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whole row would seem to the naked eye as a single point. The history of the discovery of Neptune, which was mentioned in the preceding chapter, affords the most striking example that we possess of the certainty of these predictions.

I shall now endeavour to give the reader some idea of the manner in which the mathematical astronomer reaches these wonderful results. To make them, he must, of course, know the pull each planet exerts upon the others. This is proportional to what the physicist and astronomer call the mass of the attracting planet. This word means quantity of matter, and around us on the surface of the earth, it has nearly the same meaning as the word weight. We may therefore say that, when the astronomer determines the mass of a planet, he is weighing it. He does this on the same principle by which the butcher weighs a ham in the spring balance. When the butcher picks the ham up he feels a pull of the ham toward the earth. When he hangs it on the hook, this pull is transferred from his hand to the spring of the balance. The stronger the pull the farther the spring is pulled down. What he reads on the scale is the strength of the pull. You know that this pull is simply the attraction of the earth on the ham. But, by a universal law of force, the ham attracts the earth exactly as much as the earth does the ham. So what the butcher really does is to find how much or how strongly the ham attracts the earth, and he calls that pull the weight of the ham. On the same