May 23, 1889] 



NATURE 



81 



Saturn's mass has been obtained from observations of 

 its two largest satellites, Titan and Japetus. Bessel's re- 

 searches made it 1/3502, whilst Struve found a value 

 1/3498. This gives roughly the fraction 1/3500 as the 

 planet's mass. 



Newcomb deduced, from observations of the four 

 satellites of Uranus, a mass 1/22,600, and by observa- 

 tions of N^eptune's one satellite found a value 1/19,380 

 as the planet's mass. 



Before the discovery of the Martian satellites by Hall, 

 the mass of the planet was a matter of great uncertainty. 

 The discoverer's observations of the satellites led him to 

 assign i 3,100,000 as the mass of Mars, a result probably 

 not far from the truth. 



The Masses of Planets without Satellites. 

 For the determination of the masses of Mercury and 

 Venus a different and much less exact method of proce- 

 dure is used. If the masses of Venus and the earth were 

 known, the perturbations they would give to the motion 

 of Mercury could be easily calculated. Let the orbit be cal- 

 culated which Mercury would have if it existed alone with 

 the sun, and then let its true path be found. By compar- 

 ing the two paths the disturbing effect of Venus and the 

 earth may be also found. In a similar manner the cal- 

 culated and true paths of Venus may be compared ; the 

 disturbing masses being Mercury and the earth. In this 

 way a series of equations is obtained from which the 

 masses of Mercury and Venus may be isolated. The 

 result in the case of Mercury is 1/5,000,000. 



The Mass of Jupiter. 

 M. Tisserand gives a full discussion of the methods 

 of determining Jupiter's mass, which, being so consider- 

 able, shows itself in its effects upon many bodies of our 

 system. 



Beginning with comets, he quotes the comet of Lexell 

 as a typical case. In 1769 this comet approached very 

 near to Jupiter, and by the planet's action was brought 

 within our range of vision and given a period of 5| years. 

 Its return in 1776 could not be observed, and before 

 another revolution could be completed, viz. in 1779, the 

 comet was shown by Lexell to have again approached 

 very near to Jupiter, nearer than the fourth satellite. 

 The probable result was that the elliptic orbit was trans- 

 formed into a parabolic one by the predominance of 

 the planet's attraction over that of the sun, and the comet 

 left our system, never to return. 



From observations of the perturbations of Winnecke's 

 comet, M, de Haertl found Jupiter's mass to be 1/1047-175, 

 whilst Faye's comet gave the value 1/1047788. 



Some of the asteroids approach very near to Jupiter, 

 amongst these are (^ Themis, Q Pales, and (^ Hilda, 

 and from observations of the motion of Themis the planet's 

 mass has been found 1/1047-538. Estimations have also 

 been made by observations of the perturbations of Saturn, 

 but, since the necessary series should cover a cycle of 900 

 years, and only 120 years are available, the method is not 

 yet very exact. This accounts for the anomalous result 

 1/1070-5 found by Bouvard in 1821. 



It is also mentioned that Airy, from 1832 to 1836, ob- 

 served the motion of the fourth satellite and found for 

 Jupiter a mass 1/1047-64, whilst Bessel in 1841 found 

 1/1047-905. 



The following are the masses of the planets given by 

 M. Tisserand, with the earth as unit : — 



Mercury VV Jupiter ... 



Venus % Saturn ... 



The Earth ... i Uranus ... 



Mars ^V Neptune ... 



Cavendish's method for determining the mean density 

 of the earth is next explained, and it is shown that, know- 

 ing the relative masses of the planets as given in the 

 above table, we may express their weights in pounds. 



310 

 93 

 14 

 17 



Determination of the Masses of Asteroids. 



Some pages are devoted to a discussion of these small 

 bodies. It has been found that the effect of each asteroid 

 is to give a motion to the line of apsides of Mars's orbit. 

 The sum of these effects is the same as would be pro- 

 duced by taking a mean orbit of all the asteroids and 

 distributing them uniformly in it. Leverrier made a cal- 

 culation on the assumption that the total mass of the 

 asteroids was equal to that of the earth, and he found 

 that, if they had a mass only equal to one-fourth that of 

 the earth. Mars would be disturbed by an amount 

 clearly perceptible to us. M. Swedstrup has found the 

 assumption too high, and has calculated that the 

 sum of all the asteroids known up to August 1880 

 is only about 1/4000 of the earth's mass, or about 1/50 

 that of the moon. Three comparatively large asteroids 

 have had their diameters measured. Sir W. Herschel 

 found the apparent diameter of Ceres and Pallas to be 

 o"-35 and o"-24 respectively ; the equivalent in kilometres 

 being 250 and 170 For Vesta, Miidler found an ap- 

 parent diameter o"-65, or 470 kilometres. If these bodies 

 be supposed to have the same density as the earth, their 

 proportional masses will be found — Ceres, i 130,000; 

 Pallas, 1/420,000 ; Vesta, 1/20,000. By photometric 

 means, the diameters of these asteroids have been deter- 

 mined by Prof Pickering, and also of some much smaller, 

 such as Eve, with a diameter of 23 kilometres, and 

 Menippe, whose diameter is only 20 kilometres, being 

 no larger than the meteorites met by the earth daily. 



Determi7iatio7i of the Masses of Satellites. 



The method of determining the mass of our satellite 

 based upon the fact that it is the common centre of 

 gravity of the earth and moon, and not the earth itself, 

 which moves in an elliptic orbit round the sun, is fully 

 explained by the writer. By means of it, the mass of 

 the moon has been found 1/81 that of the earth. Ob- 

 servations of the proportion of lunar to solar precession, 

 as well as lunar and solar tides, also furnish a means of 

 determining the moon's mass. 



Masses of fupiter's Satellites. 



These bodies, so proportionally small, the greatest 

 being only 1/10,000 of the planet's mass, cannot have 

 their masses accurately determined by the measurement 

 of the angle subtended by the linejoining the planet to the 

 common centre of gravity ; for, since the line joining the 

 planet to its satellite is divided into parts inversely pro- 

 portional to their masses in order to find this point, the 

 line in question is very small. Hence the best method of 

 determining the measures of the satellites in this case is, 

 according to M. Tisserand, by measurement of the dis- 

 turbances upon each other. This method was propounded 

 and worked out by Laplace with the following results, in 

 terms of Jupiter's mass : — 



1st satellite 

 2nd ,, 



1/59,000 

 1/43,000 



3rd satellite 

 4th ,, 



1/11,000 

 1/23,000 



This proportion would give the third satellite a mass 

 about double that of our moon. 



The Satellites of Saturn. 



Titan, as its name suggests, is the largest of the family, 

 and consequently exercises a considerable influence over 

 the others. Prof. Hall found that under its action the 

 major axis of Hyperion's orbit made a complete revolu- 

 tion in about eighteen years. Newcomb, Tisserand, 

 Stone, and Hill have each investigated the matter, but it 

 is mainly due to the two latter observers that Titan's 

 mass has been found 1/4700 that of Saturn. Prof 

 Pickering has compared the diameters of the other satel- 

 lites with that of Titan by photometric means, and, if 



