13th.—To-morrow is the last day of the visit of these charming Lumleys. I shall be very sorry to lose them, for I have liked them better every day. The second has the sweetest voice that can be, and joined in some of our glees, which she easily learned. Once or twice they sang all together for us, in the way they do at home; and, among other things, a beautiful little hymn, which we discovered was written by Mrs. L. If I can, I will send it to you and Marianne; and, perhaps, some time or other, we three may also sing it together. Oh! when will that time come?
Even now that I know their history, it is difficult to perceive in their appearance and manners that they have lived in such complete retirement, for they always express themselves in good language; and, though timid, they are not in the least awkward. Whatever they do, they do well. They are excellent arithmeticians, and answered some puzzling questions of my uncle’s with a facility that surprised him. The power of calculating in the head he thinks highly useful; and, on this occasion, he encouraged me to try with the rest, by shewing me how to seize upon the leading points of a question. At first I made no attempt, but spent the time, that others were at work, in thinking that I had no chance of success. Having at last, however, recovered from this silly fit, I exerted myself, and actually gave the first answers to the three following questions: though I will not say that some of the party did not good-naturedly wait a little for me. I send them to Marianne, though I know they will appear trifling to her, for she was always quicker at arithmetic than I was; but tell her the great thing is, to do them in her head.
How much time, in the course of thirty years, does a person gain, who rises at six o’clock in the morning, over another who sleeps till nine; supposing that the former goes to bed at eleven, and the latter at midnight?
There is a cistern in this house, which contains 180 gallons of water: it is supplied by a feeding pipe, which admits 15 gallons in ten minutes; and the tap, or discharging pipe, lets off 12 gallons in six minutes. Now suppose, when the cistern was exactly half full, that both cocks were opened, and that, at the end of an hour afterwards, the tap-cock was shut: in what time will the cistern be filled?
Herodotus mentions a brass vessel, that was shown in Scythia in his time, which was six digits in thickness, and contained 600 amphoræ, or about 4300 gallons. It had been made of arrow points, collected by the king from his subjects, in order to ascertain their number—each individual being obliged to bring one. Such a vessel would be 11 or 12 feet in diameter; and, from the thickness of the metal, must have weighed about 71,000 pounds troy. Now, if each arrow point was half an ounce, the question is—Of how many fighting men could the Scythian monarch boast? for it is not probable that the women and children were included in that kind of warlike census.
My uncle was pleased at the efforts I made, even when I failed, because it shewed that I had conquered my old enemy—indolence.
I wrote down these questions while they were fresh in my mind; and then we all went to take our last walk together to Franklin’s farm. We found him and his active wife fixing on the situation of the house and garden, and orchard.
They have chosen a place where there is a pretty slope in the ground, so that the drains will have a good fall from the house. The garden is to be in front, and the orchard at one side. They are going to double-trench the ground, by digging it to twice the depth of the spade. It is to be left in that state during the winter; and the soil, being thus exposed to the action of air and frost, will be improved. In the course of the winter they will plant a young hedge round the garden.
This day was one of those lovely, mild, sunny days in October, of which I have often heard you speak.
When Autumn scatters his departing gleams.