MEASUREMENTS ON FEEBLY MAGNETIC SUBSTANCES The methods which have been described, by which the suscepti bility of ferromagnetics may be determined, are not applicable to dia- and paramagnetics whose susceptibility is usually very small. The methods employed are generally based on the measurement of the forces exerted on a body in a non-homogeneous field, use being made sometimes of the fact that the apparent susceptibility of a substance depends on the medium by which it is surrounded. If a small magnet of pole strength in and length ds is brought into a magnetic field, so that ds lies along and the magnetic potential (the work done in bringing a unit positive pole to the point) at the negative pole is V1 and at the positive pole V2, the potential energy II' of the magnet, measured by the work done in bringing it into position, is given by The specimens were placed in suitable containers and were supported on a frame of such form that they could be surrounded by an electric heating oven. The main objection to the method, for accurate determinations, is that it is difficult to ensure that the specimens are placed exactly at the region for which the force has been calculated, and that the field and its gradient are found for the same points. For relative measurements where high sensi tivity is desired the method is very suitable.
In another form of the non-homogeneous field method, used by Foex and Theodorides, a translational, instead of a torsional, balance is used. The specimen is supported between the poles of the magnet, so that the force is horizontal, by a pendular system, which also carries a current-bear ing oil ; the force acting on the specimen is compensated by the attraction between this coil and a stationary pair of coils.
In the Gouy method (see fig.
23) a uniform cylinder or prism of cross sectional area, A, is sus pended with one end in a homoge neous field between the poles of a magnet where the field is H, and the other end in a region where the field is small and equal to H'. The force along the axis of the specimen is then given by Usually may be made negligible compared to The force may be determined by direct weighing with a special sensitive balance ; or by a torsion method, the specimen being supported horizontally. As the field may be uniform over a fairly large region,
it may be accurately determined, either by the ballistic method, or from the force on a current-bearing wire, substituted for the specimen. The Gouy method is probably the most satisfactory for absolute measurements, though less sensitive than the Faraday Curie method for comparative determinations.
In a dynamical method due to Rowland, an elongated specimen is suspended between the poles of a magnet and its time of swing determined. The period is inversely proportional to the square root of the susceptibility, being independent of the form of the specimen. For absolute measurements a careful "topographical survey" of the field is necessary, and elaborate corrections must be applied.
the Faraday or Gouy method, the suscepti bilities of liquids may be found by using them as the surrounding medium for solid specimens whose apparent susceptibility is measured in the usual way, or by placing the liquids in suitable calibrated containers. Most convenient for liquids is the Quincke capillary ascension method which is based on the same principle as the method of Gouy. It has been extensively used and is cap able of high accuracy. A U-tube is employed, one limb being of wide and the other of narrow bore ; the narrow tube passes be tween the poles of a magnet, the meniscus being in a region where the field H is uniform (see fig. 24), while at the wide tube sur face the field is negligible.
When the field is applied the meniscus will rise or fall by an amount b. Let p be the change of pressure, e, p the susceptibility and density of the liquid, Ko, Po of the gas; then for very small displacements it is desirable to keep the level of the meniscus constant, the pressure change being estimated by chang ing the amount of liquid in the wide tube, or with a flexible con nection, by changing its height. The Quincke method may be applied inversely to the measurement of magnetic fields. An ap paratus has been devised by du Bois for this purpose, the sensi tivity being increased by having the narrow tube inclined.