Miscellaneous Papers of the University Observatory, Oxford Volume . 1

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1902 Excerpt: ...suggestion arose in the following way: --4. The brightness curve in the previous paper was obtained by plotting brightness against distance. This gives a curve of hyperbolic 'Roy. Soc. Proc., ' vol. 66, p. 403. b 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. 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 + a) will be increased, and log y therefore diminished, and we get a curve such as CD. (If a 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...