438 Mr. Herapath on True Temperature, and the [Dec 



to be by our theory. Whether such a law between the difference 

 and force of tensions is correct, it would be speculative to affirm; 

 but this seems very evident from a comparison of the experi- 

 ments, that had Dr. Ure carried his experiments to the same 

 temperature, he would have brought out a much greater tension 

 than Mr. Southern has. It is, however, very curious that Dr. 

 lire's theorem, according to Dr. Thomson, makes the tension at 

 343-6° Fahr. only 210, or full 30 in. lower than Mr. Southern's 

 experiment. But if it is so much below Mr. Southern's obser- 

 vations, what would it be below his own if carried to the same 

 length ? There is every reason to believe the error would have 

 been at least 50 inch, or upwards of a fifth part of the whole 

 tension. 



What could be the cause of Mr. Southern's tensions being 

 progressively lower than Dr. lire's, it is difficult to say decidedly ; 

 but I rather think it must be owing to his thermometer. If the 

 instrument indicated too high a temperature in the higher 

 Tegions, the errors would undoubtedly commence from the boiling 

 of water, and increase probably proportionally as the temperature 

 ascended. Suppose the error at 250° Fahr. was 1-83°, at2 - 934 c 

 it would be 3-9°, and at 343-6° about 6-3°. Reducing Mr. 

 Southern's temperatures by these quantities, they become 

 248-17°, 289-5°, and 337-3°, the temperatures at which the ten- 

 sions ought to be 60 in. 120 in. and 240 in. By Dr. lire's obser- 

 vations, it would seem that at 248*17° the tension is about 60-03 

 and at 289-9°, which is only -4° higher than 289*5°, it is also 



in. 



about 120 in. So also by the theorem which I have shown to 

 agree so nearly with Dr. Ure's observations the tension at 337-3° 

 is very nearly 240 in. Hence with this simple correction the 

 two observations may be very nearly reconciled. 



The examples in the following table I have endeavoured to 

 collect as the most disadvantageous to the theory. In other 

 instances I think it will in general be found that the differences 

 are less. To these examples I have added some calculations 

 from a theorem given by Dr. Ure. 



