] 1 PB0CEEDING8 OP THE AMERICAN ACADEMY. 



copper surfaces, in contacl with the water, the temperatures / + 0.82 and 

 t — 0.82 respectively. This makes each copper coating to have a tem- 

 perature gradient ofO .1 per cm., with a difference of 3 .18 between its 

 outer surface and the water stream flowing across it. The ratio of the 

 temperature gradient to the external difference is therefore about ,'_,. 



According to this we may infer that a Btream of water flowing across 



one face of a copper wire, with a speed equal to that of the flow across 



surface of our disk, and with a temperature t degrees above the tern- 



perature of the face of the wire will maintain within that wire a gradient 



of temperature equal to t -:- 32, all lateral action being excluded. 



The point of attachment of the platinum wire to the copper is about 

 midway of the exposed part of the copper, and is as much as 3.0 cm. 

 from the cuter end of the plug, [f the copper wire terminated at this 

 point of attachment, and Buffered conductive contact with the water only 

 at its terminal surface, the change of temperature from the cuter end of 

 the plug, Buppoeed non-conductive, to the end of the wire would accord- 

 ingly be about ; ;; J . ,V it as the difference of temperature between 

 the end of the wire and the water flowing past it. Ii. therefore, the wire 



at the cuter end of the plug exceeds in temperature the stream o\ water 

 li\ ii .."». as uc w ill assume, the fall of temperature within the wire would 

 be about .0 1. and the end of the wire would be about . 16 above the 



temperature of the stream. This conclusion, however, is based on a 

 false assumption as to the area of contact of the wire with the water; in 

 fact, this area of contact is about BlXtj times as great as the cross-section 

 of the wire, and the point of attachment of the platinum is near the 

 middle of this area, so that we shall not be very far from the truth in 

 assuming that the temperature of the copper at the cross-section next the 

 point of attachment of the platinum is the Bame that it would be if the 



Wire had contact With the water only at this cn»s-eeiioii hut had sixtj 



times ae gr< at a Burface conductivity as such an area reallj has i n contact 



with the Btream. This leads to the conclusion that the fall of temper- 

 ature within the wire, from the outer end of the plug to the point of 



attachment of the platinum, is about i ; V times as great as the difference of 

 temperature between the point of attachment and the Btream. This last 

 difference would therefore he rather less than 0°.l, but we will call it 



that. 



The problem now is to find how much the mean temperature of a plat- 

 inum wire 0.012 cm. in diameter and II cm. long will exceed that of the 

 uai tm iii which it is placed, if one end of this wire is kept .1 



above the temperature of the water This problem is of a familiar sort. 



