$$123,124] Phases of Venus: Sun-spots 155 



according to which celestial bodies were perfect and un- 

 changeable. The fact, noticed by all the early observers, 

 that the spots appeared to move across the face of the sun 

 from the eastern to the western side (i.e. roughly from left 

 to right, as seen at midday by an observer in our latitudes), 

 gave at first sight countenance to the view, championed by 

 Scheiner among others, that the spots might really be small 

 planets revolving round the sun, and appearing as dark 

 objects whenever they passed between the sun and the 

 observer. In three letters to his friend Welser, a merchant 

 prince of Augsburg, written in 1612 and published in the 

 following year,* Galilei, while giving a full account of his 

 observations, gave a crushing refutation of this view ; proved 

 that the spots must be on or close to the surface of the 

 sun, and that the motions observed were exactly such as 

 would result if the spots were attached to the sun, and it 

 revolved on an axis in a period of about a month ; and 

 further, while disclaiming any wish to speak confidently, 

 called attention to several of their points of resemblance 

 to clouds. 



One of nis arguments against Scheiner's views is so 

 simple and at the same time so convincing, that it may 

 be worth while to reproduce it as an illustration of Galilei's 

 method, though the controversy itself is quite dead. 



Galilei noticed, namely, that while a spot took about 

 fourteen days to cross from one side of the sun to the 

 other, and this time was the same whether the spot passed 

 through the centre of the sun's disc, or along a shorter 

 path at some distance from it, its rate of motion was by 

 no means uniform, but that the spot's motion always 

 appeared much slower when near the edge of the sun 

 than when near the centre. This he recognised as an 

 effect of foreshortening, which would result if, and only if, 

 the spot were near the sun. 



If, for example, in the figure, the circle represent a 

 section of the sun by a plane through the observer at o, 

 and A, B, c, D, E be points taken at equal distances along 

 the surface of the sun, so as to represent the positions 

 of an object on the sun at equal intervals of time, on 

 the assumption that the sun revolves uniformly, then the 



* Historia c Dituostrasioni intorno alle Macchie Solan. 



