following observations and replace the figures here given by his own, he will have no difficulty in grasping the method. First determine the _bias_ of the balance; suppose the unloaded balance swings +1.25 and -1; the bias then is (1.25-1)/2 = +.125 or one-eighth of a division to the right. Now having put on the button to be weighed let the readings be +7.5 and +9.25, and (7.5+9.25)/2 = +8.375. Then the effect of the button has been to move the pointer from +.125 to +8.375, or 8.25 divisions to the right; we should, therefore, add the weight equivalent of 8.25 divisions to the weights, whatever they may be on the right hand pan of the balance; if the divisions were to the left (- divisions) we should subtract. The value of 1 division is easily determined. Suppose the button in the example were a 1 milligram weight, then we should have found that 1 milligram = 8.25 divisions .'. 1 division = .121 milligram. This method of working adds very considerably to the power of a balance in distinguishing small quantities. [Illustration: FIG. 44_a._] _By the Microscope_.--The use of the microscope also is a real advantage in estimating the weights of minute buttons of gold where there is no undue risk in sampling, and where an error of say 1 in 20 on the quantity of gold is tolerable. For ores with copper, lead, zinc, &c., as well as for tailings rather poor in gold, this leaves a wide field of usefulness. The method is described on page 440, but the description needs supplementing for those who are not accustomed to the use of a microscope. The eye-piece of a microscope (fig. 44_a_, A) unscrews at _a_, showing a diaphragm at _b_, which will serve as a support for an eye-piece micrometer. This last, B, is a scale engraved on glass, and may be purchased of any optical instrument maker, though it may be necessary to send the eye-piece to have it properly fitted. When resting on the diaphragm it is in focus for the upper lens, so that on looking through the microscope, the scale is clearly seen in whatever position the instrument may be as regards the object being looked at. Suppose this to be a small button of gold on a shallow, flat watch-glass, on the stage of the microscope. Bring the button under the "objective" (_i.e._, the nose of the microscope), which should be about a quarter of an inch above the watch-glass; then looking through the instrument, raise the tube until the button of gold, or at least some dust on the glass, comes into focus. If the button is not in the field, rest the thumbs and index fingers, using both hands, on the edge of the watch-glass, pressing lightly but steadily, and give the glass a slow, short, sweeping motion; the button will perhaps appear as an ill-defined blackness, because not quite in focus. Bring this into the centre of the field. Raise or lower the microscope until the button appears with sharp outlines. If the scale does not cover the button, rotate the eye-piece; this will bring the scale into a new position.