288 Dr. T. R. Robinson on the Determination of [Apr. 4, 



of Y except tlie square ; secondly, that with cups of a given size a is 

 not changed by varying the arms from 24 to 12 ; and, thirdly, that 

 it is as the area of the cups. 



Five instruments were used, No. I, cups 9 inches, arms 24, like the 

 Kewones; No. II, cups 4 inches, arms 24; No. Ill, cups 9 inches, arms 

 12 ; No. IV, cups 4 inches, arms 12 ; No. V, cups semi-cylinders, 9 inches 

 by 9. The results with these are given in tables which show along 

 with Y, v, and W the vortex current, the frictions 1, 2, and 4, the air's 



density, and^ = ??i. This last is seen to differ in each anemometer, and 



to be variable in each, ranging from 21'58 to 2'32. It increases 

 with E and decreases as v increases in such a manner as shows that it 

 will remain finite even when v is quasi-infinite. 



Putting (I) in the fom^a^-^, or (II) ?7 = a -2^- 7 f J 



and treating those for each instrument by minimum squares, he got 

 values for a, /3, and 7, which, however, were unsatisfactory. 



Dividing the 40 belonging to No. Ill into three groups, in the first of 

 which are all whose v<^5, in the second those from 5 to 9, in the third 

 those ^>9, each gave discordant values for the constants. Those of a 

 least so, those of 7 most ; the latter, indeed, rambled so much that no 

 reliance could be placed on them. The matter was not mended by 

 combining the entire. Thinking this discordancy might arise from 

 equ. (I) containing a term cv, he tried this, but with a result so much 

 w r orse that such a term, if it exist, can have no sensible influence. The 

 results for the other instruments were similar. In fact, the method of 

 minimum squares applies very imperfectly to a case like this, where 

 the coefficients of the unknown quantities and the absolute terms are 

 themselves affected with errors. Besides this, in the final equations of 

 this process the coefficients of 7 and /3 are so much less than those of 

 a that they, especially 7, must be less accurately determined. It is also 

 to be noted that these constants may be changed within certain limits, 

 and still satisfy the equations approximately. 



It was, however, suggested to him by Professor Stokes that, as 

 equ. (II) has only two variables, 17 and £ it could be plotted on a 

 plane surface, and this gave valuable information. The plottings for 

 the five instruments are given, and show distinctly both the general 

 agreement of (I) with the observations and the cause of the dis- 

 cordances. 



Though in all the dots are much scattered, yet through a large por- 

 tion of each the general direction is a right line with (in some cases) 

 a barely perceptible downward curvature. 



Since the curvature is nearly as 7 this last must be very small, and 

 assuming it=0, the equation aV 2 — 2fiVv— F=0 will be sufficiently 

 accurate. Towards the vertex of the curves (where v is small) the 



