146 THE SCIENTIFIC PAPERS OF 



are given in tables 4 to 7, and are also laid down on the diagram 

 according to the same scale as the platinum curve. 



Setting aside some palpable errors, these results also produce 

 lines curving downwards to the absolute zero on the abscissal axis, 

 and agree very closely with the measured results obtained by 

 Dr. Matthiessen * between the limits of and 100 Centigrade. 

 They also agree, generally, with the results I obtained by means of 

 another series of observations which I undertook for testing the 

 progressive increase of resistance beyond the range of the mercury 

 thermometer, and which will be noted further on. 



Encouraged by these concordant results, I have endeavoured to 

 find a general expression for the increase of electrical resistance in 

 conductors with rise of temperature, which should be based upon a 

 rational dynamic principle. 



The experimental curves represented on the diagram differ so 

 little from a straight line, between the limits of and 100 Cent., 

 that the early observers, whose observations did not go beyond 

 those limits, naturally concluded that the electrical resistance 

 increased in an arithmetical ratio with the temperature. In 

 taking the amount of increase between these limits, in copper or 

 silver wire, it was, moreover, found to coincide very nearly with 

 the increase of volume of permanent gases by heat. 



Clausius has drawn from these data the conclusion " That the 

 resistances of metals are directly proportional to their absolute 

 temperatures." f Matthiessen, however, found that the increment 

 of increase of resistance was not absolutely constant between the 

 limits of and 100 Cent., but that the ratio of increase in pure 

 metal was expressed by the formula 



1 - '0037647 t + 0-00000834 t a , 



where R represents the resistance at zero Centigrade and R* at 

 any other temperature on the same scale, which ratio agrees very 

 closely with my own results between those limits ; whereas, at 

 temperatures exceeding 100, great discrepancies are at once 

 apparent. This will be seen from the following statement of 



* Vide Philosophical Transactions, 1862. 



t Vide Poggendorff's Annalen, Vol. CIV. p. 650, 1858. 



