uniformly distributed through this sphere there is matter equal in mass to 1000 million suns like ours. If this matter becomes subject to gravitation, it all begins to move at first with almost infinite slowness, especially near its centre; but nevertheless, in twenty-five million years many of these suns would have acquired velocities of from twelve to twenty miles a second, while some would have less and some probably more than seventy miles a second. Now such velocities as these agree generally with the measured velocities of the stars, hence Lord Kelvin thinks there may be as much matter as 1000 million suns within the above-named distance. He then states that if we suppose there to be 10,000 million suns within the same sphere, velocities would be produced very much greater than the known star-velocities; hence it is probable that there is very much less matter than 10,000 million times the sun's mass. He also states that if the matter were not uniformly distributed within the sphere, then, whatever was the irregularity, the acquired motions would be greater; again indicating that the 1000 million suns would be ample to produce the observed effects of stellar motion. He then calculates the average distance apart of each of the 1000 million stars, which he finds to be about 300 millions of millions of miles. Now the nearest star to our sun is about twenty-six million million of miles distant, and, as the evidence shows, is situated in the denser part of the solar cluster. This gives ample allowance for the comparative emptiness of the space between our cluster and the Milky Way, as well as of the whole region towards the poles of the Milky Way (as shown by the diagrams in chapter IV.), while the comparative density of extensive portions of the Galaxy itself may serve to make up the average.