TABLE FOR CALCULATING OUNCES TO THE SHORT TON FROM THE YIELD OF GOLD FROM 100 GRAMS OF ORE. ----------+---------+-----------+---------+-----------+--------- Milligram.|Ounces to|Milligrams.|Ounces to|Milligrams.|Ounces to | the Ton.| | the Ton.| | the Ton. ----------+---------+-----------+---------+-----------+--------- 0.01 | 0.003 | 0.4 | 0.117 | 7.0 | 2.042 0.02 | 0.006 | 0.5 | 0.145 | 8.0 | 2.333 0.03 | 0.009 | 0.6 | 0.175 | 9.0 | 2.625 0.04 | 0.012 | 0.7 | 0.204 | 10.0 | 2.916 0.05 | 0.014 | 0.8 | 0.233 | 20.0 | 5.833 0.06 | 0.017 | 0.9 | 0.262 | 30.0 | 8.750 0.07 | 0.020 | 1.0 | 0.292 | 40.0 | 11.666 0.08 | 0.023 | 2.0 | 0.583 | 50.0 | 14.583 0.09 | 0.026 | 3.0 | 0.875 | 60.0 | 17.500 0.10 | 0.029 | 4.0 | 1.167 | 70.0 | 20.416 0.20 | 0.058 | 5.0 | 1.458 | 80.0 | 23.333 0.30 | 0.087 | 6.0 | 1.750 | 90.0 | 26.250 ----------+---------+-----------+---------+-----------+--------- Suppose a balance at rest in perfect equilibrium, with the pointer exactly over the middle point of the scale. Let the scale be a series of points at equal distances along a horizontal line; then, if a small weight be placed on one pan, the pointer will deviate from its vertical position and come to rest opposite some definite part of the scale, which will depend upon the magnitude of the weight added. The law determining this position is a very simple one; the deviation as measured along the points of the scale varies directly as the weight added. For example, with an ordinarily sensitive balance, such as is used for general purposes, one milligram will move the pointer along, say, three divisions of the scale; then two milligrams will move it six divisions; half a milligram, one and a half divisions; and so on. Of course, with a more sensitive balance the deviations will be greater. Now the point at which the needle comes to rest is also the middle point about which it vibrates when swinging. For example, if the needle swings from the third to the seventh division on the right then [(7+3)/2] it will come to rest on the fifth. In working by this method the following conventions are useful: Always place the button to be weighed on the left pan of the balance, the weights on the right; count the divisions of the scale from the centre to right and left, marking the former + and the latter -; thus -5 is the fifth division to the left. Then the position of rest is half the algebraic sum of two readings. For example, let the readings be 7 to the right and 3 to the left, then (+7-3)/2 = +2. The mean division is the second division to the right. If the student will place himself in front of a balance and repeat the