S6 Mr Forbes's description of a New Anemometer. 



will represent the quantity 2 a, and having thus obtained a 

 scale for the measurement both of velocity and time, we may 

 describe the rectangular hyperbola AGE, having C D, D B, 

 forming portions of its assymptotes. The abscissae D B, D H, 

 &c. will then express the times, (increasing uniformly) and 

 the ordinates B A, G H, &c. the corresponding retarded velo- 

 cities. Having thus obtained a measure of the times and ve- 

 locities, the union of them or the areas A G H B, A E F B, 

 &c. represent the spaces described. 



But since the hyperbolic areas may be expressed by the na- 

 tural or Napierian logarithms, from the equality of the rec- 

 tangles ABCD = IGHD, which is the modulus of the 

 hyperbolic logarithms, or 1, and is here equivalent to 2 a, 

 the difference of the hyperbolic logarithms of any two ordi- 

 nates will express the area intercepted between them, and its 

 measure will be obtained in terms of 2 a. 



But in the case where the velocity is not that of a projec- 

 tile, but of the impulsive medium, the velocities will not be 

 measured by the ordinates, but by the diiference between them 

 and the initial velocity ; and the spaces not by the hyperbolic 

 areas, but by the difference betwixt them and a rectangle de- 

 scribed by a uniform velocity in the same time. That is, put- 

 ting S = space moved over, and t = the time of exposure to 

 resistance — B F, A B being as formerly = V, and B D = ^, 

 we have 



S = V ^ — ■! hyp. log. (e f #) — hyp. log. e >2a 



e ■4' t 

 = \ t — 9>a-\- hyp. log. Or for common logarithms sub- 



2 a 

 stitute -jT- for 2 a, M being the modulus of the common sys- 

 tem. 



Having thus given a solution of the problem of the extent 

 of deflection occasioned by a current of air under any circum- 

 stances, I proceed to describe the instrument which is intended to 

 show its effect. It is represented in Plate II. Fig. 2. From the 

 flat board C D, of which the figure represents a section, rise two 

 iron supports G E and H F, which should be as thin as is consist- 

 ent with strength in the direction as right angles to the view 

 in the figure. Rising from above these in the way there shown, 

 is the horizontal wind sail A, which must have a cap and vane 



