The Englishman Peter Barlow investigated areas of mathematics, physical sciences and engineering in the first half of the nineteenth century including: railway technology, number theory, astronomical optics, electromagnetism and strengths of materials. My talk focuses on his work related to terrestrial magnetism. I examine Barlow’s scientific publications and related contemporary accounts to address the following questions: What were his ideas about terrestrial magnetism and who influenced him? How and why did Barlow's thoughts change with time? and How does he fit within the context of early Victorian investigations of terrestrial magnetism? Historians of science have written little directly about Barlow; few accounts deal with his work in any detail. I will hopefully show that Barlow's work is deserving of more attention.

Peter Barlow was born in Norwich, England in October 1776. Despite lacking formal education, he completed a competitive exam to become assistant mathematical master at the Royal Military Academy in Woolwich in 1801. Promoted to professor of mathematics in 1806, he remained there until retiring in 1847. His position brought him access to the arsenal, foundry and dockyard for his experiments and allowed Barlow contact with colleagues with similar interests. Barlow was one of a group including Edward Sabine, Charles Babbage, John Herschel, and Michael Faraday interested in magnetic and geomagnetic subjects. He was elected fellow of the Royal Society of London in 1823 and was awarded the Copley Medal in 1825 for his studies of magnetism and improvements in navigation.

What was the state of the study of terrestrial magnetism when Barlow turned his attention to it? Navigators had long observed the declination and inclination of the compass needle. Declination measured the deviation of the needle from stellar north while inclination, commonly called the "dip", measured the tilt of the needle from horizontal. These deviations had been known for centuries, but their systematic observation and mapping was not well established until the eighteenth century. Measurements, usually made for navigational reasons, were collected for scientific purposes beginning in the late eighteenth-century. However, the "pure" and "applied" aspects of terrestrial magnetism remained closely linked. The development of precision instruments accompanied the proliferation of observations. New improved instruments measured the magnetic intensity, in addition to declination and dip. These three standard magnetic components changed irregularly over time and with geographic location. Hence, study of terrestrial magnetism naturally lent itself to global scale investigation.

The early nineteenth century saw increased systematization, standardization, and international cooperation in the collecting of geomagnetic observations. With the amassing of more precise and complete data, those who studied the subject grew confident that a theory of the earth's magnetism would eventually emerge. At the turn of the century Alexander von Humboldt collected geomagnetic measurements in the Americas and later helped establish a world-wide network of observatories. Humboldt, the main proponent of the "cosmical" view, saw all terrestrial phenomena in terms of interconnected "telluric" forces. These forces emanated from the earth and interacted with influences beyond the earth's atmosphere. An older idea, originating with William Gilbert, treated the earth like a globular lodestone or terrella. Edmund Halley and, later, Charles Augustin Coulomb took this position also, although with modifications. By the 1820s and 30s, the cosmical view had overshadowed this older view.

Barlow's first published mention of magnetism was in the Mathematical and Philosophical Dictionary of 1814. Believing the earth to act as a giant magnet he wrote:

In 1819 Barlow's first magnetic experiments were reported in the Edinburgh Philosophical Journal. His investigations focused on deflections of the compass needle produced by ship-board iron. These deviations caused increasing navigational problems as larger amounts of iron were used to outfit and construct nineteenth-century ships. Using a compass and a large iron sphere, Barlow determined a "plane of no attraction" or set of points where the needle behaved as if no iron were present. He then systematically moved the compass in circles around the iron ball, attempting to derive a general law for the needle's deflections from the plane of no attraction. The law deduced from these experiments allowed Barlow to compute the deviation for any compass position around the sphere. Also the needle deflected the same amount whether the sphere was hollow or solid. Barlow concluded that magnetic power resided only in or near the surface of the objects.

Extending and refining his experiments, Barlow summarized the results in An Essay on Magnetic Attractions in 1820. He found that a properly-placed iron plate near the ship's compass could compensate for compass deflections caused by ship-board iron. This correction allowed for more accurate and safer navigation. The bulk of the work dealt with the application of this corrective plate. At the end of the essay, Barlow addressed theoretical concerns:

Barlow found that the complicated analysis resulting from such a theory rendered "it wholly useless as a practical theory."

In 1804 Jean-Baptiste Biot had mathematically demonstrated that, if the earth acted like a lodestone, then the poles must be indefinitely near each other at the center of the earth to fit with the observations. Barlow commented on Biot's finding:

Given this difficulty and others, Barlow concluded that the earth was not a giant magnet. Research over the next few years strengthened this rejection.

Explaining magnetism in terms of imponderable fluids was not a new idea in the nineteenth century. In the 1780s Charles Coulomb had elaborated a two fluid theory of magnetism paralleling his earlier theory of electricity. Barlow, accepting some version of a subtle fluid theory, did not specify which one until the second edition of An Essay on Magnetic Attractions in 1823. This expanded version was divided into three parts. Part one extended the experiments related to the corrective plate. In the second part, he developed his theory of magnetism. Barlow noted that soon after the publication of his 1820 Essay, Charles Bonnycastle

Barlow modified Bonnycastle's version of Poisson's two fluid theory of electricity. With this theory in mind, Barlow derived formulae for predicting the deflections of a magnetic needle at any position from an iron sphere. Then he compared the computed results with his colleague, Samuel Hunter Christie's, observations. From this comparison Barlow concluded that "it would be useless to expect a closer approximation between theory and practice."

Next, Barlow addressed terrestrial magnetism. He considered the earlier formulae when the variable designating the earth's magnetic intensity went to zero. The iron sphere, he wrote,

The computations closely coincided with known observations. Barlow commented, "Hitherto we have found a very close approximation between the laws of magnetism appertaining to a simple iron ball and the observed magnetic phenomena of the earth." However, when he applied the analogy to predict the position of the terrestrial magnetic axis, it failed to yield a close match. Despite the discrepancies, he insisted that his hypothesis was consistent with known principles. Barlow also assumed that the earth induced magnetism in iron objects. This was reflected in the title of part two, "A Theoretical Investigation of the Laws of Induced and Terrestrial Magnetism." But if the earth induced magnetism to iron bodies then what induced magnetism in the earth itself? In the next several years Barlow addressed this question.

In 1820 the study of terrestrial magnetism received impetus from Hans Christian Oersted’s discovery that electric current in a wire deflected a magnetic needle. In 1822, Thomas Seebeck found that differentially heating a circuit of appropriate metals produced an electric current. Electromagnetism and thermoelectricity gave those who believed in the "cosmical" view renewed hope for a synthesis of "telluric" forces. Humboldt linked variations in the three magnetic components with the motions of thermal, chemical and luminous aspects of electromagnetism. Charles Babbage and John Herschel proposed that atmospheric electricity arose from the thermoelectric interaction of sky and earth, thus producing terrestrial magnetism by induction. In the 1820s, André-Marie Ampère proposed that electric fluids were the cause of magnetism. Barlow followed this trend in unifying natural forces.

In part three of his 1823 Essay, Barlow had reported on his repetition of the experiments of Oersted, Ampère, Faraday, and others. He had explained electromagnetism in terms of two galvanic and two magnetic fluids without speculating on terrestrial magnetism. However, in 1825 Barlow wrote in a letter to John Herschel, "there are strong reasons for assuming, that the magnetism of the earth is of that kind which we call induced magnetism; but at present we have no knowledge of the inductive principle." That same year Poisson had remarked that the question of whether magnetic fluids were distinct or mere modifications of electricity was still uncertain. By 1831 Barlow decided this question for himself in support of Ampère's idea. This was evident in his paper titled, "On the probable Electric Origin of all the Phenomena of Terrestrial Magnetism."

In this paper Barlow observed that the earth's magnetic intensity remains relatively constant, yet the earth's position is constantly changing. Hence, terrestrial magnetism could not be induced by an outside body; the cause must be internal. He wished to show that "all terrestrial magnetic phenomena are due only to electricity, and that magnetism, as a distinct quality, has no real existence." Barlow said that an artificial globe with galvanic currents distributed across its surface would "exhibit, while under electrical induction, all the magnetic phenomena of the earth." A wooden globe with latitudinal grooves cut in it was constructed to test this hypothesis. In these grooves nearly ninety feet of copper wire were laid. After refining his model Barlow concluded:

This electrified globe demonstrated a force "competent to produce all the phenomena of terrestrial magnetism, without the aid of any body usually called magnetic" and showed that magnetism has "no real existence in nature." Barlow further speculated by commenting on thermoelectricity:

If the copper wires on the globe were replaced by bimetallic strips and heated then "...all the phenomena it now exhibits by aid of the galvanic battery might be represented by the application of heat only." Finally, Barlow suggested that the differential heating of metals within the earth's crust was ultimately caused by the sun.

By 1833 Barlow was no longer confident with his earlier ideas. This doubt appeared to spring from difficulties in explaining irregular geomagnetic variations. He now hoped to develop charts of magnetic variation free from theoretical notions. In accordance with this, he left his charts blank in areas where sufficient data were not available. Barlow remarked,

Barlow's ideas changed over nearly a twenty-year span. In 1814 he agreed that the earth acted as a giant magnet. From 1819-1822 his experimental results made him increasingly critical of established hypotheses. From 1820 onward he rejected the view which treated the earth as a permanent magnetic body. By 1831 Barlow subsumed all magnetic phenomena to the action of electricity and speculated that the sun's heat was the ultimate cause of terrestrial magnetism. However, by 1833, he seemingly doubted these notions.

Barlow's research fits within the context of early nineteenth century geomagnetical studies. His support for the cosmical view was effected by the discoveries Oersted, Ampère, Seebeck, and others. This is evident in his unification of previously disparate forces of nature: magnetism, electricity, heat. As with others supporting the cosmical view, he did not strictly separate geomagnetic measurements in the field and measurements made in laboratory experiments. This is exemplified in his analogy between the iron ball and the earth. In addition, Barlow's work illustrates that "pure" and "applied" aspects of terrestrial magnetism were closely linked. Finally, Barlow's emphasis on careful accumulation of observations in hopes of deriving general laws was typical of the Humboldtian approach to nature.