110 Mr. H. L. Callendar on the 



is probably a little too low. Moreover, on account of the 

 wide discrepancies at present existing in the estimates of the 

 temperature of the freezing-point of silver on the air- 

 thermometer scale, according to different authorities, the 

 result would in any case serve only as a rough verification of 

 the formula (d). The difficulties in the way of making 

 accurate determinations with an air-thermometer at this 

 temperature are undoubtedly considerable ; but I have 

 recently succeeded in devising a special form of instrument 

 with which I hope to be able to obtain more trustworthy 

 results. 



Sir Wm. Siemens was the first to attack the problem of 

 determining the variation of electrical resistance at high 

 temperatures. He showed that the formula given by 

 Matthiessen, 



K /R=l-at + /3t 2 (m) 



was entirely inapplicable except between the limits 0° and 

 100° C. His own experiments led him to suggest the 

 formula 



E=aT* + /3T + 7 (S) 



This formula has been very widely quoted and adopted, 

 but it does not, so far as my experience goes, represent the 

 results of observation so well as the simpler formula 

 R/R =l + a£ + /ift 2 , which was used by Benoit, and which is 

 equivalent to formula (d). 



1 have only recently succeeded in finding a published 

 account of Sir Wm. Siemens's experiments *. It appears 

 from this that they were undertaken rather with a view of 

 graduating a commercial pyrometer than of investigating the 

 law of change of electrical resistance. Temperatures up to 

 350° were determined by mercury thermometers in an air- or 

 oil-bath, and it does not appear that any corrections were 

 applied to their readings. The individual observations are 

 somewhat irregular, and often show divergencies amounting to 

 2 per cent, and over. Only three observations at higher tem- 

 peratures are given ; they show a mean deviation of about 

 30° C. A copper ball-pyrometer was used to determine the 

 temperatures, which are given as 810°, 835°, and 854° C. ; 

 the corresponding temperatures deduced by formula (S) from 

 the observed resistances of the platinum pyrometer were 

 772°, 811°, and 882° C. 



The formula Siemens gives for iron makes the rate of in- 

 crease of its resistance diminish considerably with rise of 

 temperature. The formula given by Benoit makes it increase 

 * ' Transactions of the Society of Telegraph Engineers/ 1875. 



