MAGNETISM 237 Dalla Bella
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liobisou. we have Dalla Bella l and Robison, 2 the well-known professor of natural philosophy in the university of Edinburgh, working at the same subject. The former used the method of Hooke and Musschenbroek, but discussed more carefully the exact nature of the resultant action. His results indicated the law of the inverse square. Robison used both the method of deflexion and the method of oscillation, the peculiarity in his apparatus being the movable magnet, which was composed of two magnetized spheres connected by a slender rod, and suspended either in the field of the earth alone, or at different distances from a large magnet. He made several independent investigations, and seems to have arrived in each case at the law of the inverse square as his final result. Joulomb. The researches of Coulomb, 3 from which many date the commencement of the modern theory, present many features of great interest. He used the improved form of Michell s torsion balance, which had served him so well in his electrical experiments. In order to realize as nearly as passible the ideal case of a linear solenoid, whose action can be represented by positive and negative magnetism concentrated at its ends, he worked with magnets made of thin steel wire magnetized longitudinally. The circum stances of the experiment are thus considerably simplified, for the acting magnet may be so arranged that the action of one of the poles may be neglected, or, failing that, the action of both can be easily calculated. In one of his experiments lie took a magnetized steel wire 25 inches long, and 1 lines thick, and placed it vertically in the magnetic meridian before a horizontal magnetic needle some 3 inches long, delicately suspended by a silk fibre. The rod was raised and lowered at a given distance from the needle until the attraction on the near pole of the needle, as tested by the rapidity of the vibrations, was a maximum ; it was then found that the lower end of the bar was about 1 inch below the needle. Again, the rod being placed horizontal and perpendicular to the magnetic meridian on a level with the needle, it was displaced until the needle returned to the magnetic meridian ; it was then found that the needle was directed to a point about 1 inch from the end of the bar. Both these experiments thus indicate that the magnetism at one end may be supposed concentrated at a point about an inch from the end of the bar. It is clear that, in these experiments, provided the rod is sufficiently long or the distance between it and the needle not too great, the action of the distant pole may be neglected, for the double reason that the pole is more distant and that the force exerted by it is nearly perpendicular to the direction ia which it can be effective. Making this assumption, Coulomb observed the number of vibrations, when the vertical rod was absent, and when it was placed at various distances. The forces thence deduced were found to vary very nearly as the inverse square of the distance. Statical experiments with the torsion balance led to a like result. Later re- Later than Coulomb we have the experiments of Bidone, 4 searches. Hansteen, 5 Steinhauser, 6 and Scoresby. 7 By far the most important among these is Hansteen, whose methods were a great step towards the more complete treatment finally adopted by Gauss. He uses Taylor s "end on" method of deflexion, and also the method of Hooke and Musschenbroek. The acting magnet was a bar magnet, the action of which lie represents by a distribution of positive and negative magnetism on its two halves whose density at a distance x from the centre is Xx r . The force at distance D due to an element dp of positive magnetism Le assumes to be d/j.!D n . He finds that in all his experi ments the value n = 2 best represents the results obtained ; but that various values of r may be adopted with almost equal advantage; he inclines, however, to the value r = 1. 1 Mem. d. Acad. Real d. Sc. d. Lisboa. - See Ency. Brit., supplement to 3d ed. , 1801. 3 Mem. de VInsL, 1785, 1788. 4 Gren s Journal, 1811 ; Oilb. Ann., 1820. 5 Magnetismus der Erde, 1819. 6 I)e Magnetismo Tdluris, 1806-10. 7 Jamieson s Xew Edinburgh Journal, 1831. Hans teen. In his classical memoir on the absolute measurement of the earth s magnetic force, Gauss took up the question in Gauss. the most general manner yet attempted. Assuming that the force due to an element of positive magnetism varies as the inverse rath power of the distance, he showed that, when the distance between the magnets is sufficiently great compared with the greatest linear dimensions of either (more than four times as great in his own experiments), the deflexions </> and < for the "end on" and "broadside on " positions of the deflecting magnet are given by tan0 = L l ?-<"+ 1 ) + L 3 ?--("+ 2 ) + &c., tan = L 1 V-<"+ 1 > + L 3 r -("+-) + & c . ; where Lj/L^ = n. He made a series of deflexion experi ments, and found that his results could be represented with sufficient accuracy by the formulae 8 tan</> = Q-086S70r- 3 -0 0021S5r- 5 , The following table shows the closeness of the agreement between theory and experiment (r is measured in metres ; $ and < denote observed and < and </> calculated values): r <J>
- -</>
4>
- -0
1-1
1 57 24-8 + 2-8 1-2 1 29 40-5 -6-0 1-3 2 13 51-2 + "0 8 1 10 19-3 + 6-0 1-4 1 47 28-6 + 4-5 55 58-9 + 0-2 1-5 1 27 19 1 - 9-6 45 14-3 -6-6 1-6 1 12 7-6 - 3-3 37 12-2 -3-2 17 1 9-9 - 5-0 30 57 9 -1-2 1-8 50 52-5 + 4-2 25 59-5 -3-4 1-9 43 21-8 + 7 8 22 9-2 + 2-6 2-0 37 16-2 + 10-6 19 1-6 + 5 9 21 32 4-6 + 0-9 16 247 + 4 9 2-5 18 51-9 -10-2 9 36-1 -2 5 3-0 11 07 - 11 5 337 -0-2 3-5 6 56-9 - 0-2 3 28-9 -1-0 4-0 4 35 9 - 37 2 22-2 + 17 We have here a double proof of the law of the inverse square, first, in the fact that tan</> and tan</> can be expressed so accurately by two terms of a series, the first of which contains r 3 ; second, in the fact that the coefficient of the first term in tane/> is exactly double that in tan< . These researches of Gauss are remarkable, not only for the great generality of the theory, but also for the novelty of the experimental method, and the exceeding accuracy and refinement of the observations. The law of the inverse square has in fact been regarded as settled ever since they were made. They are important from another point of view, to which we shall return presently. MAGNETIC MEASUREMENTS, RELATIVE AND ABSOLUTE. he mos. important magnetic determinations that have to be made are the direction of the axis of a magnet re- latively to its mass, the magnetic moment of a magnet, the direction of a magnetic field, and the strength of a magnetic field, or its component in any given direction. In most of these cases the measurement may be either relative or absolute. For example, we may determine the moment of a magnet either relatively, in terms of the moment of some other magnet arbitrarily chosen, or abso lutely, in terms of the fundamental units of space, mass, and time. The complete theory of measurements of the latter kind is due to Gauss, and the carrying of them into practice to him in conjunction with Weber and the Magnetischtr Verein, of which these two German philoso phers were the leading spirits. We shall discuss the Cliief niagnetic
8 Intensitas Vis Magueticfe, &c., 21, 1833.