216 Mr. J. J. Watcrston on a Difference m the march 



the inclination of the straight lines that connect the standard 

 point 100° with the points corresponding to the respective den- 

 sities at the temperatures 50°, 60°, 70°, 75°, 80°, and 90°. In 

 column 4 are given the cotangents for the same densities com- 

 puted with the temperatures corrected by the formula. [Appen- 

 dix, TIL] The mode of computing the values of (//) the cotan- 

 gents is explained in Appendix, III. The equation is 



k= hzil 



in which t is the temperature reckoned from the zero of gaseous 

 tension (found by adding 273"' 89 to the temperature by ther- 

 mometer), e the tension in millimetres. The tabular numbers 

 are the numbers resulting from computing the above formula 

 divided by 100. The letters refer to fig. 2, and the columns 

 (6, 7) of differences show the differences between the cotangent 

 at A, and the others respectivelj^ 



The mode of drawing fig. 2 will now be apparent. MA, NB, 

 OC, &c. are parallel; the distance between AM and NB = 

 (60-481—50-512); the distance between AM and CO = 

 (70-413 — 50-512) &c. upon one scale, and by another scale the 

 cotangent differences are laid off on AM : those with positive 

 signs on one side of A towards M ; those with negative signs 

 on the other side of A towards L. Lines are then drawn to S, 

 and the points of the projection are found at the intersection of 

 these lines with their respective parallels. Thus, 



AM = -01733 by scale 1 inch to •01 = 1-733 inch. 

 An =-01904 „ „ =1-904 „ 



&c. 



