II. ELECTKICAL EHEOMETRY. 27 



with the same terrestrial magnetic force T tan. d. Diminishing, therefore, the 

 intensity, h, until the deviation of the needle at the centre and near the circum- 

 ference are the same, we shall have 



7f/=: 7i-,/„ whence — = A. 



The difficulty is now reduced to determining the ratios of the intensity of the 

 currents corresponding to the two positions. This may be easily done, following 

 the principles of Ohm, and using the apparatus invented by Wheatstone for 

 measuring the resistances of electric circuits. From Ohm's theory we know that 

 the electrical forces or intensities k, k^, are in inverse ratio of the total resistances 

 in voltaic circuits ; therefore, marking by p and pi, the total resistance in our two 

 cases, we shall have 



Combining this equation with the preceding, we shall have 



(^) ^ = ^; 

 A pi 



that is, the functions/, /j, are in direct ratio with the total resistances of the circuits. 



The total resistance of a circuit comprehends the resistance of the voltaic battery 

 used in the experiment, and of the connecting wires through which the electricity 

 passes. All these resistances must be reduced to a certain unit of measure, and so 

 we shall obtain what is called by Ohm the reduced length of the circuit. Some 

 instruments are required for this purpose, and we shall explain in the next para- 

 graph their construction and use. 



These were the principles on which I made the first series of experiments, an 

 account of which was published in the journal mentioned in the introduction,^ but 

 at that time I did not take note of the quantity of deviation of the magnetic needle 

 used for investigating the action of the current, being satisfied with keeping it 

 constantly the same in the same series of experiments, and measuring it only 

 approximately, thinking that the absolute angle was of no very great importance. 



Now, however, the analytical formulas teach us that the absolute angle is one of 

 the leading elements of calculation. I have therefore repeated a part of the experi- 

 ments already made, in order to supply that defect, and have found by this means 

 that the results are not greatly affected by an error of two or three degrees in the 

 deviation, on account of the shortness of the needle and greatness of the circles 

 employed, and thus the first experiments can also be usefully discussed. 



It is also necessary to observe this angle in order to take the mean of several 

 experiments, because if the angles are difierent the mean cannot be taken. It 

 was, indeed, the sensible discordance of experimental results with each other, and 

 with the numbers found by Mr. Plana, which stimulated me to inquire deeply into 

 this matter. The result of the experiments agreed tolerably well with the num- 

 bers obtained from theory when the current was strong, but not so when it was 

 weakened by the resistances introduced. On the contrary, they agreed perfectly 



Eaccolta Scientifica. Koma, Dec. 15, 1847. 



