254 



NA TURE 



[ July 10, 1884 



THE MOVEMENTS OF THE EARTH 1 



\SJV- last appealed to those branches of physical science which 

 arc connected with the determination of the velocity of 

 light, in order to see whether we could get any help in that 

 direction on a most interesting question, a question which, like 

 another to which attention has been drawn, might have been 

 considered as an open one, unless one had gone beyond the range 

 of ordinary astronomical observation with regard to it. It has 

 now been seen thai by investigating the facts connected with the 

 velocity of light, first, that we could determine that velocity by 

 two different methods with a wonderful agreement between 

 them ; and secondly, that, by taking the velocity of light and 

 dealing with it in the way we then did, a perfect demonstration 

 was obtained of the fact that the earth revolves in an orbit round 

 the sun. It was further seen that using this velocity of light, and 

 also this fact of the earth's revolution which it enabled us to 

 demonstrate, we were able to say that the distance of the earth 

 from the sun was, roughly speaking, 92A millions of miles. 



We w ill now go more into detail with regard to the precise 

 form of the earth's orbit, and consider some of the conditions 

 under which the earth's movement in that orbit takes place. In 

 proceeding to do this let us first suppose the orbit of the earth to 

 to be in the form of a circle with the sun in its centre, then 

 it is perfectly clear that the earth will always be at exactly the 

 same distance from the sun, and that consequently the sun as 

 seen from the earth will always appear of the same size ; but "it 

 the other hand if the earth does not move in a truly circular orbit 

 round the sun, then, unless she moves with great irregularity— 

 and we shall entlj that she does not, the only other 



possible course for her to take is an elliptical one, because if she- 

 took an orbit ol an} other form — that of a parabola or an hyper- 

 bola for instance— she would not revolve about the sun at all, she- 

 would not have a succession of years each of 365} days' duration, 

 but one year, a year of infinite length ; she would in fact go off 

 at a tangent into infinite space. 



Let us then consider what will happen if the earth instead of 

 moving in a circular, travelled in an elliptical, orbit, with the sun 

 in one of its foci, and not in the centre of figure ; then it is per- 

 fectly clear that the distance of the earth from the sun will vary, 

 that she is nearer tlie sun at some points of her orbit than at 

 others. So much for supposition. Let us consider the facts. 

 "We know that it is the duly of die astronomers at Greenwich to 

 make daily observations, win; .,. 1 1 d. -. of the transit of the sun. 

 by means of one of those transit instruments to which reference 

 has been made. Now if the sun, as seen from the earth, had 

 always the same apparent diameter, it is obvious it would always 

 take exactly the same inn central wire of the transit 



instrument ; but when we turn to the record of the observations 

 made at Greenwich we find this : — Take the year 1S7S. 1 >n 

 January 9 in that year the apparent diameter of the sun was 

 33' 33"'5° of arc, whereas on July 13 of the same year it was 

 31' jo"'J4 ; the apparent diameter was less, so that if these 

 observations are to be depended on — and I know of none better 

 — we were nearer the sun in January 187S than we were in 

 July. If that be so. then there should be two intermediate points 

 when the diameter of the sun was the same, with an interval of 

 six months between them. This is what was observed on two 

 such dates in this same year, on April 5 an apparent diameter 

 of 31' 58"'l6, and on October 5 an apparent diameter id 

 32' 5"' J 7- I' 1 this latter case we have a difference only of 7"'Oi ; 

 in the former case a difference of over 2', so that the Greenwich 

 observations quite justify the supposition that the earth moves, 

 not in a circle, but in an ellipse ; because, the greater the distance 

 of the sun from the earth, the smaller it must appear. While 

 we are on this subject of the ellipticity of the earth's orbit, I 

 am anxious to draw your attention to the two diagrams, so that 

 the matter may lie as clear as possible. Let us consider the 

 diagram, Fig. 43. We have drawn there an ellipse, and the earth 

 is assumed to move in [he di e< tion of the arrow round the sun 

 placed in one of its foci. s. 



Now by the construction of an ellipse we know that s B, which 

 represents the mean distance lie 1 ween the earth and the sun, is 

 exactly the same as the distance A 1 1 or p o, which represents what is 

 hnown as the semi-axis major of tlie ellipse ; further, the eccen- 

 tricity of any ellipse is defined by the ratio of OS to OA ; when 

 the distance o s is very large- as compared with o A, then the 

 ellipse is a very flattened one, and die shorter the distance us 

 ' 1 !ontinued In nn p. 113. 



as compared with o A the less flattened will be the ellipse ami 

 the more nearly will it approach a circle. It wall now be clear 

 why the two points are marked A and P, for if s be taken to 

 represent the focus of the ellipse actually occupied by the sun, 

 the point P will represent the place occupied by the earth when 

 it is nearest the sun, which is called by a Greek word, "peri- 

 helion," whilst this other point A will mark that point 111 the 

 orbit of the earth when it is farthest removed from the sun, this 

 being called by another Greek word, "aphelion." This aphelion 

 distance represents the semi-axis major plus the eccentricity, and 

 the perihelion distance of the earth from the sun is obtained by a 

 subtraction of the value of the eccentricity from that ol the 

 semi-axis major. These statements are general with regard to 

 ellipses, and in order to make the point quite clear, we have 

 shown them on the very flattened ellipse of Fig. 43, but the true 

 form of the earth's orbit very nearly approaches a circle. If 

 we want to find the greatest distance and the least distance of 

 the earth from the sun at the opposite points of the orbit, we 

 take the best value we can get of the mean distance SB, or OA, 

 which is the same thing, and it is found that the eccentricity 

 comes out about iA millions of miles, so that the greatest distance 

 ol the earth is less than 94A millions, whilst its distance at peri- 

 helion is a little more than 91^. So much then for the facts 

 with regard to the varying distances at which the earth ts found 

 loan the sun at different periods of the year. 



The next point is this : i-f the earth moves in this elliptic path 

 round the sun, does she always move with the same velocity. 

 dor, she go more quickly at some times than at others, or does 

 she travel always with a steady, constant pace? Now here 

 again the question can easily be answered by an appeal to the 



Fig. 43. 



Useful transit instrument. Our sidereal clock gives us a method, 

 lung the interval, true to the hundredth part of a 

 second, between one transit of the sun over the central wire of 

 the instrument and another, and so enables us to determine the 

 number of degrees, minutes, seconds, tenths of seconds, and 

 hundredths of seconds of arc passed over by the sun in that time. 

 If tlie earth, therefore, in her revolution round the sun moves 

 with an equal unchanging motion then it is clear that the 

 number of degrees, minutes, and seconds of are passed over in 

 any given time will lie always the same. Let us again consider 

 the In ts according to the Greenwich record. On December 27, 

 1S77, the transit of the sun's centre occurred at iSh. 25m. 

 44'9s. sidereal time, but on the day before it took place at 

 l8h. 21m. i8"5s. If this second quantity be subtracted from the 

 first, the difference comes out as 4m. 26 '4s., that being the amount 

 of are passed over by the earth in that interval. Now on June 

 29 of the same year we get oh. 33m. 51 "7s., whereas on the 

 281I1 the time was oh. 29m. 43'3s., a difference of 4m. 8'4S. It 

 is thus obvious that the motion of the earth is not uniform, and 

 that being so, the question arises, Is this want of uniformity 

 constant, or is it irregular? Is there, in short, any law governing 

 it? It will lie seen that there is a most perfect law about 

 it ; that when the sun looks biggest, that is to say, wdien 

 we are nearest the sun, the earth moves most quickly, 

 and that when the sun looks smallest from the earth, when 

 the earth is at its greatest distance from the sun, it moves 

 with its least velocity. This fact brings us face to face 

 with a most fundamental law of astronomy — that law which is 

 known as the second law of Kepler. This can be gathered from 

 Fig. 44. Here s represents the sun in one focus of the ellipse 



