100   MOTION OF A SPINNING BODY

has steered the torpedo through the predetermined angle, that is till the line from the center of the cam-disk to the center of the square part of the cam is parallel to the axis of the torpedo. From that moment, the torpedo will be steered in a straight course.

The Dieter* method of angle fire is to keep the cam-disk fastened to the gyroscope so that the line from the center of the disk to the center of the square part of the cam remains parallel to the gyro spin-axle, and turn the entire gyroscope through the required angle about an axis perpendicular to the torpedo axes. The operation is similar to that of the preceding method.

Other methods for producing angle fire have been devised by Kaselowsky, Waldron, Patterson, Blountt and others.

A torpedo proceeding along a straight course has but one chance to hit a given target. If, however, after reaching the neighborhood of the target, the torpedo be caused to go around and around in circular paths, then there are more chances of a hit. Devices to cause a torpedo to proceed on a straight course for a predetermined distance and then execute circular paths have been developed by several inventors.$

61. Airplane Cartography. - During the Great War methods were developed by which military maps were made from a series of photographs taken by a camera mounted on an airplane. As the airplane moved back and forth in parallel paths, the camera took a series of overlapping views on a long film which afterward could be cut up and fastened together so as to form a mosaic of the district covered. The points which were common to overlapping parts of successive pictures served to bring the separate pictures into register and also to show any difference in scale of successive pictures.

Since the war, the method has been greatly improved and its use extended to civil operations. It is estimated that over rough terrain one camera on an airplane can take in one hour the pictures for a reconnaissance map that would be as accurate and detailed as the data that would be taken in one month by a party of one hundred surveyors.

In order that all the pictures in a strip may be on the same * U. S. Patent. Dieter, No. 1153678, 1915. f U. S. Patents. Kaselowsky, No. 661535, 1900; Waldron, No. 983467,

1911; Patterson, No. 1332302, 1920; Blount, No. 1527777, 1925.

t U. S. Patents. Dieter, Nos. 1303038 and 1303044, 1919; Meitner and May, No. 1401628, 1921; Trenor, No. 1517873, 1924; Bevans, No. 1527775, 1925.

MOTION OF A SPINNING BODY   101

scale, the distance between the camera and the ground would need to be constant. It is, however, impossible and unnecessary to maintain this distance constant. Any difference in the scale of adjacent pictures is shown in the overlapping portions. The pictures that are out of scale are enlarged or diminished to the required degree by photography and the new pictures used in the mosaic.

In order that the photographs may be without distortion, the external axis of the camera must be maintained in the direction of the radius of the earth. If the camera be suspended pendulumwise, the axis will be deflected from the vertical when the velocity of the airplane changes in either magnitude or direction. It is practically impossible to keep the velocity constant under usual atmospheric conditions.

62. Direct Control of the Direction of the Axis of a Camera. - The first aviator photographers had no means to correct the deflection of a camera produced by acceleration of the airplane, except by manual adjustment. The camera was supported pendulously and moved back as soon as a deflection was observed. Some aviator photographers still use the same method. This method, however, brings the camera back to only approximately the correct position after a noticeable deflection has occurred. The pictures taken while the original deflection is occurring and while it is being corrected are distorted.

Probably the most obvious plan to prevent the deflection of the camera is to apply the First Law of Gyrodynamics, by attaching to the camera one or two gyroscopes.* This plan is faulty in that when a gyroscope exerts a torque in erecting a camera, the gyro itself is acted upon by a torque, and this torque causes the spinaxle and the attached camera to turn about an axis perpendicular to the torque-axis. Thus, the camera is given an undesired displacement. Again, even though the spin-axle were directed toward the center of the earth at one instant and the direction of the spin-axle remained fixed in space, the spin-axle will not point to the center of the earth at later instants. Consequently, the pictures taken at later instants will be distorted.

63. Indirect Control of the Direction of the Axis of a Camera. - A camera or other device can be tilted by a torque produced by a motor that is started in either direction, stopped or reversed, by a

* U. S. Patents. Fairchild, No. 1546372, 1925; Lucian, No. 1634950, 1927; Titterington, No. 1645079, 1927.