820 
DR. T. R. ROBINSON ON THE DETERMINATION OF 
A complete hydrodynamics! solution of the problem is altogether beyond our power. 
On the other hand, the irregularities of the observations prevent us from going, by 
observation alone, more than a certain way towards the determination. We must, 
therefore, endeavour to combine as best may be the indications of mechanical theory 
with the results of experiments. 
In his paper “ On the Cup Anemometer,” in the Transactions of the Royal Irish 
Academy, Dr. Rdbinson has shown that (supposing the density constant, say =1) 
the relation between the moment of the impelling force and the moment of the 
friction is either accurately or approximately of the form 
F=aV /s — 2/3V'v— yv z , (2) 
which would give for the locus of the point whose coordinates are £ r\ the parobola 
V =a-2ft- 7 P. ( 8 ) 
If now we turn to the plotting of the observations, we see that the best smooth 
curve to represent the observations, free from sinuosities which the observations do 
not warrant us in supposing real, is either accurately or approximately a straight line, 
rj — a 2(3 '£ ; . 
(4) 
in fact, so nearly does a straight line represent the observations that it is not easy to 
say to which side the concavity of the line, if curved it be, should he. On the whole 
there appears to be a slight indication of a gentle concavity towards the origin. 
It may be remarked in passing that the formula (4) which the experiments show to 
be at least very approximately true, leads to a very simple expression for v in terms 
of V', namely — 
v=aV'-L 
where a and b are constants. 
The figure shows that there cannot be much doubt as to the distance from the 
origin at which the curve intersects the axis of £ nor as to the direction of the curve 
at that point ; and generally that the curve is well determined in its right hand half, 
though it becomes more uncertain towards the left. If X be the value of ^ at the point 
of intersection, and — t the tangent of the inclination a, t that point, the equation of the 
curve, assumed to be a parabola, will be 
r) = t(k — £) — C(\ — gy~ 
( 5 ) 
or again, if we suppose known two points (p, h) and (q, Jc) lying in the well-determined 
part of the curve, its equation will be 
( 6 ) 
and as (X — £)- or (p — p) (£—q) will be small throughout the well-determined part of 
