OF ARTS AND SCIENCES. 



89 



TABLE IV. — Reckkagel's Results compared with the Formula. 



6=290° a =.000 000 33 



T= t -f- a t (100 — t) (b — t) 



It will be seen that the values of the constants are not very different 

 from those which satisfy Regnault's experiments. 



There seems to be no doubt, from all the experiments we have now 

 discussed, that the point of maximum difference is not at 50°, but at 

 some less temperature, as 40° to 45°, and this agrees with my own 

 experiments, and a recent statement by Ellis in the Philosophical 

 Magazine. And I think the discussion has proved beyond doubt 

 that the formula is sufficiently accurate to express the difference of 

 the mercurial and air thermometers throughout at least a range of 

 200°, and hence is probably very accurate for the range of only 

 100° between 0° and 100°. 



Hence it is only necessary to find the constants for my thermom- 

 eters. But before doing this it will be well to see how exact the 

 comparison must be. As the thermometers are to be used in a 

 calorimetric research in which differences of temperature enter, the 

 error of the mercurial compared with the air thermometer will be 



dt ( 



2(b + t>)t + 3t^, 



which for the constants used in Recknagel's table becomes 



Error = ^ — 1 = .000 000 33 j 29000. — 780 t + 3 i 2 1 . 



This amounts to nearly one per cent at 0°, and thence decreases to 

 45°, after which it increases again. As only 0°.2 at the 40° point 



