of Air- and Mei'cury -Thermometers, 315 



observations is inclined at an angle of 45° to the axis of tem- 

 perature, the distance of the points above the straight line 

 measured in the vertical is equal to 0'51 at 50°, to 0*48 at 60°, 

 to 0-42 at 70°, &c. It is hardly possible to recognize this de- 

 flection on the chart, however lai-ge the scale employed, but it 

 may be made quite apparent to the eye by projecting the points 

 orthogi'aphically with the distances extremely foreshortened in 

 the direction of the gradient. 



The points computed from M. Regnault's observations with 

 temperatures uncorrected being laid down as before described on 

 a plane surface ; suppose we look along the line of these points 

 with the eye close to the plane on which they are marked, we 

 shall see inequalities of position under a highly exaggerated 

 aspect, in consequence of the extreme foreshortening of the lon- 

 gitudinal intervals between them. Suppose the same observa- 

 tions with M. Regnault's temperatures corrected by the formula 

 are ako projected in this way ; we obtain the means of eifectively 

 comparing their positions, and thus of testing the value of the 

 assumptions made with respect to the correction of the thermo- 

 meter and the gradient of density. 



§ 5. Let S (Plate I. fig. 1) be the standard point on the chart 

 corresponding to the density of steam at 100°, and m the point 

 corresponding to density at 50°. Join Sm (in the figure, to save 

 confusion, the lines joining the several points and S are not 

 drawn), and draw mG parallel to the axis, and SG perpendicular to 

 it. In mG, take ma equal to the assumed correction of the mercury 



thermometer at 50°, viz. 0°-512. We have -757^ = cotangent in- 



aG ... 



clination of mS to axis; ^7^ = cotangent inchnation of aS to axis ; 



our 



and ma = diflference of cotangents x SG. In the same way we 

 have nb = difference of cotangents of inclination of nS andbS to 

 axis X SK = the assumed correction of the mercm-y thermometer 

 at 60^, and so on for the other points. 



Let the orthographical projection be made in the direction Sa 

 inclined to the plane of the paper about 1°. The effect will be to 

 reduce distances in the direction aS to one-sixtieth, and main- 

 tain them in the same relative proportion : thus SB to SA (fig. 2) 

 is equal to bK to aG (fig. 1) = (100°-G0''-481)to(100°-50°-512). 

 The differences ma, nb &c. (fig. 1) are reduced in the ratio of 

 V^, the scales of the chart being supposed to be adjusted so 

 as to make SaG = 45°. Also ma (fig. 1) becomes MA (fig. 2), 

 nearly perpendicular to AS ; the abscissa of M from S upon SA 

 being 50, while SA = 48'488, and the ordinates are the difference 

 of cotangents. 



The following Tabic contains in column 3 the cotangents of 



