There is a treatise of his extant, in which he remarks (I cite from memory) that as some people believe it possible for numbers to express a quantity as great as that of the grains of sand upon the sea-shore, while others deny this, he will show that they can express one even larger. To prove this beyond dispute, he begins by taking a small seed, beside which he ranges single grains of sand in a line, till he can give the number of these latter which equal its length. Next he ranges seeds beside each other till their number makes up the length of a span; then he counts the spans in a stadium, and the stadia in the whole world as known to the ancients, at each step expressing his results in a number certainly _greater_ than the number of sand-grains which the seed, or the span, or the stadium, or finally the whole world, is thus successively shown to contain. He has then already got a number before his reader’s eyes demonstrably larger than that of all the grains of sand on the sea-shore; yet he does not stop, but steps off the earth into space, to calculate and express a number _greater_ than that of all the grains of sand which would fill a sphere embracing the earth and the sun! We are going to use our little unit of heat in the same way, for (to calculate in round figures and in English measure) we find that we can set over nine hundred of these small cubes side by side in a square foot, and, as there are 28,000,000 feet in a square mile, that the latter would contain 25,000,000,000 of the cubes, placed side by side, touching each other, like a mosaic pavement. We find also, by weighing our little cup, that we should need to fill and empty it almost exactly a million times to exhaust a tank containing a ton of water. The sun-heat falling on one square mile corresponds, then, to over seven hundred and fifty tons of water raised _every minute_ from the freezing-point to boiling, which already is becoming a respectable amount! But there are 49,000,000 square miles in the cross-section of the earth exposed to the sun’s rays, which it would therefore need 1,225,000,000,000,000,000 of our little dies to cover one deep; and therefore in each _minute_ the sun’s heat falling on the earth would raise to boiling 37,000,000,000 tons of water. We may express this in other ways, as by the quantity of ice it would melt; and as the heat required to melt a given weight of ice is 79/100 of that required to bring as much water from the freezing to the boiling point, and as the whole surface of the earth, including the night side, is four times the cross-section exposed to the sun, we find, by taking 526,000 minutes to a year, that the sun’s rays would melt in the year a coating of ice over the whole earth more than one hundred and sixty feet thick.