the bag as he spoke, and with tottering steps (it was about as much as he could do to carry it) he left the room.
`And you shall have a similar cadeau,' the old lady whispered to her niece, `when you've calculated that percentage!' And she followed her brother.
Nothing could exceed the solemnity with which the old couple had risen from the table, and yet was it--was it a grin with which the father turned away from his unhappy sons? Could it be--could it be a wink with which the aunt abandoned her despairing niece? And where those--were those sounds of suppressed chuckling which floated into the room, just before Balbus (who had followed them out) closed the door? Surely not: and yet the butler told the cook--but no, that was merely idle gossip, and I will not repeat it.
The shades of evening granted their unuttered petition, and `closed not o'er' them (for the butler brought in the lamp): the same obliging shades left them a `lonely bark' (the wail of a dog, in the back-yard, baying the moon) for `a while': but neither `morn, alas', nor any other epoch, seemed likely to `restore' them--to that peace of mind which had once been theirs ere ever these problems had swooped upon them, and crushed them with a load of unfathomable mystery!
`It's hardly fair,' muttered Hugh `to give us such a jumble as this to work out!'
`Fair?' Clara echoed bitterly. `Well!'
And to all my readers I can but repeat the last words of gentle Clara:
Problem. Two travelers spend from 3 o'clock till 9 in walking along a level road, up a hill, and home again: their pace on the level being 4 miles an hour, up hill 3, and down hill 6. Find the distance walked: also (within half an hour) time of reaching top of hill.
Answer. 24 miles: half-past 6.
Solution. A level mile takes ¼ of an hour, up hill 1/3, down hill 1/6. Hence to go and return over the same mile, whether on the level or on the hillside, takes ½ an hour. Hence in 6 hours they went 12 miles out and 12 back. If the 12 miles out had been nearly all level, they would have taken a little over 3 hours; if nearly all up hill, a little under 4. Hence 3 ½ hours must be within ½ an hour of the time taken in reaching the peak; thus, as they started at 3, they got there within ½ an hour of ½ past 6.
Twenty-seven answers have come in. Of these, 9 are right, 16 partially right, and 2 wrong. The 16 give the distance correctly, but they have failed to grasp the fact that the top of the hill might have been reached at any moment between 6 o'clock and 7.
The two wrong answers are from GERTY VERNON and A NIHILIST. The former makes the distance `23 miles', while her revolutionary companion puts it at `27'. GERTY VERNON says, `they had to go 4 miles along the plain, and got to the foot of the hill at 4 o'clock.' They might have done so, I grant; but you have no ground for saying they did so. `It was 7 ½ miles to the top of the hill, and they reached that at ¼ before 7 o'clock.' Here you go wrong in your arithmetic, and I must, however reluctantly, bid you farewell. 7 ½ miles, at 3 miles an hour, would not require 2 ¾ hours. A NIHILIST says, `Let x denote the whole number of miles; y the number of hours to hill-top; Therefore 3y = number of miles to hill-top, and x -- 3y