THE CONSTANTS OF THE CUP ANEMOMETER. 
819 
In the present case, since by hypothesis the anemometer is in a permanent state, 
the moment of the friction is equal to the total impelling force of the air, i.e., the 
total pressure arising from the motion of the air, without distinction of impelling or 
retarding, but reckoning the latter as a negative impelling force. Now, in cases of 
rapid motion like that of the air passing the cups of the anemometer, it is well 
ascertained that the resistance varies as the square of the velocity, all other circum- 
stances being the same. Hence, with a given anemometer, when only the scale of the 
velocities changes, i.e., when V varies as v, the moment of the total impelling force 
may be expected to vary as the square of the velocity. When the density changes 
it may be expected also to vary as the density. Hence we may expect that when 
v varies as V', then F varies as pV' 3 , or in other words that 
F =W'^(f). (!) 
where denotes some function the form of which is not at present under con- 
sideration. 
Let — =£, —=77, and for each observation let the point whose coordinates are £ 77 
V p V 
be laid down on paper. If Fp~ l were merely some arbitrary function of V' and v, the 
points so laid down would be spread out over the paper, but if equation (1) be true 
they will lie in a definite curve. 
The actual experiments were executed in series, in each of which only one inde- 
pendent variable was changed, so that if the experiments were infinitely numerous 
and infinitely exact the locus of the point whose coordinates are 77 would be a 
definite continuous curve. And the test of the truth of (l) is that the curves 
belonging to the different series shall coincide, instead of being arranged in some order 
of sequence. 
Plate 68 shows the result of plotting the observations taken with anemometer 
No. III. On inspecting the figure it will be seen that the different series fit very 
well into one another. Departures there are no doubt in the individual observations 
from a mean curve, but these appear to be casual, not methodical and depending upon 
the order of the series. 
The result of the observations then is confirmatory of the fundamental supposition 
made hitherto, that when the friction is so arranged that the velocity of the air 
passing the anemometer bears a given ratio to the velocity of the cups, the moment 
of the total impelling force varies as the square of either velocity. 
Assuming then the truth of equation (l)/“ we have next to inquire what is the 
form of the function <j> ? 
* It formed no part of tlie object of the experiments to determine the relation of the impelling force 
to p, which merely comes in as a small correction for reducing observations made on different days to 
a common standard. It is the dependence of F on V' and v that is contemplated in the text, 
