78 RESISTANCE OF THE SECONDARY WIRE UNDER VARIATIONS OF TENSION. 



TABLE A. 



and therefore we infer that the foregoing ratio holds. 



266. Currents of very low tension give proofs of the same fact. A thermal pair of 

 platina and palladium passed 44 through the primary, and 19-50 through the secondary 

 wire; and when, by increasing the temperature, 236 passed through the primary, 115 

 went through the secondary wire. In a pair of palladium and silver, 165 and 1130 

 being passed successively through the primary, 43 and 313 went through the secondary 

 wire. In a pair of iron and platina, 170 and 249 being successively sent through the 

 primary, 79 and 112 respectively passed through the secondary wire. 



267. But let us farther suppose that the quantity of electricity passing at different 

 times through the primary wire A is constant, its tension alone undergoing an increase. 

 If A formerly conducted all that was presented to it, it will, under this new condition 

 of things, of course still do the same. Such, however, will not be the case with B, for 



a greater quantity is now enabled to pass it than before, and the ratio - will give a 



d 



greater value ; we shall therefore, in this case, have a measure of the tension. But if 

 the tension still keeps increasing, b will continually approach to equality with a ; and 

 when the tension is infinitely high, these quantities are accurately equal to each other ; 

 or, in other words, when the elastic force of a current is infinitely high, its tension is 

 unity. 



268. If, on the other hand, the tension becomes lower and lower, b continually de- 

 creases, and, finally, might be found equal to zero. The value of the ratio then be- 

 comes zero ; and, therefore, at the two extremes, or where the tension is unity and 

 where it is zero, the secondary wire, so far from ceasing to act, still truly indicates the 

 condition of the current. 



269. While, therefore, A conducts freely the whole current, B will measure its ten- 

 sion under all circumstances ; but, in point of practice, we can never make the adjust- 

 ment here hypothetically indicated, or so arrange a wire A that it shall conduct all the 

 electricity presented to it. Let us, therefore, here inquire how this variable condition 

 of both wires will affect the result. Let the tension (f) so change by any amount as 

 to become (n ), then a corresponding change will happen in a and b, admitting the 

 principle that the quantities passing through A and B are increasing functions of (f). 



If, then, (f) becomes (n f), a will become (n a). Now, if the equation - = t holds, 



a 



b = at; but, when the change impressed on (f) has happened, b will be equal 

 to the conjoint values of (n a) and (n f) ; and, if these values be substituted in the for- 

 mer ratio, the result is still equal to (n f) ; so that, whatever may be the change im- 

 pressed on (#), the formula - = t will always indicate it. 



Of 



270. Having thus settled, by the foregoing simple reasoning, the fundamental doc- 



