2 BROWN : 



eral idea of it can be set before those who take ati interest. 

 Our problem may be said to owe its solution to Dr. Edmund 

 Halley, mathematical philosopher and Astronomer Royal, 

 I ^75" 1 742. In the year 17 16 this eminent man of science pre- 

 sented a paper on the subject to the Royal Society of London. 

 He could entertain no hope of seeing^ the next Transit of 

 Venus ; but he set forth what he said would be a satisfactory^ 

 method of calculating the sun's distance by means of that 

 phenomenon and bequeathed the task to posterity. Aroused 

 by him, the " curious " of all nations applied their minds to 

 the question and an amazing mass of learning and labour has 

 been brought to bear upon it. One need but refer to the 

 Philosophical Transactions of the time in the English lan- 

 guage, not to speak of those in other European tongues, to 

 have the fullest realization of this fact. 



The Earth moves in orbit from left to right as we face the 

 sun. The motion is "against the clock" and is called 

 " direct." The other planets move in the same way. 



By a law of planetary motion, moreover, those bodies 

 which are nearer to the sun move faster in their orbits than 

 those which are farther off. Just as when the water in a 

 bucket is set whirling the outer parts move more slowly than 

 those which are near the little vortex in the centre. 



If, therefore, an inferior planet should pass exactly between 

 the earth and the sun it might be seen by certain of the inhab- 

 itants of the Earth as a black spot passing across the sun's 

 disc from left to right or with what is known as " retrograde 

 motion," for it is seen to be " with the clock." 



This sometimes happens to the planet \^enus when her 

 course brings her to pass through the plane of the Earth's 

 ecliptic, or, as it is expressed, when she is "in her nodes." 

 And the occurrence is made use of in calculating the sun's 

 distance from the Earth. 



ily Kepler's third law, tlic squares of tlw times ajr as the 

 nthcs of the men)/ d/stcif/ees, which means that if the number 



