Coulomb's Experiment

Experimental determination of the law according to which bodies charged with the same type of electricity repel each other.

In a memoir presented to the Academy in 1784, I determined by experiment the laws governing the torsion in a metal thread. I found that this force is proportional to the angle of twist, to the fourth power of the diameter, and inversely proportional to the thread's length. The constant of proportionality depends, upon the metal used, and can be determined experimentally.

In the same memoir I showed that by using this force of torsion it is possible to measure accurately very small forces; for instance, one ten-thousandth of a grain. In the same memoir I gave the first application of this theory, an attempt to evaluate the constant force attributed to adhesion in the formula that expresses the friction on the surface of a solid body moving through a fluid.

I submit to the Academy today an electric balance built according to the same principles; it measures very exactly the state and electric force of a body, however small its charge.


Experience has shown me that to perform several electric experiments in a convenient way I should correct some mistakes made when building the first balance of this type. However, since the balance is the first of this type, I shall describe it, keeping in mind that the accuracy and precision of the experiments I am going to perform may vary. Figure 10 shows a detailed diagram of the complete balance.

Over a glass cylinder 12 inches in diameter and 12 inches high., a flat piece of glass 13 inches in diameter was placed, which covers the entire structure. This plate has two holes of about 20 lines in diameter, one of them at its center, f, on which a glass tube 24 inches high is placed. This tube is cemented in place with the cement currently used in electrical apparatus. On top of the tube at h is placed a torsion micrometer, shown in detail la Figure 2. The top part of this micrometer, No. 1, has a knob b, index io, and a suspension clamp q, which fits into the hole G of part No. 2. Part No. 2 is made up of a circle ab, which has a 360 scale on its edge, and a copper tube F that fits into the hole H of Part No. 3, which is attached to the top of the glass tube fh of Figure 1.

The clamp q (Fig. 2, No. 1) has nearly the form of the tip of a crayon holder, which can be narrowed by means of the ring q. It is in this clamp that one end of a very fine silver wire is placed. The other end of this wire is attached at P (Fig. 3) by means of a clamp on the rod Po. This rod is made of copper or iron and its diameter is barely one line. The upper end P is split, making a clamp that is closed by means of the sliding ring F . This cylinder enlarged and pierced at C by a sliding needle ag. The whole Weight of the cylinder must be such that it can keep the silver wire stretched without breaking it. The needle ag as can be seen in Figure 1, is suspended horizontally at its center and at about half the height of the glass container.

It is made either of a silk thread coated with Spanish wax or of a straw similarly coated. It is about 18 lines long and terminates in a cylindrical thread of shellac; at one end of this needle is placed a small ball which is made of pith and is two or three line in diameter, At the end g is a small piece of paper soaked in turpentine; this paper counterbalances the ball a and slows down the oscillations.

We have said that the glass cover AC has a second hole m; it is through this hole that a small rod mj b is introduced. The lower part of this rod (j b) is made of shellac, and at b terminates in another small pith ball. Around the glass container, at the height of the needle, is scale ZQ divided into 360 degrees. This scale was made for simplicity out of paper fastened around the container at about the height of the needle.

To start the operation of this instrument the flat glass cover is placed more or less in position by lining up the hole m with the first division of the scale ZOQ drawn on the glass container. The index io of the micrometer is placed at the zero mark of the micrometer scale. Then the entire micrometer is turned on the glass tube fh until, by looking past the vertical thread and the center of the ball, the needle ag is seen at the first division of the scale ZOQ (that is, when the center of the ball a is lined up with the zero mark). The ball b., suspended by the thread mj b, is then introduced through the hole m, in such a way that it touches the ball a., and that the center of the ball (b) and the suspension thread are lined up with the zero mark of the scale ZOQ. The balance is now ready to operate; we shall, for example, determine the fundamental law by which, electrified bodies repel each other.


The repulsive force between two small spheres charged with the same type of electricity is inversely proportional to the square of the distance between the centers of the two spheres.


A small conductor is charged, this is nothing but a large-headed pin insulated by inserting it at the end of a rod of Spanish wax (Fig. 4). This pin is introduced through the hole m and touches the ball b, which is in contact with ball a. Upon removing the pin the two balls are charged with the same nature of charge and separate from each other by a distance that can be measured by lining up the suspension thread and the center of the ball a with the corresponding division m the ZOQ scale. The index of the micrometer is now turned in the sense pno; the suspension thread lP is thus twisted and a torsional force proportional to the angle of twist is product which tends to pull the ball a toward the ball b. Comparing the torsional force with the distance between the two balls, the law of repulsion is determinated. Here, I intend only to carry out some trials which are easily reproduced, and which will make evident the law of repulsion.

First Trial. Having charged the two balls with the head of the Pin with the micrometer index set at O, the ball a of the needle is separated from the ball t by 36 degrees.

Second Trial. Turning the suspension thread through 126 degrees by means of the knob O of the micrometer, the two balls are found separated and at rest at 18 degrees from one another.

Third Trial. After turning the suspension thread through 567 degrees, the two balls are separated by 8 degrees and a half.

Explanation and Result of This Experiment

When the balls are not charged they touch each other and the center of ball a, held in place by the needle, is not displaced by more than half the diameters of the two balls from the point where the torque due to the suspension thread is negligible. It is worthwhile to note here that the silver thread lP which provides suspension is 28 inches long, and so thin that a foot of it is not heavier than 1/16 grain. To calculate the force necessary to twist this thread., by acting on the point a which is four inches away from the wire (lP) or from the center of suspension, I have found by using the formulas explained in a paper on the laws of torsion in metal threads, published in the volume of the Academy for 1784, that to twist this thread through 360 degrees it is necessary to apply at point a, a force of 1/340 grain to operate the lever aP which is four inches; since the torsional forces are proportional to the angle of twist, the least repulsive force between the two balls will cause a marked separation one from the other, as proved in the aforementioned paper.

In our first trial we found that where the index of the micrometer is over the point O, the balls are separated 36 degrees, which therefore produces a torsional force of 36 = 1/3400 grain; in the second trial the distance between the balls is 18 degrees, but since the micrometer has been turned through 126degrees, it follows that at a distance of 18 degrees the repulsive force is equivalent to 144 degrees. That is, at half the first separation the repulsion of the balls is four times as great.

In the third trial the suspension thread was turned 567 degrees, and the two balls were only 8 degrees apart, the total torsion is therefore 576 degrees; four times that of the second trial, and the distance between the balls lacked only half a degree of being decreased to half of that at which it stood in the second trial.

It results, then, from these three that two balls charged with the same type of electricity exert a repulsive force on each other, inversely proportional to the square of the distance between them.