232 PHILOSOPHICAL TRANSACTIONS. [aNNO 1777- 



.1 Construction and application of tlie table of Equation, for the Expansion of 

 the Quicksilver in the tubes of Barometers. — In the application of the barometer 

 to the measurement of heights, various modes of calculation have been adopted. 

 Tiie easiest and best method seems however to be, by means of the tables of 

 common logarithms, which were first thought of by Mr. Mariotte, and after- 

 wards applied by Dr. Halley, Mr. Bouguer, Mr. de Luc, and others. They 

 have all proceeded on the supposition, that air is a truly homogeneous and elas- 

 tic fluid, whose condensations being proportionable to the weights with which it 

 is loaded, its dilatations are in the inverse ratio of the weights; and in conse- 

 quence of this law, that the heights of the atmosphere ascended, are in geome- 

 trical progression, while the corresponding successive descents of the quicksilver 

 in the tube of the barometer, are in arithmetical progression. 



Mr. de Luc makes use of an arithmetical or uniform equation for the heat of 

 the quicksilver in his barometer, by which their relative heights are reduced to 

 what they would have been in the fixed temperature of 544-° of Fahrenheit. In 

 the formulce adaj)ting his rule to English measures, (vol. 13, pp. 520, 530) it 

 has been shown, that the easiest and simplest method is, to make the difference 

 of temperature of the two barometers the argument for the equation; and that 

 it is sufficient to reduce cither column to what would have been its height in the 

 temperature of the other. But whatever may heretofore have been the method 

 of using the equation for the heat of the quicksilver, while it was considered as 

 arithmetical; now that it has been shown, from the preceding experiments, to 

 be progressive, there seems at least to be propriety in applying to each barometer 

 the equation answering to its particular temperature. And though, for this pur- 

 pose, any fixed temperature might have been assumed at pleasure, as that to 

 which both barometers were to be reduced; yet, the freezing point being funda- 

 mental i-.i all thermometers, and that being also the zero of the scale for the 

 equation depending on the heat of the air, as will be shown hereafter, it has 

 been preferred to any other. 



From the experiments it appears, that a column of (juicksilver of the tem- 

 perature of 32^", sustained, by the weight of the atmosphere, to the height of 

 30 inches in the barometer, when gradually affected by different degrees of heat, 

 suffers a progressive expansion; and that, having acquired the heat of boiling 

 water, it is lengthened tVo'tto P^rts of an inch: also, that the same column, 

 suffering a condensation by 32° of cold, extending to the zero of Fahrenheit, is 

 shortened -rViniTr pai'ts, the weight of the atmosphere remaining in both cases 

 unaltered. But in the aj)plication of the barometer to the measurement of alti- 

 tudes, since the pressure and length of the column change with every alteration 

 of the vertical height, the equation, depending on the difference of temperature 

 of the ([uicksilver, will necessarily augment or diminisli by a proportionable part 



