Surveying and Levelling Instruments, Theoretically and Practically Described. / For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field.

by William Ford Stanley

170.—The operation of grinding is very much the same as that described for lenses, [p. 17]. The surface is required to be traversed in every direction longitudinally and transversely, which is effected as far as possible by a twist of the hand alternately to the right and left. The tube should also be frequently taken off and turned end for end. Slight variations of curvature are readily made by differences of pressure of the hand on parts of the tube; and a little coaxing is allowed to get the centre of the tube quick where the tube is to be used for levelling only, and not for measuring small angles, so that in this case the finished tube is slightly parabolical. The finishing touch is produced with wash-emery. The inside should be left smooth but not polished, as the slight roughness of a fine ground surface assists the capillary action by causing better adhesion of the spirit, and gives a quicker run to the bubble. Where the tubes are required of a given radius they are tested frequently, during the grinding, upon the bubble trier, by placing two corks in the ends of the tube, which is nearly filled first with water for rough trial, and then with spirit for final correction.

171.—The Bubble Trier is a bar or bed 12 to 20 inches long, with two extended feet ending in points at one end, and a micrometer screw at the other, the point of which is a resting foot, thereby forming a tripod. This stands on a cast-iron or slate surface plate. The micrometer screw has a fine thread, and a large head with divisions upon it to read seconds of arc. The tube is supported on the bar by two Y's, which are adjustable for distance apart, according to the length of the tubes to be tried.

172.—The Sensitiveness of a Level Tube, the upper curvature and ground surface being equal, depends very much upon the capillary action due to its internal diameter, the larger tube, from the freedom of restraint by capillarity, being the more active. As regards the ultimate settling to gravitation equilibrium, perhaps there is no difference, but small tubes are sluggish and take time to work. The following are about the usual dimensions of the interior of sensitive tubes—8 inches × 1 inch diameter, 7 inches × ·9, 6 inches × ·8, 5 inches × ·7, 4 inches × ·6, 3 inches × ·5, 2½ inches × ·45, 2 inches × ·4, 1½ inches × ·35, 1 inch × ·3. The larger the volume the greater the expansion of liquid with heat; the longer the tube the less torsion it is liable to suffer from sealing, so that if possible, as expansion is a serious defect, it would be better to have short tubes, if these could be sealed without disturbance of curvature. Much shorter tubes are used in America than in Great Britain.

173.—The Curvature of a Level Tube is worked to radius according to the delicacy of the work to be performed with it afterwards. The radii of curvature of different level tubes used for scientific purposes vary from about 30 feet to 1000 feet or more. The radius of any curve may be conveniently measured by the relation of its versed sine to its chord of arc, the chord being the length of the tube. If this is first calculated out, a piece of shellac may be attached by melting it down upon the centre of the edge of a parallel glass straight-edge, to represent by its thickness the versed sine. The spot of shellac may be brought to the exact height required from the straight-edge by filing and stoning, at the same time taking its protuberance by a calliper gauge provided with vernier or micrometer to read ·001 inch. The versed sine of a given radius is formed for a given chord—

versed sine = rad - √(rad² - (½ cho)²).

174.—The general instruction, however, given to the maker is the distance of run of the bubble that is required to give seconds or minutes of arc; and perhaps this is after all the best test for accuracy of the tube which, like all other articles in glass submitted to the process of grinding, is subject to a certain amount of local error. By this method the local error is discovered by testing with the bubble trier. When the run is given, the radius of the curve of the tube may be found if desired by the use of a common multiplier, as follows, very approximately—

Arc equal to radius expressed in minutes, 3437·74677.

" " " seconds, 206264·80625.

The run of a good sensitive tube is frequently made 1/30 inch to the second, here (omitting decimals)—

arc sec (206264·8) × 1/30 inch = 573 feet radius nearly.