78 Royal Society. 



In the above table, the Iiorizontal force was obtained by vibrations, 

 and reduced to 6° Reaumur. Before and after my journey in 184-7, 

 the force was determined at Dorpat by Gauss's method, and the 

 needle employed compared therewith and reduced to the intensity in 

 London = J 37'2. Subsequently I preferred for trying the needles, 

 PoissOn's method, at least for traveling purposes; but some alterations 

 require to be introduced in Poisson's formula, as he has overlooked 

 some things. With the same needle which I employed in both my 

 journeys, I have made more than 60 determinations of absolute 

 force at Dorpat, partly in a room and partly in ihe open air, and in 

 temperatures varying from— 13° 11. to + 25° R., and have found a 

 very good accordance. I also made several such determinations in 

 the journeys of 1848 and 1849. 



As I do not possess an observatory, and cannot employ a Bifilar 

 in my dwelling-house, it has not been possible for me to compare 

 the variations of the force with my determinations ; I have however 

 made use of the following method : — If X be the magnetism of the 

 earth and m that of the needle, I seek not X but m ; this latter 

 quantity depends on the temperature t and the time T, as the needle 

 is not constant ; but if I combine all the values of m by an equation 

 of the form 



and calculate the constants, the error is about ^^ m. Besides this, 

 several simultaneous observations with Gauss's apparatus have shown 

 that the value of m was itself correct. 



The Inclinations have in part been determined by two needles 

 which agreed very well with each other ; they are so balanced that 

 I can always take the mean of the eight arcs. On the other hand 

 they are subject to the error of the axle, which I cannot exactly cor- 

 rect, but which does not however exceed 5'. It was only last sum- 

 mer, when I examined the subject more closely, that I became aware 

 you had likewise the idea of loading the needle, and observing in 

 different azimuths. In our latitudes the best loading is such as will 

 cause the north pole to be in one set about 10° above, and in a 

 second set 10° below the horizontal line. Three series which I made 

 with one needle were calculated by my friend Claussen, who in 

 doing so was led to a method of entirely eliminating the form of the 

 axle. Take a well-balanced needle, the axles of which are not cy- 

 lindrical ; different degrees of magnetic force can be given to it with- 

 out reversing the poles. Taking the strongest force as unity, it is 

 not practically advantageous to go to lower ratios than i or ^. 

 Though vibration experiments with dipping-needles are not gene- 

 rally advantageous, yet they suffice in this case, as an approximately 

 correct proportion of the intensities is all that is wanted. It is suf- 

 ficient to make, with each degree of intensity, the two observations 

 with the face east and face west, without reversing the needle on its 

 supports ; if the latter is done, it gives a second determination, af- 

 fording a check upon the first. You will then find that the mean of 

 the two observations in one position of the axles is less than the 

 true inclination, and in the other position greater ; the difference in 



