Fifty years ago it was considered the triumph of the instrument-maker’s art that a balance had been made so sensitive that one could weigh a piece of paper, then write his name with a hard pencil on the paper and determine the difference between the new weight and the old—that is, the weight of the name. This meant determining a weight as small as one-tenth or possibly one-hundredth of a milligram (a milligram is about ¹⁄₃₀₀₀₀ of an ounce). Some five years ago Ramsay and Spencer, in London, by constructing a balance entirely out of very fine quartz fibers and placing it in a vacuum, succeeded in weighing objects as small as one-millionth of a milligram, that is, they pushed the limit [Pg 104] of the weighable down about ten thousand times. The work which we are now considering pushed it down at least ten thousand times farther and made it possible to weigh accurately bodies so small as not to be visible at all to the naked eye. For it is only necessary to float such a body in the air, render it visible by reflected light in an ultra-microscope arrangement of the sort we were using, charge it electrically by the capture of ions, count the number of electrons in its charge by the method described, and then vary the potential applied to the plates or the charge on the body until its weight is just balanced by the upward pull of the field. The weight of the body is then exactly equal to the product of the known charge by the strength of the electric field. We made all of our weightings of our drops and the determination of their radii in this way as soon as we had located with a sufficient degree of precision to warrant it.[52] Indeed, even before is very accurately known it is possible to use such a balance for a fairly accurate evaluation of the radius of a spherical drop. For when we replace in (18) by and solve for a we obtain The substitution in this equation of an approximately correct value of yields with an error but one-third as great as that contained in the assumed value of , for is seen from this equation to vary as the cube root of . This is the method which, in view of the accurate evaluation of , it is now desirable to [Pg 105] use for the determination of the weight or dimensions of any minute body, for the method is quite independent of the nature of the body or of the medium in which it is immersed. Indeed, it constitutes as direct and certain a weighing of the body as though it were weighed on a mechanical balance. VI. THE EVALUATION OF AND With and known, we can easily determine and from the equation for if we write this equation in the form