INTRODUCTION. XIX 



The apparatus has a tripod stand, a plummet for levelling the table-top, a thermometer to 

 l>e placed in the box with the magnet, annular weights of different diameters for determining 

 the moment of inertia of the magnet and stirrup, a block to facilitate adjusting the weights 

 upon the magnet, extra suspension tube, and all necesary adj listing tools, &c. 



On unpacking the cases after their arrival from London, magnet V No. 4 was found greatly 

 oxydized, and in consequence thereof the whole of the experiments were made with W No. 5 of 

 3.67 inches, and X No. 2 of 3 inches length. 



Having no purposely-constructed magnetical observatory, an orchard just east of Santa 

 Lucia, and near our residence, was selected as the most appropriate place for work, and until 

 June 11, 1850, the observations were made under an arbor ; after that da^e, beneath the shade of 

 an olive tree 100 yards north of the arbor. 



Unfortunately, at a very early period of the work, the thermometer used with the vibrating 

 magnet was broken, and, as it was impossible to replace it in Chile, of necessity the temperature 

 within the box is assumed to be the same as that of the external air. 



FORMULAS OF REDUCTION AND CALCULATION OF THE CONSTANTS. 



The absolute horizontal force of the earth's magnetism was determined by observation of 

 the angular deflection of a suspended magnet, produced by the influence of a second magnet 

 placed on a support at well-determined distances, in a line drawn from the centre of the first 

 perpendicular to its direction, and by observing the time of vibration of the deflecting magnet. 

 The first part of the process furnishes the ratio of the magnetic moment of the second magnet 

 to the earth's horizontal magnetic force, the latter being to the former as 1 to the sine of the 

 angle of deflection multiplied by half the cube of the distance employed ; and the second, the 

 product of the same two quantities, which is the quotient of a constant, we may call - 2 K, divided 

 by the square of the time of vibration ; ;r representing the ratio of the circumference of a circle 

 to its diameter, and K the moment of inertia of the suspended magnet, with the stirrup in 

 which it rests during vibration, the mirror, &c. 



,Continuing the notation of Colonel Sabine, R. A., in Appendix 1 to the " Manual of Scien- 

 tific Enquiry," and Captain C. S. B. Riddell, R. A., in the " Magnetical Instructions for the 

 use of Portable Instruments," both published by authority of the Lords Commissioners of the 

 Admiralty, let 



m =. the magnetic moment of the deflecting bar. 

 X=r the earth's horizontal force. 



r =. the distance between the centres of the magnets. 



u =: the angle of deflection. 

 T = the time of vibration. 



P = a coefficient depending upon the distribution of the free magnetism of the deflecting 

 and suspended magnets. 



Then = 



X 1 + P T 8 



r* 



P being a constant coefficient, is determined experimentally from observations at several dis- 

 tances calculated by the formula 



_ r 3 r, 6 sin u' rf r 6 sin u 

 r, 4 sin u 1 r* sin u 



The mean of all the values determined in this way was P = 0.00243, which has been 

 employed throughout the reductions. 



