However, the possibility of determining if we know can be seen in a general way without detailed analysis. For the determination of the radius of the drop is equivalent to finding its weight, since its density is known. That we can find the charge on the drop as soon as we can determine its weight is clear from the simple consideration that the velocity under gravity is proportional to its weight, while the velocity in a given electrical field is proportional to the charge [Pg 102] which it carries. Since we measure these two velocities directly, we can obtain either the weight, if we know the charge, or the charge, if we know the weight. (See equation 9, p. 70.) V. WEIGHING THE DROPLET The way which was first used for finding the weight of the drop was simply to solve Stokes’s uncorrected equation (11) (p. 91) for a in the case of each drop. Since the curve of Fig. 4 shows that the departures from Stokes’s Law are small except for the extremely slow drops, and since appears in the second power in (11), it is clear that, if we leave out of consideration the very slowest drops, (11) must give us very nearly the correct values of . We can then find the approximate value of by the method of the next section, and after it is found we can solve (15) for the correct value of . This is a method of successive approximations which theoretically yields and with any desired degree of precision. As a matter of fact the whole correction term, is a small one, so that it is never necessary to make more than two approximations to obtain with much more precision than is needed for the exact evaluation of . As soon as was fairly accurately known it became possible, as indicated above, to make a direct weighing of extraordinarily minute bodies with great certainty and with a very high degree of precision. For we have already shown experimentally that the equation [Pg 103] is a correct one and it involves no assumption whatever as to the shape, or size, or material of the particle. If we solve this equation for the weight of the particle we get In this equation is known with the same precision as , for we have learned how to count . It will presently be shown that is probably now known with an accuracy of one part in a thousand, hence can now be determined with the same accuracy for any body which can be charged up with a counted number of electrons and then pulled up against gravity by a known electrical field, or, if preferred, simply balanced against gravity after the manner used in the water-drop experiment and also in part of the oil-drop work.[51] This device is simply an electrical balance in place of a mechanical one, and it will weigh accurately and easily to one ten-billionth of a milligram.