74   MOTION OF A SPINNING BODY

Problem. A gyro of moment of inertia with respect to the spin-axis of 128 lb.-ft.2 is spinning at latitude 45° N. with an angular speed of 2000 r.p.m. The gyro is mounted so that the center of gravity of the wheel and that of

each of the supporting gimbal rings coincides with the intersection of the axes of the knife-edges of the two rings. Find the mass and the position that an added body must have so that when placed 4 in. from the center of mass of the gyroscope it will cause the spin-axle to remain in the meridian plane.

43. An Instrument for Measuring the Crookedness of a Well Casing. - In drilling or in boring a deep well it is very difficult to maintain the bore hole vertical or straight. Crooked holes may prevent the rotation of the drill or may cause the drill to twist off. The bottom of a well a couple of thousand feet deep may be more than a hundred feet to one side of the vertical through the top of the hole. It may be on the property of a proprietor other than the one who owns the land on which the upper end of the well is situated. Until recently no method has been known to measure the direction and amount of the bends of a deep well bore.

By means of the Surwel gyroscopic clinograph, a permanent record of the position, direction, length and amount of any bends in a well casing can now be obtained. The apparatus is enclosed within a cylindrical case several feet in length and five and onehalf inches outside diameter. This case contains a universal spirit level, a universally mounted gyro with horizontal spin-axle, a watch, a movie camera, miniature incandescent lamps, and batteries of dry cells to spin the gyro and operate the lamps and movie camera.

The upper spherical surface of the spirit level carries a series of concentric circles spaced so as to indicate the inclination of the axis of the case from the vertical in any direction. The bubble cell is provided with an expansion coil which keeps the bubble the same size whatever the temperature of the apparatus.

Any turning of the instrument about its geometrical axis while being lowered into the well is indicated by the gyro which spins about a horizontal axis at a speed of about 11,000 revolutions per minute. The natural turning of the spin-axle relative to the earth, due to the rotation of the earth, is neutralized by a precession of equal speed in the opposite direction produced by the weight of a small mass attached to the north bearing of the spin-axle (Art. 41). The vertical pivot of the gyro-casing carries a pointer which indicates the direction, in azimuth, of the spin-axle. Besides the

MOTION OF A SPINNING BODY   75

t,vo hands of the watch there is a pointer that marks the time the apparatus started down the well.

The instrument is lowered into the well at a known constant rate. The movie camera takes a series of pictures at a regular interval which depends upon the speed with which the instrument is lowered. The first picture is taken as the instrument starts down the well. Each picture shows the time as well as the in- clination of the instrument and the amount the instrument may have twisted about its axis from its original position, at the in- stant the picture was taken. From the views of the three scales shown in any one picture the distance of the apparatus from the top of the well at any instant can be determined, as well as the direction and magnitude of the inclination from the vertical of the bore hole at that instant.

44. The Weston Centrifugal Drier. - In laundries water is removed from wet clothes by a " centrifugal drier " consisting of a metal cylinder with perforated sides capable of rotating at high speed about a vertical axis. In most models, the perforated cylin- der is rigidly fastened on the upper end of a vertical shaft. If the wet clothes are not packed uniformly about the axis of rotation the shaft will be subjected to considerable stresses when rotated at high speed.

In the Weston centrifugal machine used to separate molasses from sugar crystals, this difficulty is avoided by hanging the per-

forated cylinder from a universal joint on the lower end-of a vertical shaft. In case the center of mass of the suspended system is not on the axis of rotation, it will move away from the vertical'line through the point of support, Fig. 57. The suspended system now is acted upon by a gravitational torque in the direction represented by the symbol at L in the figure. When

the suspended system is rotating in the direction represented by hs, it will precess in the direction represented by wp.

A pin, in line with the axis of the perforated cylinder, fits loosely in a block of metal B that can slide around on the bottom of an outer cylinder. When the axis of the perforated cylinder is not

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