THE CONSTANTS OE THE CUP ANEMOMETER. 
809 
motion, and possibly some information as to the value of constants. In the parabola 
of equation (IV.) its ordinate at the origin of £=a ; its tangent there = — 2/3 ; where 
V 
the curve meets the axis of £ the £=\ is the limiting value of and the tangent 
there = — 2(£d-A.y). 
Plate 68 shows the plotting of No. III., in which £ is on a scale twenty times that 
of rj to prevent crowding ; the dots are marked with numbers expressing the series 
to which they belong. The irregularity of their distribution is notable : least so at 
the higher values of £, where for a considerable distance from the limit their general 
direction is nearly a right line, which would be represented by v)—a — 2 £'£ A slight 
curvature downwards may, however, be traced, indicating a y of small magnitude. 
Near the origin of f the dots ramble so much that no curve can be drawn through 
them with any certainty ; but their predominant tendency is in favour of a downward 
curvature. Four of them are so far above the right line as to explain fully the 
enormous negative value of y derived from the first set of equations. It is evident 
that this right line r) = a — 2 £'^ or its primitive a'V' 2 — 2/3' VT=F must very nearly 
satisfy the observations ; and, at least for the higher speeds, would suffice to give V' 
in terms of v and F. This supposes that the coefficient of that part of the resistance 
which depends on v 2 is =0, a supposition by no means improbable. 
(37.) Assuming y=0, the second and third of each of these equations — 
1. a' = 9-999 2. a'= 11-308 3. a'=lP550 All. a'= 9’989 
£' = 11-645 £'=12768 £'=13-037 £'=10-928 
These are much more consistent than the results when y is also sought. It is obvious 
that nine or ten of the aberrant dots can in no wise contribute to a correct deter- 
mination of a and £, and therefore that observations when £ is low and rj large had 
better be omitted in the minimum squares. And lastly, it may be inferred from this 
plotting that even if we had accurate values of a, £, and y, we cannot expect to get 
very correct values of V'. 
(38.) These considerations induce me to assume my measure of a, or rather 0"9 of 
it to be the true one, and to substitute it in the second equation. 
This reduction of it is arbitrary, but I have given reasons for thinking my measures 
a little too large, and the general tendency of No. III. and No. I. is to give it even 
smaller. If on comparing V' with that given by the constants thus obtained, it 
is found systematically erroneous, they may be corrected by (V.), combined with 
dV —m?da + 2 md/3 + dy 
v 2 (am— £) 
I also reject the observations where v<5 as unlikely to give reliable results. I find 
from v= 5 to v=9 ; a=10'896; £=11-360; y=5T76.* 
* The first and. third are deduced from values of d and ft’ by the formula V. ; I consider them better 
than the direct value. 
5 l 2 
