MendenhaU — Differential Resistance Thermometer. 115 



a millimeter, and still leave the scale tolerably "open." In one 

 of the instruments already made 1° C. corresponds to about 

 5 mm of the scale. Sunning down through the stem is a fine 

 platinum wire about -08 mm in diameter. The lower end may be 

 secured in the bulb so that it is kept straight in the bore of the 

 stem, and at the lower end a heavier wire is sealed in the glass 

 so that metallic contact can be made with this wire both at the 

 upper end and through the mercury at the lower. It is evident 

 that the resistance between these two points will depend largely 

 (but not entirely) on the length of the platinum wire which is 

 above the mercury in the tube and this will depend on the 

 temperature to which it is exposed. When this temperature 

 rises the resistance is decreased by an amount equal to the dif- 

 ference between that of the platinum wire which disappears and 

 that of the mercury which takes its place — less the increase in 

 the resistance of the wire and mercury due to increase of tem- 

 perature. 



Let I = length of platinum wire exposed at 0°. 



sz= resistance per unit length (= length of 1°) of wire. 



g = resistance per unit length (= length of 1°) of mercury. 



h = temperature coefficient of platinum. 



h = temperature coefficient of mercury. 

 R = total resistance at 0°. 

 R t = resistance (including all) at t°. 



Then 



R t =R;- {s(l-Jcl) -g\t- {Jcs -gh)t\ (1) 



This equation is not quite rigorous, but the approximation is 

 very close. It is of the form — 



R t =R -B*~Ci! 2 . (2) 



The simplest and best way of dealing with it is to determine 

 the constants of the equation (2) by a series of observations 

 making use of the method of least squares. From the result 

 the resistance for any degree of temperature may be calculated, 

 or better, a curve can be constructed from which the tempera- 

 ture corresponding to any resistance can easily be read. 



The advantage of this method over the use of a simple resist- 

 ance coil is that the change in resistance accompanying a given 

 change in temperature, is much greater and in fact it may be 

 made as great as one desires. As a result the telephone may 

 be substituted for the galvanometer in the resistance measure- 

 ments, thus greatly simplifying the apparatus as well as increas- 

 ing the rapidity with which observations may be made ; or if 

 preferred, a much less sensitive galvanometer may be used. It 

 also possesses the very great advantage of allowing an increase 

 of delicacy as the range of temperature decreases. For earth 

 temperatures this is very desirable and it will easily be seen that 



