The author has suggested an empirical law, which seems to him to regulate the arrangement of the planets and satellites. Bode long ago proposed an empirical law, which he thought regulated the distances of the planets from the sun; namely, that their distances form a series, increasing by the successive powers of the number 2. Mr Paterson has propounded another similar law, in regard to their sizes; namely, that throughout the planetary system there is a regular alternating increase and decrease in size, as the planets increase in distance from the sun, or the satellites from the planets they accompany: that there is a progressive increase from the first to the third, a decrease from the third to the fifth, an increase, again, from the fifth to the seventh, and again a decrease from the seventh to the ninth.