332 THE WORLD MACHINE 



his point of view had been shifted from one side of the earth's 

 orbit to the other and back again, and still he could observe 

 no change of position in the star, relative to its neighbours. 



If yet unable to fix its distance, Kepler bethought himself 

 of a method that might at least determine the lower limit. 

 His idea was simply this : The outermost of the planets then 

 known completes its orbit in a little less than thirty years. 

 In a year, then, Saturn passes through an arc of about twelve 

 degrees of its circle ; in six months, half this. The position 

 which it should occupy against the bank of stars may then be 

 determined accurately for any desired moment. But if Saturn 

 be observed from the earth at intervals of six months that is 

 to say, from one side of the sun to the other its apparent 

 shift of position averages about six degrees. And its distance 

 from the earth is known. 



Kepler estimated that the limits of error in observation 

 attained in his time certainly did not surpass two minutes of 

 arc. If, therefore, no shift like that of Saturn could be dis- 

 covered for the new star, it follows that it must be as much 

 more distant as six degrees are greater than two minutes. This 

 was 180 times. Saturn being ten times the distance of the 

 earth to the sun, it was clear that the new star was at least 1800 

 times this distance. The same method was, of course, applicable 

 to any star, and as the limits of possible error were steadily 

 reduced, this lower limit of distance was steadily raised. 



It had reached at least ten times 1800 earth-distances when, 

 fifty or sixty years later, the fertile mind of Huyghens caught 

 up the problem from quite another point of view. By that time 

 the ancient plan of classifying the stars according to their relative 

 brightness had been taken up anew. Through the aid of the 

 telescope they were able to fix this relationship with a far greater 

 accuracy than anything hitherto known. Accustomed to such 

 minuteness of observation, Huyghens conceived the idea of 

 comparing the brightest of the stars with the sun. To effect this 

 comparison he placed across the end of his telescope an opaque 

 disk, which he pierced with a pin-point. Turning his tube now 

 towards the sun, he found that its brightness, shining even 

 through this minute aperture, vastly exceeded that of Sirius. 

 Decreasing the aperture yet further by means of a small objective, 

 Huyghens calculated that he must reduce the diameter of the 

 sun 27,000 times in order to bring it down to the brightness 



