NEW EXPERIMENTS

TRACT 34.

which measures time to 40th parts of a second.—Next, bya happy contrivance, the friction of the axes was almostintirely taken off. This was effected by means of sockets ofa peculiar construction, for the axes to work in. Firstimagine the half of a short cylinder, of 2 or 3 inches long,cut lengthways through the axis, and of a diameter a verylittle more than the ends of the axis that are intended to workin it : if this were all, it is evident that the axis, in vibrating,would touch this socket in one line onty, because theirdiameters were unequal. Next imagine the inside of thissocket to be gradually ground down towards each end, fromnothing in the middle ; so that the inside resembled a tubehaving its two ends bent downwards, and rising highest inthe middle. Then it is evident that the axis will touch thesocket in this one middle point only. And further, theunder sides of the axis itself were ground a little, to bringthe undermost line to a blunt edge, something like the pivotsof a scale beam. The consequence was, that the frictionwas not sensible in a great number of vibrations ; and here-after we commonly made the gun and pendulum vibrate forjust 10 minutes, and divided the counted number of vibra-tions by 10, for the mean number per minute—And formeasuring the arcs of vibration more certainly and accu-rately, we constructed a strong wooden circular arch, ofabout 4 feet in length, cut out to a radius of just 10 feet.This arch is divided into chords of equal parts, each the1000th part of the radius, or i^th parts of an inch, asbefore described in Art. 16. This arch being placed 10 feetbelow, and concentric with the axis, and the groove in themiddle of it filled with the soft composition of soap and wax,the stylette, or small sharp spear, traces in the groove theextent of the vibration, and the corresponding divisions oneach side of the groove show the length of the chordVibrated. And as these chords are in 1000th parts of theradius, the value of r, in the theorem for the velocity ofthe ball, will be 1000 for all the following experiments;and then that theorem will become