47 



index of his rotations. The sun and the stars are alike perfectly 

 fixed and immovable in their relations, and these their mutual 

 relations are never in the slightest degree affected by the earth's 

 movements. The changes of place which they, and particularly 

 the sun, seem to undergo, are apparent only, and not real, and 

 are the result exclusively of the earth's own continual change 

 of place, and therefore the indicator of the sun's rotations must 

 be a point of the heavens as invariable, or as little variable in 

 position as he is himself, provided always he turn round on his 

 axis with a uniform velocity, which there seems to be no reason 

 to doubt. But if the sun and the earth were to change places 

 and conditions, the earth becoming the fixed centre of the orbit, 

 and the sun revolving about her as a planet or satellite, the case 

 would be entirely different, for then the fixed and invariable 

 axis of the earth and the sun's equally invariable radius-vector 

 would become the true measure and indication of the sun's rota- 

 tions, while, on the contrary, the star or other fixed point of the 

 heavens, by which they were previously measured and indicated, 

 would ftill continually short of the true measure in proportion to 

 the angular distance to which the sun would be continually mov- 

 ing away from it ; and what would happen with the sun in such 

 a case does most certainly happen in the case of every planet, 

 satellite, or other body whatsoever moving in an orbit ; namely, 

 that when the orbit is a perfect circle, the radius-vector connect- 

 ing the body's axis with the centre of the circle will invariably 

 subtend or form a right angle with the orbit, and the centre 

 itself will remain invariably in the same place, and this invariable- 

 ness of the centre and the radius must most entirely preclude 

 the possibility of rotation on the part of a circumference which 

 keeps the same point continually in one with them. To my 

 own judgment this is so perfectly evident, that I can never cease 

 to wonder how any body could ever have doubted it, or gone so 

 far wrong as to maintain the contrary received opinion. 



An error of the like kind prevails respecting the true measure 

 and indication of the moon's revolutions round the earth, as I 

 find it stated in the following extract : — " The moon performs 

 its revolution round the earth in 27 days, 7 hours, 43 minutes, 

 1 1 seconds, usually called a periodical month. It is to be ob- 

 served, however, that the moon employs more than this time to 

 return to the sun after each conjunction. The cause of this dif- 

 ference is, that the earth, and consequently its satellite the moon, 

 advances in the ecliptic, while the moon is describing her orbit ; 

 so that before the moon comes into the same position relatively 

 to the sun, 2 days and about 5 hours elapse beyond the time 

 required for completing a revolution round the eartL The 

 whole time occupied in returning to the sun is 29 days, 12 hours, 



