d=2a sin 0/2, which Coulomb treated as approxi&9 a0. He found that when the angle was decreased from 36 18, the force quadrupled, within an error of less than 1% However, to quadruple again the angle had to be reduced, not to 9, but to 8. Coulomb noticed this error but made no further comment on it. Evidently he did not expect his apparatus to give a more precise result even though it was capable of it. Of course, we know that the experiment was eporting the force accurately. It was the theory that was in error! At or 9, the parameter d /a is somewhere between 3.7 and 5.5, where we see from Fig. 1 that the force is about 5%0 less than 1/d2 Coulomb was so eager to prove the 1/d2 law that he overlooked the experimental observation of po- larization Because Coulomb did not specify the exact diameters of his pith balls, we also calculated the repulsive force curve for balls with diameters in the ratio 3: 2. The resulting force at the distance d/(a, +a,)=2 or more is only slightly CENTER TO CENTER DESTANCE, d less(1%)than the force shown in Fig. l, leaving our conclusion intact. However, at close approach, the repul ion between dissimilar balls falls significantly (-50%) Fig. 1. Behavior of the electric force between identical charged spheres as below the curve for identical balls shown in Fig. 1 a function of center-to-center distance It is too much to expect Coulomb to have understood the concept of equipotential surfaces in 1785. However, he did know that the electrical"fluid"was mobile on the pith balls since if it were not so he could not have charged them. He failed to recognize, however, that this same mobility would ause the charges to move on the balls in the presence of the electrical force, thus spoiling his effort to identify the cen- ter of a ball with the center of the Coulombs torsion balance was and is an extremely sen sitive and precise device for physical measurements. How ever, it is a small miscarriage of justice to name the electro- static force law in his honor. Most scientists of his time expected the force law to be 1/d- and others had mea sured it to be 1/(d2+e), for example. It was Priestleywho recognized that if cork balls inside a charged cup were un affected by the charge on the cup then F-1/d2 exactly.He drew this conclusion from Newton's work on the force of gravity within a hollow sphere. This theoretical insight is ar more satisfacte tory in establishing F-1/d2 than any ex periment, which, as can be worked out from Table I, will give a force law more like Frep -1/D-1/D+-2/D etc. where D=d/a When Coulomb attempted to measure the attractive force between unlike charges he met a serious problem. The force increases so rapidly at small distances that his torsion lance for which the force was linear with distance, could not compensate. To measure the attractive force he used a suspension with so little restoring torque that its natural period of oscillation was very long. He then bro charged sphere close to a suspended disk and measured the period under conditions in which the restoring force was, for all practical purposes, the electrical force. See Fig ere in this experiment was 6 in. in rad Is and the small disk was about 2 in. in radius. The separa- tion in various trials ranged from 9 in.(center-to-center)to 18 in Coulomb tells us he charged the disk by induction when it was“ some inches”away There are two ways of estimating the charge on tI sna disk. a disk carrying charge g has a potential plified diagram of Coulomb's apparatus for measuring electro- 1.5708(=m /2)times the potential of a sphere of the same radius.If we compute the potential at the center of the disk 1196 Am J Phys., Vol 58, No 12, December 1990 Jack A. Soule 1196