it with the value found from the theory you will see that there is cause for satisfaction. McLaughlin evaluated the other constants and dimensions of the system; these agree equally well, but that follows automatically because there was only one missing word to be supplied. In both determinations the missing word or mass ratio turned out to be 5.0.

This is not quite the end of the story. Why had the first guess at the mass ratio gone so badly wrong? We understand by now that a disparity in mass is closely associated with a disparity in brightness of the two stars. The disparity in brightness was given in Algol's original message; it informed us that the faint component gives about one-thirteenth of the light of the bright one. (At least that was how we interpreted it.) According to our curve this corresponds to a mass ratio 2 1/2, which is not much improvement on the original guess 2. For a mass ratio 5 the companion ought to have been much fainter in fact its light should have been undetectable. Although considerations like these could not have had much influence on the original guess, they seemed at first to reassure us that there was not very much wrong with it.

Let us call the bright component Algol A and the faint component Algol B. Some years ago a new discovery was made, namely Algol C. It was found that Algol A and B together travel in an orbit round a third star in a period of just under two years -- at least they are travelling round in this period, and we must suppose that there is something present for them to revolve around. Hitherto we had believed that when Algol A was nearly hidden at the time of deepest eclipse all the remaining light must come from Algol B; but now it is clear that it belongs to Algol C, which is always shining without interference. Consequently the mass ratio 2 1/2 is that of Algol A to Algol C. The light from Algol B [Note: It may be of interest to add that although the proper light of Algol B is inappreciable, we can observe a reflection (or re-radiation) of the light of Algol A by it. This reflected light changes like moonlight according as Algol B is 'new' or 'full'.] is inappreciable as it should be for a mass ratio 5.

The message from Algol A and B was confused, not only on account of the missing word, but because a word or two of another message from Algol C had got mixed up with it; so that even when the missing word was found to be 'five' and confirmed in two ways, the message was not quite coherent. In another place the message seemed to waver and read 'two-and-a-half'. The finishing step is the discovery that 'two-and-a-half' belongs to a different message from a previously unsuspected star, Algol C. And so it all ends happily.

The best detective is not infallible. In this story our astronomical detective made a reasonable but unsuccessful guess near the beginning of the case. He might have seen his error earlier, only there was a false clue dropped by a third party who happened to be present at the crime, which seemed to confirm the guess. This was very unlucky. But it makes all the better detective story of it.

The Story of the Companion of Sirius

The title of this detective story is 'The Nonsensical Message'.

Sirius is the most conspicuous star in the sky. Naturally it was observed very often in early days, and it was used by astronomers along with other bright stars to determine time and set the clocks by. It was a clock star, as we say. But it turned out that it was not at all a good clock; it would gain steadily for some years, and then lose. In 1844 Bessel found out the cause of this irregularity; Sirius was describing an elliptic orbit. Obviously there must be something for it to move around, and so it came to be recognized that there was a dark star there which no one had ever seen. I doubt whether any one expected it would ever be seen. The Companion of Sirius was, I believe, the first invisible star to be regularly recognized. We ought not to call such a star hypothetical. The mechanical properties of matter are much more crucial than the accidental property of being visible; we do not consider a transparent pane of glass 'hypothetical'. There was near Sirius something which exhibited the most universal mechanical property of matter, namely, exerting force on neighbouring matter according to the law of gravitation, That is better evidence of the existence of a material mass than ocular evidence would be.