340 



KNOWLEDGE 



[June 8, 1883. 



molecular motion into mcclmnical movement." I ought, 

 perhaps, to mention one other experiment performed to 

 illustrate the molecular homogeneity (as opposed to the 

 generally received theory of hajjhazard intermingling) 

 when in a state of neutrality. A complete ring of .steel 

 wire, ten ccntimotrcs in diameter, was revolved over the 

 pole of a niajjnet and gradually withdrawn, the revolution 

 being maintained until removed some feet from the 

 magnet Such a ring is perfectly neutral, and exhibits no 

 polarity, although it would do if made to simply touch the 

 magnet. On cutting or .snapping the ring, very strong 

 polarity becomes evident, and, therefore, excellent testi- 

 mony is borne to the position taken up by Prof. Hughes. 



Assuming that what Professor Hughes advances is 

 correct — and I, for my part, can see no reason for 

 doubting it — what is the effect upon our conception 

 of magnetism ! There will not be wanting those who 

 will maintain that if we deprive the Ampurian theory 

 of the electric currents, we shall get Hughes's theory. 

 But if we so treat Ampere's propositions we rob 

 them of their one beauty. The molecular theory is one 

 which has been at least suspected by many electricians, 

 but to Professor Hughes belongs the credit of assigning to 

 magnetism a place )jy the side of gravity, two forces which 

 are indestructible and inconvertible. Magnetism can never 

 be changed to any other form of force, although it may be 

 made a channel of transference. It is therefore most com- 

 pletely separated from electricity — a form of force which, 

 like heat, may be imparted or withdrawn, converted or 

 destroyed. 



LAWS OF BRIGHTNESS. 



III. 



By Richard A. Proctor. 



NEXT let us consider the relative absolute brightness 

 of the planets under different circumstances. 

 In the first place, let us inquire what is the total quantity 

 of light sent from a hemisphere (smooth), illuminated and 

 viewed in the same directions : — 



Fig. 5. 



Let A I) B (Fig. 5) be a section of the illuminated 

 hemisphere, tlie lines of light being as I A, I' E, .tc. Let 

 D be the middle of the visible disc, E another point. Then 

 the illumination has its maximum value at D. At E it is 

 less in the ratio of the sine of the angle T E I'. But the 

 angle E C A is equal to the angle T E I', and the sine of 

 the angle E C A is the ratio E M to E C. Hence the 

 illumination at E is less than that at D in the ratio of E M 

 to E C— that is, of E M to D C. So that if we represent the 

 illumination at I) by the line D C, the illumination at E will 

 be represented by the line EM. Now let AB (Fig. G), represent 

 the disc shown by the hemisphere, growing gradually 

 fainter to the edges ; and let A' B' (Fig. 7) be a ilat disc 

 illuminated all over as the hemisphere is illuminated at D. 



Thin, if a il h be an ideal hemisphere corresponding to the 

 illuminated hemisphere A D B in dimensions, k corre- 

 sponding to E and d to D, we have seen that if d c repre- 

 sent the brightness at D, «j tti will represent the brightness 

 at E ; so that obviously if the small solid space d c 

 represent the total light from the small area D, the 

 small solid space c m will represent the total light from 

 the small area at E. Henee, supposing the whole 

 disc divided into a number of very small areas, 

 such as those at E and D, we see that when all the 

 corresponding small solid spaces have been taken into 

 account, we get the total light from the disc represented 



B -, 



Fig. 0. 



by the volume of the hemisphere adb. Doing the like for 

 the flat disc A B (and retaining the same scale of construc- 

 tion) we get the total light from the flat disc, represented 

 by the volume of the cylinder a' d' V, whose base a' V is 

 equal to n 6, and its height d' c' equal to d c. Now, the 

 volume adb is two-thirds of the volume a' d' b', by Archi 

 medes' property of the sphere and cylinder. Hence the 

 total light reeeived from a hemisphere, both Dluminated 

 and viewed directly, is two-thirds of the total light from a 

 flat surface equal to the great circular section of the 

 hemisphere, and illuminated directly. 



This relation only enables ns to estimate and compare 

 the lirilliancy (total) of the superior planets in opposition 

 (for Venus and Mercury in superior conjunction may be 

 left out of consideration). We may apply the relation at 

 once to determine the theoretical relative brilliancies of 

 the superior planets, on the supposition — first, that they 

 are smooth spheres ; and secondly, that their surfaces are 

 of equal reflective power. It will be understood, of course, 

 that by reflective power is understood the power of return- 

 ing light by general reflection, the quality which makes 

 opaque bodies look more or less bright under the same 

 circumstances of illumination. Zollner calls this quality 

 the albedo, or, as it were, the inJiiteness of surfaces. 



Now, obviously, all we have to do, to determine the 

 theoretical relative brilliancy of the superior planets in 

 opposition, is to multiply the number representing the area 

 of each planet's disc into the number representing its illu- 

 mination. For we have seen that the total brightness of a 

 planet in opposition bears a constant ratio to that of a flat 

 disc illuminated directly and looking precisely as large as 

 the planet. Now, the apparent diameter of a planet at any 

 time varies as its real diameter di'vided by its distance, so 



that the apparent size of its disc varies asl | 



\ distance / 



We have only to multiply this by the number representing 



the illumination to get the relative total brilliancy. The 



following table gives the results. In calculating it the 



