THE CONSTANTS OF THE CUP ANEMOMETER. 
821 
the curve, the constant C or C' will admit of considerable latitude of variation with- 
out much affecting, the satisfaction of the observations. Conversely, if we attempt to 
determine the constant C or C' from the observations, in addition to the two elements 
X, t, or h, k, the determination will be extremely precarious. And if we arrange the 
formula (5) or (6) according to powers of so as to throw it into the form (3), the 
precariousness of the determination of C or C' will more or less affect all the three 
constants a, (3, y. 
Accordingly, if we take this formula, and attempt to determine the three constants 
a, /3, y, from the observations, it may be that by different processes we shall arrive at 
results differing considerably, not only as regards y, but even, though to a less degree, 
as regards a and /3. It is not until we use the values of a, A 7, so obtained for the 
determination of two out of the three elements of the parabola which are well or 
fairly determined by the observations, that we perceive the accordance which under- 
lies the apparent discrepancy. 
If the simple formula (4) so nearly fits the observations, it is by no means merely as 
an empirical formula of interpolation presenting two arbitrary constants whereby an 
approximate accordance may be brought about, or in the way that a small arc of an 
arbitrary curve may be approximately represented by a straight line. The observa- 
tions were also plotted by taking for coordinates V' : v and F : v 2 instead of v : V' and 
F :V' 3 , and in this case the curvature of the curve was very decided. Accordingly, 
though the observations may be satisfied by the first two terms of the formula (2) 
almost as well as by the three, that is by no means true of the last two, though in 
both cases alike we have two arbitrary constants at our disposal. 
Explanation of the Plates. 
In these plates the results of the experiments made with the five anemometers are 
graphically represented. In the plottings the abscissa is throughout 20r-p V'. In 
Nos. I. and III. the ordinate represents -i- pV' 2 ; in Nos. II., IV., and V. 
it represents the same divided by the ratio of the area of the mouth of the cups to that 
of the mouth of the cups in Nos. I. or III. ; that is, it represents the above expression 
multiplied by 81 -f- 16 for Nos. II. and IV., or by 7 t-f 4 for No. V. 
In the plottings, 0’75 inch is taken as the unit. 
The reference numbers represent the order of the series, 1 meaning no weight on 
the brake, 2 the lowest weight, and so on. 
In the experiments with anemometer No. I., the full dots represent the first set, 
experiments Nos. 1 to 79 ; No. 45 being omitted for a reason already stated. The 
small circles refer to the second set, experiments Nos. 80 to 123. 
