Brightness of the Corona of January 22, 1898. 37 



form close to the two axes of reference, and difficult to compare the 

 observations with, for reasons which are tolerably obvious. The curve 

 is still hyperbolic if log (brightness) be plotted against distance ; but 

 if the brightness varies as any power of the distance, and we plot log 

 {brightness) against log (distance), we get a straight line, which is 

 particularly easy to compare observations with. The only difficulty is 

 that we must know where to measure our distance from ; for if we add 

 or subtract a constant to the distance, it will change the straight line 

 into a curve. And unfortunately the point from which the distance 

 was to be measured seemed just one of the things to be determined. 



5. But after some preliminary experiments I found that it was not 

 difficult to find the proper origin from which to measure the distance, 

 by the very condition that the curve was to be a straight line. 



Fig. 1. 



If in the equation 



log y + n log x = const. 



represented by the straight line AB in fig. 1, we write (x + a) for x, 

 then the calculated values of log y, when x is large compared with a, 

 will be nearly the same as before ; but when x is small log (x + oc) will 

 be increased, and log y therefore diminished, and we get a curve such 

 as CD. (If en be negative, we get a curve such as EF.) And a very 

 few trials (perhaps one alone suffices) give the value of a, which will 

 straighten the curve. 



6. These values immediately pointed to the sun's centre as the 

 proper origin for measurement ; and when the observations were 

 plotted on this assumption, the curve was practically a straight line, 

 and the slope of this line indicated that the index n was 6, giving the 

 law already stated, viz. : — 



Brightness <x (distance from sun's centre) - ' 5 . 



7. But one further point is to be noted. The curve was practically 

 straight for some distance from the limb, but then always turned 



