54. 



Let K be the total, H the horizontal, V the vertical force, and a 

 the nearly known azimuth; then 



V 1 



K cos I=H cos a ; K sin I=V ; tan 1= rf • * 



H cos a 



,T cos"! ,/V\ HV . 



whence a 1= " fj i + sin a . « a. 



cos a \tij 



If on the right we substitute for cos its value, then 



.J H^cosa ,/V\ , HV . , 

 dl= d j + — sin ad a. 



As the possibility of error is inversely as the force, I multiply the 

 equation by K, to give to the different determinations equal weight, 

 thus 



jr,j H^cosa , /V\ , HV . , 

 Kdl=-^d^-^-^—s.nada 



having determined the dips in the customary manner with the ap- 

 proximately known values of a, I obtain the values d I, which serve 



to find d ; 2. e, the correction of I. 



I possess now with ray instrument six needles, which I hope to com- 

 pare very accurately with each other in the course of this year ; but 

 some months must first elapse, as I make all these determinations 

 in the open air, and the bad autumn we have had has interrupted 

 me in the work. I have had two of my needles fitted according to 

 Fox's method, with wheels on their axles ; two others have brass 

 indexes, as was formerly proposed by Bernoulli and Euler (Berlin 

 Trans. 1755), and I can now determine the absolute intensity with 

 the inclinatorium. I know Fox's method only from a short notice 

 in the London and Edinburgh Phil. Mag. ; if I do not mistake, he 

 proposed also to determine the declination by the same apparatus. 

 With ordinary needles there remains an uncertainty. If we load 

 the S. end of the needle so that the N. end is about 10^ above the 

 horizon, the S. end sinks down; and if we seek the azimuth in which 

 the needle is perpendicular and then observe at about half a degree 

 of azimuth on either side, the inclination alters so rapidly with the 

 azimuth, that I have thus been even able to follow the diurnal 

 variations of the declination ; and the magnetic meridian may thus 

 be determined for the observations of absolute declination whilst 

 travelling. 



I will not trouble you further as my letter is already so long, and 

 will only add one request. The Phil. Trans, arrive here rather late, 

 and the last communications which I have seen of yours contain 

 Keely's determinations. All the observations of the Erebus and 

 Terror have not yet appeared ; in the Atlantic I know only the total 

 intensities but without inclinations or declinations, and yet I am very 

 anxious for some determinations that have been made between 10° 

 and 20° of longitude in the higher latitudes to compare my calcula- 

 tions with them. If your time permits, I should be very much obliged 



