The tangent galvanometer was first described in an 1837 paper by Claude-Servais-Mathias Pouillet (1790-1868), who later employed this sensitive form of galvanometer to verify Ohm's law. To use the galvanometer, it is first set up on a level surface and the coil aligned with the magnetic north-south direction. This means that the compass needle at the middle of the coil is parallel with the plane of the coil when it carries no current. The current to be measured is now sent through the coil, and produces a magnetic field, perpendicular to the plane of the coil, and directly proportional to the current. The magnitude of the magnetic field produced by the coil is B; the magnitude of the horizontal component the earth's magnetic field is B'. The compass needle aligns itself along the vector sum of B and B' after rotating through an angle Ø from its original orientation. The vector diagram shows that tan Ø = B/B'. Since the magnetic field of the earth is constant, and B depends directly on the current, the current is thus proportional to the tangent of the angle through which the needle has turned.

The tangent galvanometer at the right is one of my favorite pieces of demonstration apparatus. It was made toward the end of the 19th century by an unknown manufacturer, and has been in almost continuous use in laboratory work and demonstrations at Kenyon College since that time.

A refinement was made by Hermann von Helmholtz (1821-94) in 1849. He suggested the use of two identical current-carrying coils placed parallel to each other to form the arrangement now known as Helmholtz coils. If the separation of the coils is equal to their radii, the small compass needle moves in a magnetic field which is essentially uniform. The instrument at the left is in the collection at St. Patrick's College, Maynooth, Ireland and on the right is one from Wesleyan University.

Here are two Glasgow instruments. On the right is one made by Harvey and Peck of Glasgow, and it dates from the latter years on the nineteenth century.    On the right is a tangent galvanometer made for William Thomson (Lord Kelvin), and used by James Joule in his researches on the mechanical equivalent of heat at Glasgow.

The Helmholtz-type tangent galvanometer at the left is in the collection of the University of Cincinnati. The small button in the middle of the coil reads "Elliott Bros/449/Strand/London.    At the right is a similar tangent galvanometer in the Millington/Barnard Collection of the Unversity of Mississippi.

The instrument at the left was purchased by Wittenberg College from Queen of Philadelphia cost $30.    The similar tangent galvanometer at the right is at Westminster College.

The graceful tangent galvanometer, made ca. 1875 by Yeates & Son of Dublin, is in the museum of St. Patrick's College, Maynooth, County Kildare, Ireland. At one time the galvanometer was covered by a spherical glass dome.

Tangent galvanometers are easy targets for those needing a compass for other reasons. The German instrument at the left  by Hartmann in the Yale University Collection, with its striking geometry, has lost its compass.     And, the early 20th century tangent galvanometer by W. G. Pye & Co. of Cambridge, which cost £1/5s in the 1911 catalogue, has also had its compass borrowed. This is in the Union College collection in Schenectady, New York

The instrument at the left at the University of Vermont is by Nalder of London. It has a single winding for large currents and multiple windings for small currents. The telescopes are used for reading the direction of the compass needle.    At the right is a second tangent galvanometer Vermont, this time by James W. Queen of Philadelphia.

The tangent galvanometer at the left is in the museum in the physics department at Glasgow University in Scotland. The identification label is reproduced below

On the right is a small and beautifully made tangent galvanometer made by Elliott of London at the beginning of the twentieth century. It has a magnetic adjuster at the top, suggesting that it had to be calibrated by external means. It is at Washington and Lee University   The tangent galvanometer survived into the twentieth century, but in rather subdued forms. The instrument at the left was listed in the 1916 catalogue of the L.E. Knott Apparatus Company of Boston at $2.20. The compass is missing from this humble example from Vassar College. The (missing) compass was held by non-ferrous sheet-metal springs in the middle of the coil.

At the right is a small tangent galvanometer in the Greenslade collection. It is described in the 1929 catalogue of the Central Scientific Company of Chicago as:    "Galvanometer, Tangent. A brass ring 20 cm in diameter, mounted on mahogany base, with leveling screws. The needle, 20 mm long, has an agate cap, aluminum indicator and stop, and is mounted in a brass cup with glass cover. The winding consists of two coils of 5 and 10 turns of No. 20 copper magnet wire, brought to three binding posts, so that either 5, 10 or 15 turns may be used ............................$12.00"    The "stop" in the description is an arrangement by which the compass needle can be immobilized for transport. The compass cup can be adjusted up and down on the central post.

The tangent galvanometer at the left was made by the MacIntosh Battery and Optical Company of Chicago. This firm was bought out by W. A. Olmsted Scientific Company. This company literally disappeared in a fire on March 17, 1898, when a fire destroyed the company and killed Olmsted himself.     It is in the Greenslade Collection.

This Universal Tangent Galvanometer by Queen is in the collection of Virginia Military Institute. The compass unit is missing, but the instrument is otherwise complete. The distance between the coils can be varied; for the most uniform field the distance between the coils must be equal to the radius of the coils.

From Robert T. Lagemann, The Garland Collection of Classic Physics Apparatus at Vanderbilt University (Folio Publishers, Nashville, 1983):     "This [galvanometer] incorporates a small magnetic needle, about 2.5 cm in length, suspended between two Helmholtz coils mounted about 4.8 cm apart on a horizontal axis. An indicating needle attached to the magnetic one reveals the angle of rotation when the current is supplied to the coils. The paper scale, marked off in degrees, reads from 0 to 90 to 0 to 90 to 0, with every ten degrees bearing a number. The wooden base carries the three adjustable brass legs. The height is about 38 cm. Marked "Queen & Co Inc. / Philadelphia"."

The tangent galvanometer at the left is in the apparatus collection of Westminster College in New Wilmington, Pennsylvania.    It was made by E. S. Ritchie & Sons of Boston, and has three coils (note the six binding posts) to give three different sensitivities.

   The 1967 Welch Scientific Company catalogue described the tangent galvanometer as an instrument for measuring the horizontal component of the earth's magnetic field. This is a complete reversal of the original use of the instrument, but would give it a new use in the twenty first century.