74 OBSERVATIONS. 



With these constants, the horizontal force = X, and the magnetic moment = m, were found 

 as follows : 



^ /J r^ sin u ^ r^ sin wN 



where r and rj = the distance between the centres of the deflecting and suspended magnets 

 in decimals of a foot, m and %i> = the corresponding angles of deflection 



p 7^ r^° sin u^ — r,^ }-° sin u 



Ti^ sin u^ — r° sin u. 

 P was determined by the above formula, by taking a mean of twenty sets of observations at 

 1 foot and 1.3, including those made during the trip, and found to be ec[ual to — 0.0022001. 

 And this value was used as a constant. 



ir- K 



m X =-?p- 



where ^ = Circumference of circle to diameter 1 ; 



K = Moment of inertia of suspended magnet and stirrup ; 

 T =z the time of one vibration given by the formula. 



I \ 86400 16 / i V ^ F ^ ^ -' / 



These symbols being the same as those used in determing the value of K. And 



t =: temperature of deflecting magnet during the experiments of 



deflection. 

 f z=z temperature of deflecting magnet during the experiments of 



vibration. 

 q =: the temperature coefficient. 



And finally, calling = = A 



mX=B 



- = V! 



and m=z V AB 

 While in Buenos Ayres I made observations, from early daylight till dark, for change of 

 horizontal force, by taking the time of 300 vibrations every hour, but I neglected to observe the 

 angle of deflection except at the beginning, middle, and end. At these times, viz : 

 At 6.30 A. M. X= 6.19309 

 At 1.30 p. M. X= .19886 

 At 6.30 p. M. X= .22289 

 At Santiago, the value given of X and m is the mean of several sets of observations imme- 

 diately preceding my departure. At the Chacra de Montumas the observations were made 

 about mid-day; at the Estero de las Cruces about 11 a. m. ; at the Alto de la Laguna about 3 

 p. M. ; at the Cumbrc about 6 a. m. ; at the Casucha de los Puc^uios about 6 a. m. ; at Uspallata 

 T A. M. ; and at Mendoza about noon. 



The total force was found by multiplying the horizontal force into the secant of the inclination. 

 In conclusion, I beg leave to state that from several causes it is difficult to make accurate 

 observations in a mountain pass; the princijml obstacles are, local attraction and strong winds. 

 In the case of my observations, there was the additional difficulty of being obliged to make 

 them in the sun, because tlie tent I had was of such construction that it was useless as a shelter 

 to the instruments. 



