54 



KESEARCHES ON 



II. 



§ 13. Theory of the Galvanometer. 



The theory of the galvanometer is simply a corollary of what has been presented 

 until now. The formulee which we have given are not yet sufficient to calculate 

 the force of the common galvanometers, having their wires disposed in rectangular 

 frames. If we were to construct a frame of an elliptical form, we might apply the 

 formulse of § 6. The calculation being, however, very complicated, we shall rest 

 satisfied here with giving the theory of the galvanometer reduced to its state of 

 greatest simplicity, viz., that of a circular current, surrounding a magnetic needle, 

 as is the case in the compass of tangents. The needle may be of any length, pro- 

 vided it be very fine, so that its poles may be regarded as the ends of an electro- 

 dynamic cylinder of very small radius. The formula available for the calculation 

 is the usual one, viz., (6) § 6, where _p is made = 0. 



I have endeavored to verify the formula for a few deviations, but not having at 

 hand an apparatus sufficiently perfect, I shall give the results only as approxima- 

 tions. The most important point is to procure a current, which may be truly an 

 exact multiple of another, without using the rheostat, without any change in the 

 resistance, and also without making use of any apparatus, which depends upon a 

 law of uncertain nature. For this purpose, I took a long copper wire, covered 

 with silk, and at the distance of two meti-es from- one of its ends, I formed a circle 

 composed of eight rings of 17.76™°*™- in diameter, then at the distance of other 

 two metres I formed a circle equal in diameter to the first, but composed of only 

 four rings, and finally at a distance equal to the preceding, I made another circle 

 of a single ring. See Plate II., Fig. VIII. The mean diameter of the three rings 

 was sensibly equal, but the wires being more than a millimetre in thickness, the 

 circle of eight rings formed a considerable volume, in comparison with that of one 

 wire only. These circles were successively placed round a comjaass, on which were 

 marked the half degi-ees, and the smaller fractions were taken by approximation. 

 Having charged a pile, the force of which was constant, and having taken due 

 precautions for the exact measurement of the deviations of the needle in two 

 opposite directions, we had the following results : — 



Diameter of the circle ..... 177.97™"' 

 Length of the needle .... 81.38°""- 



This length is the exact distance between the two poles, measured carefully several 

 times, by help of the attraction on a small magnetized needle, as Coulomb used to 

 do for the determination of the true places of the poles in a magnetic bar. 



Deviations of 

 needle. 



Given proportion of 

 the forces. 



Difference. 



Value of 





From 

 observation. 



From 

 calculation. 





10° 

 31° 18' 



46° 18' 



current 1 

 " 4 

 " 8 



1.000 



4.055 

 7.884 



0.55 

 0.116 



0.526 

 0.447 

 0.395 



