222 Mr. J. J. Waterstou on a Difference in the march 



to air, it is easy to compute Qtt, and thence the asymptote ttSH, 

 and the equation of the curve ED P. 



The degree of curvature assigned to it by this law of tempe- 

 rature, and the consequent aberration of the air- thermometer, 

 are probably in excess of the truth. The inquiry may thus serve 

 to mark the extreme limit of the disturbing influence of the de- 

 viation from the primary laws of elastic fluids on the air-thermo- 

 meter. By an extension of the experiments with plugs, there is 

 little doubt that sufficient data could be obtained for computing 

 it exactly between 0^ and 100°. 



§ 16. In the paper above referred to, I have shown that the 

 deviation from Mariotte's law follows a ratio compounded of the 

 thermal effect directly, and the G temperature inversely ; hence 

 the thermal effect being assumed to vary inversely as the square 

 of the G temperature, the deviation must follow the inverse cube 

 of the G temperature thus, 



8D 7rP_ J 1_ 



CDTQ-CD^-PQ^' 



or 



1 J__J L___i L_ 1 



i.U : ttP- ^p : PQ2 - ^,^3 : ^^2 - ^^^ ■ qjj2 neaiiy. 



We thus obtain the position of tt. Next, by joining tt and 8 

 and producing to meet the axis of temperature in H, we deter- 

 mine the non-deviation zero of gaseous tension, which thus com- 

 puted is l°-80 below A, the deviation zero derived from the ex- 

 pansion of air between 0° and 100°. 



We thus fix the ratio HC to AC, and the equation of the curve 

 is found by assuming E^S to follow the ratio of the temperature 



given above, viz. ( ^j^ ) . The equation for the locus of E, the 

 curve EDP, thus determined is 



s^T^ HC2 1 HC2 



(E^)=.=8D.^ = ^^.-^, 



in which y is the temperature reckoned from the non-deviation 

 zero H, and x the portion of the ordinate to y intercepted be- 

 tween the asymptote Htt and the curve. 



§ 17. We have now obtained the means of computing the 

 versed sine of arch DP, and thence the correction required upon 

 the air-thermometer at 50°. 



The value of M^ thus computed is . -002594 

 The mean between DS and Ptt is . . -002821 



The difference is -000227 



which is the versed sine at 50°. Comparing this with -36706, 



