OP ARTS AND SCIENCES. 155 



Let R t be the resistance at some known temperature t t , and V t and U i 

 the known corresponding deflections of the galvanometers, then 



R > = k KH^v! = R « + at > + bt ' + &C ") 

 For any resistance R u , we write in the same way : 



R u = 



h h sin U„ R" 



KUtenV,, = B o C 1 +«*« + H/" + &c -) 



From these two equations, by proportion, 



or simply, 

 1 + atu + fc// « + &c. = j^^g (1 .+ « «, + J 1/ + &c.) 



If now we know the values of t, and - — ~ for any one case, and 



' sin (// J 



the coefficients a and b, we may, by simply reading U tl and V n for 



any other current, determine the temperature from this equation. 



As, for example, to determine t u we have merely to substitute the 

 readings of the galvanometers U u and V u and solve relatively to t n . 



The coefficients a and b have already been determined by Benoist,* 

 viz., 



a = .002445 b = .000000572 



To determine U, and V, for some temperature t„ the wire was sub- 

 merged in water at that temperature. This, of course, had to be 

 repeated every time the wire was changed for a new one. 



As may be seen upon examination, the theory of the method has 

 nothing objectionable in it, and its practical accuracy depends upon 

 the determination of the coefficients a and b. These were carefully 

 determined by Benoist up to 860° C. For temperatures very much 

 beyond this, as between 1,000 and 2,000 degrees, there is a liability to 

 some error. But it is easily seen that the method is vastly superior 

 to that of determining the temperature by the method of expansion. 



Reduction to Sun's Spectrum and Determination of Wave- Lengths. 



The image of the spectrum, as formed in the plane of the face of 

 the pile, could be measured only in terms of divisions of the arbitrary 

 scale attached to the slide on which the pile was placed. In order to 

 determine the wave-lengths of the different parts of the spectrum for 



* Phil. Mag., April, 1876. 



