HALL. — CONDUCTIVITY OF SOFT IRON. 139 



Appendix. 



Does the conductive action of the copper wires attached to the platinum 

 thermometer spirals introduce error by preventing these spirals from taking 

 the temperature of the water flowing past them? 



If the warming or cooling produced by the action of the copper wires 

 were equally great at the two spirals, no harm would result, as it would 

 not affect the difference of their temperatures, which is the quantity 

 measured- but this perfect compensation can hardly be, for all of the 

 copper connections are subjected to very nearly the same temperature 

 conditions outside the supporting hard rubber plugs, while the spirals 

 themselves differ in temperature about 0°.5. The differential effect, upon 

 which alone the possibility of sensible error depends, is very much the 

 same as if one of the spirals were at the same temperature as its connect- 

 ing wires outside the plug and the other spiral 0°.5 warmer or colder 

 than its connecting wires outside the plug. It is possible to make a very 

 rough estimation of the maximum amount of error which could arise 

 from such a condition. For the purpose of this calculation it may be 

 assumed that the hard rubber plug is a non-conductor of heat, — an 

 assumption which tends to magnify the effect under discussion. The 

 length of the plug, that is, the length of the wire from air to water, is 

 2.5 cm., the diameter of the wire about 0.1 cm., the length of each copper 

 wire exposed to the water about 1.6 cm. The length of the platinum 

 wire in each spiral is about 22 cm., and its diameter about 0.012 cm. 

 The point of attachment of the platinum to the copper is near the middle 

 of the part of the copper exposed to the water. We will discuss the 

 action of a single copper wire, and assume that one half of the plat- 

 inum wire was attached to this by one end, the other end being free. 

 For this purpose it will be necessary to know something about the 

 "surface conductivity" of copper immersed in running water. Fortu- 

 nately the main experiment with the copper-coated disk gives us some 

 information in regard to this, — very inaccurate information, no doubt, 

 but sufficient for the present purpose. 



In this main experiment, with a mean temperature t in the disk, and 

 with a temperature t + 4 in the stream on one face and t — 4 in the 

 stream on the other face, the two meeting surfaces of copper and iron 

 had respectively temperatures about t + 0.8 and t — 0.8, we will say. 

 Assuming the thermal conductivity of copper to be eight times that of 

 iron, and remembering that the copper coatings are each 0.2 cm. thick 

 while the disk is 2 cm. thick, we get for the temperatures of the two outer 



