MOTTOH. 



While hip A (fy. 8) 



I 



I iWf owned into the position in ; tiwt 

 loag * le BD.the spKtator imagining 

 I dotted line* *o w the method of ptw>e.ding, 



of ptw>e.ding, 

 i A to B, M mov through B 



(c D being equal an<l parallel to AB), E through EF (E* behlUel to 



and equal to one-hall of A B), o through o H, K through K L, M through 

 I x, and let p remain at rest. Then, a spectator in A supposing himself 

 t pert, c will appear to remain at c, E will appear to move through E/, 

 i through o A, K through K /, M through M n, and p through pp. The 



motion of A has been transferred in a contrary direction to each of the 



other vessels. 



When bodies are very distant their changes of distance are not soon 



pwoejved, consequently it is only by change of direction that their 



lotion becomes visible. This is the case in all the heavenly bodies ; 



we shall now show what the apparent motion of a planet, superior 



and inferior, would be, if changes of distance, as well as direction. 



could be perceived and estimated. 



f the spectator be in motion, an object at rest appears to him tc 



hare precisely his own motion, but in a contrary direction ; for if the 



object be o and UK spectator move through A BCD, no distances would 



Fig. 4. 



be changed ff the spectator were fixed at o, and the object moved 

 through A BCD, and all directions would only undergo a diametrical 

 change. Consequently the relative motion of the object is represented 

 by allowing ft to change places with the spectator, and inverting the 

 direction of north and south, which will have the effect of making the 

 relative notion from west to east, if that of the spectator were from 

 mat to west, and rice rend. Let us suppose now that the earth moves 

 round the son in a circle, which will be near enough for our present 



FJf.5. 



purpose ; it will be immediately obvious that the direction of motion, 

 so far as concerns the order in which constellations will be described, 

 is the wine in the relative motion of the sun round the earth as in the 

 absolute motion of the earth round the sun. For though the absolute 

 dtractioos of motions are opposite , yet a, to a spectator at E, is seen 

 towards a point of the heaven* opposite to that hi which E appears 

 Iran s. [Mono*, DIRECTION or.] 



In giving to the sun the apparent motion which answers to the real 

 motion of UK earth, the same motion must bejiven to the orbit* in 

 which the jliiots are carried round the ran. The question then is as 

 fallows : If a planet more round the mm, mf with a uniform circular 



MOTION. M 



motion, while the sun mow. rouBd the earth, also uniformly and 

 circularly, what path will the plan* .ctaally tnoi o**t 



To get a notion of the poaribb spwies of curves, let w amplify the 

 question by supposing circle A BCD moving along * straight line B , 

 while a point moves round the circle from A. 



In the first place, if A did not move round at all, the line A o would 

 be described ; if A moved slowly round, the translation trf the circle 

 would cause an undulating curve like A H K to be described ; if A moved 

 as fast on the circle as the circle itself is moved forward, the undulation 

 would be changed into a curve with cusps like A L o ; while if A move 

 faster on the circle than the circle ia carried forward, the circle, so to 

 speak, will not have time to get out of the way, and prevent the 



formation of loops, as in AMXMPO.NQ, The farter A moves, the 



larger and the nearer will be the loops, so that at length no one will be 

 clear of the preceding and following, or the loops will interlace. 



If the circle move ronnd another circle, the same appearances will be 

 presented in an inverse order. Let the centre E of the circle A B c D 

 (fg. 7) be carried round the circle ET, whose centre is o. If .\ 'li-l not 

 move at all upon its circle, it would, by the motion of its circle, describe 

 a circle (dotted) equal to r.T; if A moved slowly, it would describe a 

 succession of close loops enveloping o ; if quicker, the loops would at 

 last disengage themselves from each other ; while for still more rapid 

 motion of A the loops would become cusps, and afterwards the curve 



Fig. 7. 



would simply undulate. The character of these curves will be further 

 discussed under TROCHOIDAI. CURVES, and their astronomical appli- 

 cation under PLANETARY MOTIONS. It is sufficient here to say that 

 the apparent orbit* of all the planets (or rather, the orbits an they 

 would be if changes of distance were perceptible) are trochoidal curve* 

 of the above-described species, with loops which do not interfere with 

 one another. 



The composition of motion has been virtually proved in the preceding 

 paragraphs, combined with the account of the second law of n 

 [MOTION, LAWS or.] If causes of motion act instantaneously, . 

 which would make a body describe AB (Jig. 8) uniformly, and the other 



Fig. . 



A c, in the name time, we find in the second law of motion tliat the body 

 will move so that its distance from A B at the end of any time, measured 

 parallel to A 0, Is what it would have been if the cause of motion in 

 the direction A B bad never existed nor acted. Suppose, for example, 

 that three-fifths of the whole time of motion from A to B ban elapsed ; 

 take , D three-fifths of c, and the body must be then somewhere in the 

 fine D E. Again, take A V three-fifths of A n, and by the Katnr law it 

 follows that tin- lxly mnst be in the line F o, that is, it must be at 

 the point n, which simple geometry shows to be on the diagonal A K, 

 and by three ; -Mat diagonal distant from A. The same may be 



shown for any other proportion of the whole time ; consequently the 

 body, impressed with the two motions, describes the diagoiial A K uni- 

 formly, and in the same time as that in which the separate motions, 



