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154 depends on that if; if we have watched her long enough. Ceres had only been watched for a very little time before Piazzi fell ill, and those who were accustomed to such calculations said it was not nearly long enough to enable the orbit to be calculated. You will understand the difficulty perhaps from Figure 42: if you have a large portion ABC of a circle given, it is pretty easy to find the centre O and draw the rest of the curve (dotted) from A to C. If the given part is much smaller, like DE, it is harder to find the centre P and draw the rest,

though it can still be done. But when there is only a tiny bit like GH given you, you scarcely know whether the circle should come out like GHK or like GHL: you may be watching for the burglar to come out at K when he is really at L. That was the difficulty about Ceres; she had only shown a very small bit of her circle before disappearing. Look at the minute spaces on your watch—there are 60 of them in the complete circle. If you had one of them drawn on a piece of paper, and one only, and tried from that to draw the whole watch dial, you would find it pretty hard; and Ceres did not even give the astronomers a whole space—she gave them less than