In these circumstances astronomers would scarcely have been human if they had not tried to guess the missing word. The word should have told us how much bigger the bright star was than the fainter, that is to say, the ratio of the masses of the two stars. Some of the less famous variable stars give us complete messages. (These could accordingly be used for testing the relation of mass and absolute brightness, and are represented by triangles in Fig. 7.) The difficulty about Algol arose from the excessive brightness of the bright component which swamped and made illegible the more delicate signals from the faint component. From the other systems we could find the most usual value of the mass ratio, and base on that a guess as to its probable value for Algol. Different authorities preferred slightly different estimates, but the general judgement was that in systems like Algol the bright component is twice as massive as the faint component. And so the missing word was assumed to be ‘two’; on this assumption the various dimensions of the system were worked out and came to be generally accepted as near the truth. That was sixteen years ago.[9] In this way the sense of the message was made out to be that the brighter star had a radius of 1,100,000 kilometres (one and a half times the sun’s radius), that it had half the mass of the sun, and thirty times the sun’s light-power, &c. It will be seen at once that this will not fit our curve in Fig. 7; a star of half the sun’s mass ought to be very much fainter than the sun. It was rather disconcerting to find so famous a star protesting against the theory; but after all the theory is to be tested by comparison with facts and not with guesses, and the theory might well have a sounder basis than the conjecture as to the missing word. Moreover, the spectral type of Algol is one that is not usually associated with low mass, and this cast some suspicion on the accepted results. If we are willing to trust the theory given in the last lecture we can do without the missing word. Or, to put it another way, we can try in succession various guesses instead of ‘two’ until we reach one that gives the bright component a mass and luminosity agreeing with the curve in Fig. 7. The guess ‘two’ gives, as we have seen, a point which falls a long way from the curve. Alter the guess to ‘three’ and recalculate the mass and brightness on this assumption; the corresponding point is now somewhat nearer to the curve. Continue with ‘four’, ‘five’, &c.; if the point crosses the curve we know that we have gone too far and must take an intermediate value in order to reach the desired agreement. This was done in November 1925, and it appeared that the missing word must be ‘five’, not ‘two’--a rather startling change. And now the message ran-- Radius of bright component = 2,140,000 kilometres. Mass of bright component = 4·3 x sun’s mass.