March 21, 19 18] 



NATURE 



53 



I 



A Potsdam spectrograph taken on February i8 shows 

 the typical Nova-spectrum in the stage of decline; 

 broad bright hydrogen bands on a somewhat faint con- 

 tinuous background that could be traced far into the 

 ultra-violet; groups of lines were seen at A 464, and a 

 trace of the green nebula line. 



The Minor Planets. — In 1866, when only eighty- 

 ■:4ht asteroids were known, Prof. Kirkwood detected 



ips in their distribution, at points corresponding with 



)mmensurability with Jupiter's motion. Prof. Hira- 

 yama (in Proc. Tokyo Math.-Phys. Soc, 2nd series, 

 vol. ix., 11) re-examines the question with nearly 900 

 orbits available. The gaps at the ratios 2/1, 7/3, 5/2, 

 8/3, 3/1 are still very striking, and some others are 

 probably indicated. Prof. Hirayama makes the interest- 

 ing remark that for values of the daily motion smaller 

 than 500" the asteioids seek, instead of avoiding, the 

 points of commensurability ; thus the four Trojan planets 

 have the ratio i/i, one planet has 4/3, and six have 

 3/2. These cases are shown to correspond with libra- 

 tions of a stable character, while the gaps mentioned 

 above correspond with unstable motion. It would prob- 

 ably have been l>etter to omit all asteroids observed at 

 one opposition only, as the elements of their orbits are 

 subject to considerable uncertainty. The new planet 

 DB (daily motion 881') lies fairly close to the 3/1 

 point, so its perturbations by Jupiter will be interest- 

 ing. 



As the war has severed relations with the Berlin 

 Rechen-Institut, formerly the centre for discussion and 

 distribution of minor planet information, an inde- 

 pendent bureau has been opened at Marseilles Observa- 

 tory, whence numerous circulars relating to orbits and 

 observations have been sent to us. One of the 

 ephemerides is that of Deianira, which has been ob- 

 served at only three oppositions since its discovery. 

 Its position on March 22 is R.A. i2h. i9-3m., N. de- 

 clination 18° 26', magnitude 13-1. 



TUE ROTATION OF THE EARTH. 



THE Revue ginerale des Sciences of January 30 

 contains a full abstract of a very interesting paper 

 by D. Korda in Archives des Sc. Phys. et Nat. (Geneva) 

 of November 15 last. It appears that Baron 

 Eotvos, in examining the records of gravitation made 

 at sea, found certain anomalies which he traced to the 

 speed and course of the ship. The weight of a thing 

 on .the surface of the earth is less than that due to 

 the attraction of the earth by an amount equal to the 

 centrifugal force, which at the equator amounts to 

 gj 2S8, and which, resolved in a vertical direction, varies 

 as the square of the cosine of the latitude. Any variation 

 in the centrifugal force therefore affects the weight to 

 this reduced extent. The velocity at the surface of the 

 earth may be 46,500 cm. /sec, while that of a ship in 

 the water may be 1000 cm. /sec, so that the motion 

 of the ship round the axis of the earth may vary be- 

 tween 47,500 and 45,500 cm. /sec at the equator. Cen- 

 trifugal force varies as the square of the velocity, so, 

 calling V and v the velocities of the earth's surface and 

 of the ship in the water, the centrifugal force on a 

 body in the ship may vary between (V-t;)^ and (W + v)' 

 — that is, through a range of 4V7/ depending on the 

 course. While v may be relatively small, the large 

 factor V may, and does, at times make the product so 

 great as to introduce an error in the apparent gravity 

 as determined on board ship. For example, in the 

 case supposed, which corresponds with a speed of 19-4 

 knots and at the equator, the difference in weight as 

 shown by a spring balance going east with the earth 

 and west against the earth would be as much as 

 1/3355, or more than two grains per pound — quite a 

 serious amount in a gravitational survey. 



NO. 2525, VOL. lOl] 



But it is here that the ingenuity, daring, and experi- 

 mental skill so typical of Eotvos comes in. Not con- 

 tent with finding serious disturbances in weight result- 

 ing from velocities of 1000 cm. /sec, he conceived the 

 idea of setting up in the laboratory a small delicate 

 balance on a rotating vertical axis with the accurately 

 balanced masses moving at a speed of about i cm. /sec, 

 with the view of observing the disturbance of the 

 balance. At the equator with such a speed the two 

 masses would alternately seem the heavier by 

 1/3,355,000 of themselves, whereas at his laboratory at 

 Budapest, which is very nearly at latitude 45°, the 

 difference would be one-half of this — not a very large 

 amount to play with — ibut Eotvos was able to make 

 manifest the minute change by employing syn- 

 chronism and the principle of resonance, and so obtain- 

 ing the large magnification which is possible with a 

 very small degree of damping. 



Unfortunately, the published account is most tan- 

 talising; for beyond saying that the period employed was 

 about a minute, that the maximum oscillation could be 

 read in an hour, and that the balance was small, not 

 one of the details which would assist in repeating the 

 experiment is given — length of beam, load at each end, 

 decrement, and stability are alike left undefined. The 

 mode of observation, however, is described. A 

 horizontal mirror is carried by the beam so that a ver- 

 tical ray of light may be reflected up by it. When an 

 experiment is to be made the beam is arrested and the 

 reflected ray of light traces a small circle upon a screen. 

 When the beam is liberated the two ends, alternately 

 becoming the heavier, set up an increasing oscillation 

 made evident by 'the departure from the original circle, 

 which settles down to an amount determined by the 

 equation : 



Maximum amplitude = 2Q cos 0-, 



K 



where Q is the angular speed of the earth, the lati- 

 tude, K the moment of inertia of the balance, and fe 

 its coefficient of damping. This formula quoted by 

 the author is remarkable in that almost every feature 

 of the apparatus and of the earth is eliminated. 



The present writer, desiring to verify the formula, 

 obtained a different result, and then, testing both 

 formulae dimensionally, found the formula at which he 

 had arrived dimensionally correct, while that given 

 above is not. He thinks, therefore, that it is desirable 

 to state very shortly the facts as he understands them. 

 The balance is supposed to be rotated accurately at the 

 speed of true synchronism, taking into account the 

 effect of centrifugal stability discussed in the next two 

 paragraphs. In these conditions, treating the vibrations 

 as the projection of a logarithmic spiral, and using the 

 hodograph as given by Tait and explained more clearly 

 in Clerk Maxwell's "Electricity and Magnetism," 

 vol. ii. [731], the radius A of the spiral grows until the 

 resistance proportional to the velocity is equal to the 

 maximum deflecting moment due to the action of 

 ^Yv. The value of A, then, is the maximum value, 

 and the spiral has become a circle. When this is 

 reached the actual resistance couple will be found to be 



— Tp^ — , and this must be equal to the couple 



— Y- cos2 <^, due to the ^Vv action described. From 

 this it follows that 



A = ncos«<^^, 



where T is the time of a cofnplete rotation of the 

 balance and k is the logarithmic decrement. This A is 

 the angular deviation from the mean position, so if 

 by A is meant the complete amplitude, the ex- 

 pression must be multiplied by 2. It will be noticed 



