156 



KNOWLEDGE. 



[July, 1901. 



We conclude with another example of the advantage 

 of treating the eccentricity and inclination as oscilla- 

 tions. It is well known thai as long as the arc of 

 vibration of a pendulum is very small, the period of its 

 oscillation remains constant, but when the arc of oscil- 

 lation is increased, the period of its oscillation is altered 

 by terms depending on the square and higher even 

 powers of the arc of vibration. Now this is one of the 

 simplest dynamical problems to work out, just as the 

 lunar theory is one of the most difficult; but the 

 analogy holds exactly : for the principal term in the 

 motion of the moon's node (or apse) is independent of 

 the size of the oscillations — that is to say, the moon's 

 node would still revolve iu about nineteen years even 

 if the eccentricity or inclination were double or half 

 what they are ; but the smaller terms in the series that 

 give the motions of the apse and node contain squares 

 and higher even powers of the amplitudes of the two 



oscillations. 



♦ 



%ttttvn. 



[The Editors do not hold themselves responsible for the opinions 

 or statements of correspondents.] 



> 



THE ORBIT OF THE MOON. 



TO THE EDITOES OF KNOWLEDGE. 



Sirs, — The present communication is intended to fill 

 a gap which exists in all the popular books on astronomy. 

 All those which I have seen contain nothing or little to 

 enable the reader to obtain any idea of the courses of 

 the moon in the heavens. For many years it was a puzzle 

 to me, as it was to others, for I have never yet met with 

 any one, except those who had a professed knowledge of 

 astronomy, who was able to describe in an intelligible 

 manner the course which the moon took in its circuit 

 round the earth and sun. 



I was once at the sea-side with a gentleman who had just 

 taken a University degree for which he had to pass an 

 examination in natural science, and we got on the subject 

 of the tides and moon ; he declared that he had not the 

 remotest idea how the moon took its annual coiu'se. I 

 therefore asked him to stand at a fixed distance from 

 myself to represent the moon as I would the earth, and 

 to hold his stick behind him as I was doing to trace our 

 course on the sand as we walked on. Keeping his distance 

 as if tied to me he was to walk quicker or slower, and 

 thus he would be necessarily revolving- around me, whilst 

 at the same time he was moving forward. His movement 

 would not be in circles but in curves. This demonstration 

 being on a plane is of course so far imperfect. 



The subject has of late come before me again when 

 some young people during the Christmas holidays 

 attended a lecture on the moon. They were shown the 

 moon's phases in the usual manner by making it perform 

 a circle round the earth; although this explained the 

 varying phases of the moon, they saw for themselves 

 that no such circle could really exist unless the earth 

 were stationary. I made this more intelligible to them, 

 as I have done to ot/hers. by drawing the two figures 

 pictured below. I made a circle for the earth's orbit 

 with the sun in the- centre, and divided it into twelve 

 monthly parts for simplicity, thirteen being an awkward 

 I'umber to deal with. I then made twelve marks opposite 

 the different divisions to indicate the twelve full moons. 

 This forms the outer circle. My young friends assented 

 to it as correct. They also assented to my making twelve 

 marks between these constituting Ihe inner ciiilc corre- 

 sponding to the no n'loon or dark niooii II was now 



obvious that if these marks were correct the luminary 

 must pass from one to another diuing the fortnight 

 between them ; these, therefore, I joined, and the course 

 of the moon was at once seen. I have heard persons 



a. — Earth's orbit. 



b. — Outer ch'cle of full moons. 



c. — Inner circle of no moons. 



a. — Orbit of E:irtli. 

 h. — Orbit, lit Moou made 

 by joining the poiJits. 



who have taken some little interest iu the heavens declare 

 that this simple drawing was a complete revelation to 

 them as they were so beset with the idea of the circular 

 movement of the moon as portrayed in the books that they 

 could not eradicate it from their minds. As before said 

 this diagram is on a plane, and, therefore, imperfect; but 

 a better demonstration may be made by taking a coil of 

 wire such as is used in electric instruments, bending it 

 into a circle and joining the two ends. When stretched 

 out so as to elongate the coils the spiral may be regarded 

 as showing more correctly the course of the moon. 



It must be also remarked that in my diagram there 

 is no attempt at projjortion, for it would be impossible 

 to draw on so small a scale a spiral so close to the earth's 

 orbit as to be 400 times less distant from it than the 

 space between the earth and the sun. 



Let me finally say I am no astronomer or mathe- 

 matician, and, therefore, have no pretence to tread on 

 their ground ; all I advance for myself is the fact that 

 there being no account of the course of the moon in 

 popular books, the reader being left in ignorance of this 

 subject or often misled, I have found my description and 

 drawing have made it intelligible to them, although of 

 course in a very rough and imperfect way. 



Samuel Wilks. 



P.S. — Whilst inserting my letter the Editors inform 

 me that there are astronomers who have fully discussed 

 the question of the moon's path, and have raised ob- 

 jections against the description which I have given, more 

 especially as from mathematical reasoning this path is 

 every wheie concave to the sun. — S. W. 



[The defect of the diagram to which Sir Samviel Wilks' 

 attention was called lies in the simple fact that it is not 

 drawn to scale, and consequently represents the path of 

 the new moon as convex to the sun instead of concave. 

 This concavity should not be difficult to comprehend if 

 it be borne in mind that even at the time of new moon 

 the chief motion is that of revolution round the sun, 

 which it has in common with the earth. The velocity 

 of flic moon in its orbit round the earth only amounts 

 1(1 3(M10 feet per second, while its a.veragc velocity in 

 Its iiioticni round the sun is 18.6 miles per second. — Ens.] 



SUNSPOTS AND WINTERS. 



TO THE EDITORS OF KNOWLEDGE. 



Sirs, — The accompanying rough diagram I would 

 offer for criticism: — a, h, >:, d, e, each shaded column 

 represents the average number of frost days per winter 

 at Greenwich, reckoning from September to May, during 



