It is remarked that the differences in the first table show a distinct 

 curvature with reference to the chord ; while in the second table the 

 accordance with the straight line is as perfect as could be expected. 

 With the view of bringing these facts out into higher relief and 

 presenting the deflection to the eye on a scale that should at once 

 be relatively correct and very highly magnified, the author computed 

 six values of h from the observations at 90° and 100°, at 80° and 

 100°, &c., without correcting the temperatures, by the formula 



h-t. 



h= ~^: A 



h I t, 



These are given in the following table ; they are quantities propor- 

 tional to the cotangents of the inclination of the chords to the axis 

 of temperature. 



Table III. 



The differences in this table are progressively increasing, and their 

 relation to each other is very nearly that of the corresponding dif- 

 ferences of the inclination of the chords. They are represented by 

 these inclinations in a figure, and, in order to render the divergence 

 from a straight line more manifest, the scale taken is 10° angular 

 measure to the unit of difference, the length of the chords corre- 

 sponding with the intervals of temperature below 100°. Joining 

 the extremities of the chords, a magnified view is obtained of the 

 curve determined from observations with temperatures uncorrected. 

 On this the author remarks, that if the temperatures required no 

 correction, the points so determined would lie in a straight line, 

 always taking for granted the integrity of the law of density and the 

 perfect accuracy of the observations. 



The next step was to perform the same computation with tem- 

 peratures corrected. The resulting values of h are given in the 

 following table : — 



Table IV. 



Phil Mag, S. 4. Vol. 5. No. 29. Jan. 1853. 



r 



