36 



KNOWLEDGE. 



[Febeuaey 1, 1892. 



of its surface, or the " albedo." Of these the first three 

 are easUy determined by observation, and a simple method 

 of computing the relative albedos of the different planets 

 forms the subject of the present paper. , . , , 



The method of computation is as follows. The brightness 

 of two planets will varv inversely as the square of their 

 distance from the Sun, and dinrth/ as the size of the 

 planets' discs as seen from the Earth, or, makmg due cor- 

 rection for their crescent and gibbous forms, as the square 

 of their apparent diameters measured in seconds of arc. 

 The results of this calculation will represent the relative 

 brightness the two planets should have if both had the 

 same albedo. If, however, one of them appears brighter 

 than calculation indicates it implies that its reflecting 

 power or albedo is greater than the albedo of the other. 

 As the relative apparent brightness can be measm-ed 

 with a photometer, we have all the necessary data for cal- 

 culation of the relative albedos. 



The albedo is generally represented as a decimal 

 fraction. This fraction deinotes the proportion of light 

 reflected compared with the amount received; the albedo 

 of a surface reflecting idl the light which falls upon it 

 would be represented by unity. Probably, however, no 

 such surface exists, the " albedo " of even freshly fallen 

 snow being less than unity. 



The diflerence of albedo in the planets is in some 

 cases very striking. In 1878, when j\Iercury and Venus 

 were in the same field of view of the telescope, Nasmyth 

 found that Venus was at least twice as bright as Mercury. 

 He compared Venus to clear silver and Mercury to lead or 

 zinc. From photometric observations by Pickering and 

 ZoUner, the brightness of Venus is nearly as great as if 

 its surface was covered with snow, and Zolluer found that 

 the surface of Mercury is comparable with that of the 

 Moon, which has a small albedo. This difference of 

 surface brightness is very remarkable when we consider 

 that Mercury is much nearer to the Sun than Venus. If 

 we suppose that the siu-face of Venus is covered with a 

 cloudy canopy, as has been suggested, this cloudy covering 

 would perhaps account for the planet's great reflecting 

 power. 



Owing to the uncertainty which exists as to the relative 

 apparent brightness of Venus and ]\Iercury as viewed with 

 the naked eve, it is not easy to compute correctly their 

 relative albedos. Olbers found Venus at its greatest 

 brilliancy 19 to 23 times as bright as Aldebarau, but 

 Plummer estimated it as nine times brighter than Sinus, 

 which would make it -56 times brighter than Aldebaran. 

 Mercury is perhaps about equal to Aldebaran when at its 

 greatest brilliancy. I compared the planet and the star in 

 June, 1874, in India, and found them about equal. 



Assuming that when Venus is at her greatest brightness 

 she is distant from the Sun 66 millions of miles, and that 

 in this position she subtends an angle of 40 seconds of arc, 

 and taking the corresponding quantities for Mercury as 28 

 millions and 8i seconds respectively, I find that Venus 

 should appear about four times brighter than Mercury. 

 Taking Venus as 20 times brighter than Aldebaran we 

 have the albedo of Venus equal to five times that of 

 Mercm-y. Zollner found for Mercury an albedo of 0-13. 

 Uy calculation would, therefore, make the albedo of Venus 

 equal to 0-13 x 5 or 0-65. Zollner foimd 0-50. The data 

 used in the above computation are too uncertain to yield an 

 accurate result. 



For the planets outside the Earth's orbit, let us take 

 Mars as our standard. For this planet Z5llner found an 

 albedo of 0-2672, or about double the albedo of Mercury. 

 For the minor planets we have hardly sufficient data to 

 enable us to compute then albedos ; these httle planets 



bemg so small that the apparent diameters of their discs 

 cannot be accurately measured. 



Comparing ]\Iars and Jupiter, we have the mean dis- 

 tances fi-om the Sun represented by the numbers 1-523 

 and 5-20. Their surfaces are therefore illuminated by 

 sunlight in the inverse ratio of the squares of these 

 numbers. That is, the solar Ulumination on Mars is to 

 the solar illumination on Jupiter as the square of 5-20 to 

 the square of 1-523, or as 27-04 to 2-32 ; and the apparent 

 diameter of Mars at mean opposition may be taken at 18 

 seconds of arc, while that of Jupiter is 46 seconds. Hence 

 the illuminated surface of Jupiter is (f^)^ or 6-53 times 

 that of ilars. The relative brightness of the two planets 

 should therefore be ^-^^Wtj' oi" 1"78 ; that is, Mars should 

 be 1-78 times brighter than Jupiter. Now Pickering foimd 

 the stellar magnitude of Jupiter, when m opposition, to be 

 2-52, or about 2i magnitudes brighter than the zero of the 

 scale of magnitudes, and that of Mars 2-25. This 

 makes Jupiter 1-2823 times brighter than Mars. But we 

 have seen that Mars should be 1-78 times brighter than 

 .Jupiter. Hence Jupiter is 1-78x1-2823=2-2825 times 

 bricrhter than it should be had it the same albedo as Mars. 

 The albedo must therefore be 0-2672x2-2825 = 0-609. 

 Zollner found an albedo of 0-72, but Bond computed that 

 Jupiter emits more light than it receives from the Sun 

 (Chambers' " Descriptive Astronomy," 3i-d edition, p. 117). 

 This would suggest that the planet shmes with some 

 inherent light of its own, a conclusion which has been also 

 arrived at fi-om other considerations. 



In the case of Saturn the existence of the bright rings 

 comphcates the observations of the planet's brightness. 

 Pickering's photometric measures make it about equal to 

 a star of the first magnitude when m opposition and the 

 rin"S invisible. Mars is therefore 3-25 magnitudes, 

 or^bout 20 times brighter than Saturn. Now the 

 relative distances of Mars and Saturn from the Sun are 

 represented by the numbers 1-523 and 9-539. The squares 

 of these are 2-32 and 90-99, which implies that the lu- 

 tensitv of the solar light on Mars is 39-2 times that on 

 Saturn. Taking the apparent diameter of Mars at 18 

 seconds and that of Saturn at 19 seconds, we have the 

 apparent surface of Mars (Uf or f|i that of Saturn. 

 Mars should therefore be 39-2 x ||a, or 3o-l< times 

 brighter than Saturn. But it is only 27 times brighter 

 Hence the albedo of Saturn must be greater than that ot 

 Mars in the ratio of 35-17 to 27, or the albedo of Saturn 

 — 3.5-jj X 0-2672= (0-47). Zollner fouud 0-4981. lam 

 inclmed, however, to think, from my own observations, 

 that Saturn, when in opposition and shorn of his rings, is 

 slirrhtly brighter than a star of the first magnitude. If 

 thfs be so tiie albedo would have a somewhat higher value 

 than that just computed. ,.-,,, , • , j. 



Comino- now to the planet Uranus we find the highest 

 albedo ot- all the planets. Zollner found 0-64, or slightly 

 greater than that of Jupiter, but I find a stiU higher value. 

 The relative distances of Mars and Uranus from the Sun 

 are 1-523 and 19-183. The squares of these numbers are 

 "-32 and 367-99. Hence the intensity of the solar illumi- 

 nation on Mars is ^V*^, or 158-6 times that on I ranus 

 Taking the apparent' diameter of Uranus at 4 seconds, and 

 that of Mars at 18 seconds, as before, we have the area ot 

 the disc of Mars (y)^or 20-25 times that of Uranus. 

 Hence Mars should exceed Uranus m brightness 15b-bx 

 20-25 or 3211-65 times, if both planets had the same 

 albedo Now Zollner found the stellar magnitude ot 

 Uranus to be 5-46 ; Pickering finds 5-56, and my own eye 

 observations make it about 5-4. We may thei^fore safely 

 assume its 'orightness at 5-5 magnitude. This gives a 

 difference of 7-75 stellar magnitude between Mars and 



