Elementary arithmetic, with brief notices of its history... by Robert Potts.

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happened 8' 13" later. Find the velocity of light if the radius of the
earth's orbit be 93,000,000 miles.
11. Two cogged wheels, of which one has 16 cogs and the other
30, work in each other. If the first wheel turn 18 times in 10 seconds,
how many times will the other turn in 25 seconds?
12. If two bodies move in the circumference of a circle, the swifter
making a revolution in 5 hours and the slower in 9, supposing they
start from the some point, when will one overtake the other?
13. The periodic times of four bodies being 24, 22, 20, and 18
days respectively, in what times after leaving a conjunction will they
all be again in conjunction, and what number of revolutions will each
have performed?
XXXIV.
1. A clock is set at 12 o'clock on Saturday night, and at noon on
Tuesday it is 3 minutes too fast. Supposing its rate regular, what will
be the true time when the clock strikes 4 on Thursday afternoon?
2. Find the different times at which the hour and minute hand
of a clock are in conjunction, in opposition, and at right angles to
one another, between noon and midnight. If the hands were alike,
at what times of the day might they be mistaken the one for the
other?
3. The seconds hand of a watch revolves about the same axis as
the hour and minute hands. Determine all the positions in which
the three hands are together, in the same straight line, and at right
angles, during one revolution of the hour hand.
4. If a watch be 4 min. 8 -~- sec. too slow at 9 hrs. 30 min. a.m.
on Tuesday, and loses 2 min. 45 sec. daily, what will be the time
indicated at 5 hrs. 15 min. p.m. on the following Friday?
5. A watch which is 10 minutes too fast at noon on Monday
loses 3 min. 10 sec. daily. What will be the time indicated by the
watch at a quarter past 10 on the morning of the following Saturday?
6. What is the magnitude of the angle between the hour and
minute hand of a clock at - past 11?
7. It is between 2 and 3 o'clock, and the hands of the clock are
equally inclined to the vertical on opposite sides. In what time will
they be inclined to the vertical again on opposite sides?
8. A watch set accurately at 12 o'clock indicates 10 minutes to 5
at 5 o'clock. What is the exact time when the watch indicates 5 o'clock?
If it indicated 10 minutes past 5 at 5 o'clock, what would be the exact
time when the hands indicated 5 o'clock?
9. One clock gains 2 minutes in 3 days, and another loses 6
minutes in 7 days; if they were set right at 12 noon to-day, when will
their times differ by a quarter of an hour?
10. Two clocks begin to strike 12 together; one strikes in 35
seconds the other in 25. What fraction of a minute is there between
their seventh strokes?