7 B Intelligence and Miscellaneous Articles. 



son's method the absolute value of the unknown does not affect the 

 exactitude of the determination. This difference is explained by the 

 following remark. In Mr. Wheatstone's method, the equation by which 



the unknown is determined is x J±—=k; where x is the unknown 



a 

 resistance, b the resistance of the conductors which join x to the 

 system, a the standard resistance, and k the numerical ratio whose 

 value depends on the reading of the rheostat. When x diminishes 

 in reference to b, the error relative to x increases, that of Jc remain- 

 ing constant. In Thomson's method, k is determined by the 



x 

 value of a resulting from observation, and the equation ~=k; 



the error relative to x is constant with that of a. The resistances 

 arising from imperfect contacts are also, in Wheatstone's method, a 

 source of errors which are more considerable in proportion as the 

 absolute value of x is small. In Thomson's method, th'e junctions 

 of the conductors may be arranged so as to throw these two indeter- 

 minate resistances, not upon x and a, but upon two resistances the 

 division of which on the wire of the galvanometer determines the 

 value of k. If by R and kR we designate the two parts into which 

 each of these resistances is divided, we see that by giving to R a very 

 considerable value, the resistances of contact do not appreciably 



kR 



alter the relation -~-. Finally, analogous consideration shows that 



the use of this method is still more advantageous in the case in 



which the conductor whose resistance is to be measured is raised to 



a very high temperature ; for since the conductors which join it to 



the rest of the system necessarily become heated, and in the equa- 



oc-\-b 

 tion = k of Wheatstone's method the quantity b is variable, 



in Thomson's method, by assigning to R and kR a high value, the 

 variation arising from the heating of the extremities is inappreciable. 

 The conditions which render Thomson's method superior to that 

 of Wheatstone are precisely those met with in the measurement of 

 fused metals. For (1) the unknown resistance is small as compared 

 with the accessory resistances, since on the one hand a column of 

 fused metal can neither be long nor of small diameter, and on the 

 other hand the furnace must be at some distance from the measuring 

 apparatus ; (2) there are variable resistances of contact ; (3) the 

 conductor is at a high temperature. The experiments which I have 

 made in the chemical laboratory of the Ecole Normale, under the 

 valuable and friendly direction of M. Ste. -Claire Deville, are of a kind 

 to show that the method is suited to researches of this kind. 



Apparatus. — I had two special instruments made, a rheostat 

 and what maybe called a compensator. These two apparatus are 

 from the workshop of M. Fromart. The rheostat consists essen- 

 tially of a metallic wire stretched along a divided rule on which slide 

 two rollers, each with a platinum plate which rests at its edge on 

 the wire. The part of the wire between the two plates forms the 



