74 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



Without his help the present corrected reduction of the observations could never 

 have been made ; and even with the aid of the tables kindly prepared by him, it 

 has been a work of no small labour and anxiety to bring to one strictly accordant 

 scale the whole of the observations made with eight or ten thermometers, none 

 of them deserving of being called standards, and in most of which the zero 

 appears to have oscillated at different periods. 



42. I have thought it unnecessary, as it would certainly have been most 

 tedious, to print in this paper the crude observations and the numerous tables of 

 reduction formed for the scales of the several thermometers. I have thought it 

 sufficient to give the corrected results, which, in many cases, are the mean of 

 independent readings of different thermometers. 



43. Besides the correction of scale errors, an important correction required 

 to be applied in order to reduce the readings to what they would have been had 

 the column of the mercury in the thermometer partaken of the temperature of the 

 bulb. Owing to the small transverse dimensions of the bars, whose temperatures 

 were to be ascertained, the bulb of the thermometers was often little more than 

 covered by the mercury with which the holes in the bars were filled (Art. 20). The 

 stems were therefore necessarily exposed in their whole length to the temperature 

 of the surrounding air. In the case of the higher temperatures to be measured, this 

 correction was not only large (amounting sometimes to 3° Cent., always additive), 

 but also in some degree uncertain, owing to the ascending currents of warm air in 

 the neighbourhood of the heated bar, and enveloping the stem of the thermometer.* 

 However, I believe that the formula in the note below leads to pretty accurate 

 results, checked, as it has been, by occasional observations of a small auxiliary 

 thermometer suspended in the air, touching the stem of the thermometer to be 

 reduced, about its middle. 



44. The hotter thermometers are probably slightly over corrected. I have 

 stated that in extreme cases this correction amounts to about 3° Cent., a quantity 

 which may possibly be erroneous in some cases to one-tenth of its amount, but 



* The form of the correction is very simple, being 



Degrees exposed x Excess of Temp, shewn over air. 



Dilatation of Merc, in Glass for 1° Cent. 



always additive. If T he the temperature as read, t the temperature of the air, and a the scale 

 reading of the commencement of the stem of the particular thermometer, the correction is very nearly 



+ (T-a) (T-t) 



6400 



Since t and a are usually small numbers, the correction increases nearly as the square of the tem- 

 perature to be measured. 



Fortunately, the precision of this correction is not very important to the result. It chiefly 

 affects the actual temperatures ; for it will be more fully seen hereafter, that if the same instru- 

 ment be used in the dynamical and statical experiments, being exposed in precisely the same way, 

 the measures will be relatively correct, and the deduction of the conductivity will not thereby be 

 sensibly affected. 



