1869.] 



Corrections to Pendulum Observations. 



495 



Hence we find a correction between 



o o Il*2l 



4y 1 6 and 71-64 of = "45 8 vibrations 



24-48 



47-16 „ 88-00 „ i9^5 = . 4 86 „ 

 40-84 



71-64 „ 88-00 „ y|^|="528 „ 



per diem for one 

 degree of Fahr- 

 enheit's scale. 



Comparing these results with those obtained by General Sabine (Phil. 

 Trans. 1830, p. 251, &c), we find that the pendulums employed by him 

 gave a correction of 0*44 of a vibration per diem for each degree of 

 Fahrenheit between 30° and 60°, a result which agrees well with that found 

 by ourselves between 40° and 70°, the small difference being probably 

 referable to a difference in the composition of the metal of which the 

 pendulums were made. But a considerable difference appears in the expe- 

 riments made at the higher temperature. General Sabine made some 

 experiments, previously to those discussed in the above-mentioned paper, 

 with two different pendulums in a chamber artificially heated to between 

 80° and 90°, which gave for the correction for each degree of Fahrenheit, 

 respectively for the two pendulums, 0*432 and 0*430 vibrations, cor- 

 responding to that part of the thermometer-scale which is included be- 

 tween 45° and 85°. These results are somewhat different from those 

 which are obtained for the scale-reading between 30° and 60°, and 

 General Sabine points to this difference in the following words * : — 



" In the experiments in the chamber artificially heated, the fluctuations 

 of temperature, in spite of every precaution, were considerable, and 

 rendered the determination of the mean temperature more difficult, and 

 probably less exact than in the natural temperatures ; hence it would be 

 unsafe to conclude in favour of the inference to which these facts would 

 otherwise lead, that the correction at high temperatures is less than at low 

 temperatures, or that the metal expands a smaller proportion of its length 

 for one degree between 85° and 45° than for one degree between 60° 

 and 30°." 



Our own experiments, on the other hand, seem to agree with the 

 general fact that the coefficient of expansion increases with the tem- 

 perature, and that in a series of experiments a lower range of temperature 

 will give a lower, a higher range a greater value for the expansion for one 

 degree. Nevertheless the values resulting from our high temperature- 

 experiments appear decidedly too large to be explained solely by this 

 general behaviour of bodies ; and in our reductions of the pressure-expe- 

 riments, where the differences of temperature, as will be seen in the fol- 

 lowing paragraph, are inconsiderable, we have adopted that value for the 

 temperature-correction which results from the experiments between 45° 

 and 70°, viz. 0*458 of a yibration for one degree, a result which not only 

 well agrees with those found by General Sabine, but also appeared to our 

 * Phil. Trans. 1830, p. 252. 



