MAGNETISM. 



parallel to the equator, and passing 

 through the point in question, which 

 distance might be termed its magnetic 

 longitude. Mr. Barlow assumes as his 

 first meridian, the circle which passes 

 from the pole to the magnetic east and 

 west points of the horizontal plane in- 

 stead of the vertical meridional plane. 

 We cannot help thinking, however, that 

 the multiplication of these planes would 

 have been better avoided, by assuming 

 the latter, necessarily referred to on so 

 many occasions, as the first meridian. 



(252.) Having settled these definitions, 

 the law of action deducible from the ex- 

 perimental investigation of Mr. Barlow, 

 may be very simply expressed. The 

 amount of the angular deviation of a 

 compass needle, the motion of which is 

 limited to a horizontal plane, from the 

 true magnetic meridian, at any point on 

 the surface of the sphere, is such, that 

 the tangent of the angle of deviation is 

 directly proportional to the rectangle of 

 the sine and cosine of the latitude of that 

 point multiplied into the cosine of its 

 longitude. As it is extremely convenient 

 to express propositions of this kind in 

 the concise and perspicuous language of 

 algebra, we shall present the above pro- 

 position in that form ; denoting the angle 

 of deviation by the symbol A ; the lati- 

 tude by A ; the longitude by I. The 

 formula will then be as follows, 



tan. A = sin. x cos. x sin. /. 

 But since the product of the sine and 

 cosine of an angle is equivalent to the 

 sine of twice that angle, the formula 

 admits of this simplification, and it will 

 then be, 



tan. A = sin. 2 A cos./. 



(253.) The results of a numerous 

 series of experiments made by Mr. Bar- 

 low, when the centre of the compass was 

 placed in every variety of position, with 

 respect to an iron ball, approximated so 

 closely to those which were given by 

 computation from the above formula, 

 that no doubt can remain of the accu- 

 racy of the law from which it is deduced. 

 They have been further verified by Mr. 

 Christie, by a somewhat different method 

 of procedure, of which he has given an 

 account in the Transactions of the Cam- 

 bridge Philosophical Society *. 



(254.) The next object of inquiry was 

 the law of attraction, with relation to 

 distance ; and the result at which Mr. 

 Barlow arrived was, that, when the 

 position, with regard to latitude and lon- 



* Vol. i. P . H7. 



gitude, remains the same, the tangents 

 of the angles of deviation are reciprocally 

 proportional to the cubes of the dis- 

 tances. Now as it has been estab- 

 lished, that the magnetic force varies 

 inversely as the square of the distance, 

 it will follow, that the square of the tan- 

 gent of deviation is directly as the cube 

 of the force ; or, that the tangent of de- 

 viation is directly proportional to the 

 | power of the force. In order to con- 

 vert this proportionality into an equa- 

 tion, it is necessary to introduce a certain 

 constant co-efficient for the number ex- 

 pressing the distance. This co-efficient, 

 when the distance is estimated in inches, 

 Mr. Barlow finds to be .00080382. If 

 this be called A, and the distance de- 

 noted by d, the formula, comprising all 

 the variable quantities in one equation, 

 becomes, 



tan. A = 



Ac/ 3 



(255.) The influence of the mass, and 

 also of the surface with relation to the 

 mass, of the iron sphere in modifying its 

 action, were next made the subjects of 

 investigation. Having at first employed 

 solid balls, weighing, respectively, 288 

 and 128 pounds, the results appeared to 

 lead to the conclusion, that the tangents 

 of the deviations were proportional to the 

 cubes of the diameter, that is, directly 

 as the masses. But when similar ex- 

 periments were made with hollow shells, 

 of the same diameter as the former balls, 

 Mr. Barlow was not a little surprised to 

 find that no difference was perceptible 

 between the results of these and of the 

 former trials. Hence he concluded, 

 that the power of attraction was inde- 

 pendent of the mass, and resided wholly 

 in the surface of the metal ; and all sub- 

 sequent- experiments confirmed the ac- 

 curacy of this conclusion. The in- 

 ference he drew was expressed in 

 the following proposition, namely, that 

 the tangents of the deviation are pro- 

 portional to the cubes of the diameters, 

 or to the square root of the cube of the 

 surfaces, whatever may be the weight or 

 thickness of the sphere. Subsequent 

 experience, however, taught him that 

 this law is subject to a limitation in re- 

 spect to the thickness of the metal in 

 which the magnetic power resides ; for 

 if that thickness, be less than the thir- 

 tieth of an inch, the power is not fully 

 developed, and its action is diminished. 



This conclusion has been since veri- 

 fied by Captain Kater, who found, on 



