EXPLANATION TO THE PLATE 

 OF THE SEASONS AND TIDES. 



Fig. l. Is a representation of the earth's orbit, as it would appear to a 

 spectator, at an infinite distance perpendicularly over the centre. The 

 horizontal line across the centre is the solstitial diameter, the winter sol- 

 stice to the northern hemisphere being at the left hand, and the summer 

 solstice at the right. Of course the vernal equinox is at the bottom, and 

 the autumnal at the top. The vertical line passing through S, (the 

 place of the sun), is the equinoctial diameter of the orbit, f is the other 

 focus of the ellipse ; the small space, from S to f, is the focal distance, or 

 twice the eccentricity ; and the longest diameter that could be drawn per- 

 pendicularly to the solstitial one would be half way between S and f. 



Upon the supposition that the sun is at rest, the form of the orbit will 

 be very nearly that of the figure j but as we do not know anything about 

 rest or motion in absolute space, and as the sun may have a motion of 

 many hundred millions of miles in a year, or even in a day, or an hour, 

 we know not the form of the orbit in any other way than with reference 

 to the sun. The head of a nail in a coach wheel performs a motion in a 

 circular orbit round the axle ; but, as the coach rolls on, sometimes on a 

 level, sometimes up hill, and sometimes down, sometimes straight forward, 

 sometimes curving to the right, and sometimes to the left, the path of the 

 nail, with regard to the earth, is very different, and could not possibly be 

 represented on a flat surface. If the road were straight forward, the path 

 of the nail would be a series of cycloids, having their terminations at the 

 points where the nail came in contact with the road, and the path would 

 be something like this 



there being as many loops or cycloids upward as revolutions of the wheel. 



