The double compensating shadow instruments are more readily tested for accuracy in all parts of the scale than those of any other construction. The two compensating wedges are cut with the greatest care, one from a left-handed and the other from a right-handed perfectly homogeneous quartz crystal. Since faults in these wedges are due either to lack of parallelism of surface, or of perpendicularity to the optical axis of the crystal, and since these faults of crystallization or construction must be in a very limited degree common they would not coincide once in many thousand times in the two wedges. This is easily shown by the theory of probabilities. If, therefore, the two readings made at any point, should not agree, it must be due either to a fault in one of the wedges, or to a fault in reading or a lack of adjustment, as has been mentioned. In such cases the readings should be retaken and the errors are usually easily discovered. =78. Control Observation Tube.=—Instead of using quartz plates of known values for testing the accuracy of the scale, an observation tube may be used, the length of which can be varied at the pleasure of the observer. The construction of a tube of this kind is shown in Fig. 40. The tube B is movable telescopically in A by means of the ratchet wheel shown. It is closed at D water-tight by a glass disk. The tube B fits as accurately into A as is possible to permit of free movement, and any liquid which may infilter between its outer surface and the inner surface of A is prevented from gaining exit by the washer C, which fits both tubes water-tight. The ratchet which moves B in A carries a millimeter scale and vernier N whereby the exact thickness of the liquid solution between the surfaces of the glass disks D and E can be always determined. [Illustration: FIGURE 41. CONTROL OBSERVATION TUBE.] By this device the length of liquid under observation can be accurately read to a tenth of a millimeter. The cover glass E is held in position by any one of the devices in common use for this purpose in the case in question, by a bayonet fastening. The funnel T, communicating directly with the interior of A, serves to hold the solution, there being always enough of it to fill the tube when D is removed to the maximum distance from C, which is usually a little more than 200 millimeters. Let the control tube be adjusted to 200 millimeters and filled with a solution of pure sugar, which reads 100 per cent or degrees in a 200 millimeter tube. Since the degree of rotation is, other things being equal, proportional to the length of the column of polarizing solution, it follows that if the tube B be moved inward until the distance between D and C is 100 millimeters, the scale should read 50° or per cent. By adjusting the length of the distance between B and C it is easily seen that every part of the scale can be accurately tested.