328 DETERMINATION OF THE PLACES OF THE PLANETS. 



it \\ould vibrate once a year. Assuming the Earth rotated to the 

 Sun in the way the Moon does to the Earth, viz. , once in a revolu- 

 tion, the stars would move around our sphere not once in 24 hours 

 but once a year and the transit instrument of an observatory would 

 be well-nigh useless. Such an Earth would have neither equators 

 or poles. The chief celestial circle would be the ecliptic, but the 

 difficulty of referring the Sun to the stars would be enormous and 

 would probably be far beyond either the inductive or deductive 

 power of the strongest human intellect.* The climatic consequences 

 of non-rotation would also be extraordinary, but need not be dwelt 

 on here. At first, the best timekeeper (but a very irregular one) 

 would be the Moon. If the Earth's rotation were now decreasing 

 and the rotation finally ceased, the perfection of astronomy would 

 permit us to continue exact time-keeping by means of : — 



(1) The eclipses or motion of the 1st Satellite of Jupiter whose period is 

 about 42 hours ; 



(2) The motions of some of the satellites of Saturn. 



(3) The variations of light of the very snort period variable stars ; 



(4) The movement of the Moon, once its theory is perfected. 



The peculiar principle of using the rotation of the Earth for 

 angular measurements introduces another consideration. Let it 

 be assumed that time cannot be determined by an astronomical 

 observation within one-tenth of a second, — in this time the Earth 

 has described an angle of i".5; if, however, the Earth rotated in 

 48 hours instead of 24 hours, the angle would be o".75 ; if in 

 9 hours 55 minutes (the time of rotation of Jupiter) 'the angle would 

 be 3". 7. Hence the anomalous result that the quicker our measure 

 of time, the greater the resulting error of a star's place. There is 

 another way of looking at the question : still assuming that the 

 uncertainty of a time determination is one-tenth of a second (which 

 is somewhat greater than is the case in well-equipped observa- 

 tories) the resulting place-error will be uncertain to i".5. This 

 arc is passed over by the mean-motions of the various planets in 

 the following times : — 



Mercury 9 seconds. 



Venus 23 ,, 



Earth 36 ,, 



Mars 69 ,, 



Jupiter 7 minutes. 



Saturn 18 ,, 



Uranus 50 ,, 



Neptune 100 ,, 



* If the Earth's rotation is now decreasing and ultimately becomes 

 equal in length to the solar year, astronomers with their accumulated 

 konwledge would be prepared, their theories would still be valid ; the 

 words "far beyond . . . the power of the . . . intellect" refer 

 to a previous stage of human history. Had the Sun been virtually 

 fixed in the sky at the dawn of civilization, the difficulty of interpreting 

 phenomena in terms of time would have been so great that the chances 

 of a solution or explanation on the present lines would be negligible. 

 If in addition, the skies were cloud-laden, as is the case on the 

 planet Venus, the development of ideas of the universe would be 

 entirely different. The supposed human inhabitant on Venus can 



have no knowledge of matter apart from his own planet — his universe 

 extends to the height of the clouds and no further. 



