509. "Transactions.—Muüiseellaneous. 
velocity being merely relative to the previous speed, the motion of the cups 
would be accelerated only by one-third of that additional wind-velocity, and 
that their rate of travelling would be 39 + 39 = $89 = 20. 
28. But from careful observation ‘and experiment I am convinced that 
this formula is not strictly accurate ; that, inasmuch as the cups already 
are travelling at a speed of ten miles per hour, instead of oe at rest, their 
real velocity in a sudden gust of double strength would be %, plus momen- 
tum, minus some indefinite amount to be deducted for the Mad of vis 
inertie—which would be exceedingly small in such a case—and for the 
gradual loss of momentum velocity, which also would be very trifling in so 
brief a space of time. Hence if my theory be correct, the cups in this 
hypothetical case would travel at a velocity of nearly 30 miles an hour for 
those few seconds, or almost half the actual speed of the wind, and I can 
conceive of cases where several successive and rapidly following augmenta- 
tions of wind-velocity might cause the cups to travel at very nearly the 
same velocity as the wind. This of course could only be for a few seconds, 
and under a most exceptional continuation of contributing causes, for 
after those first few seconds the cups soon would settle down to their 
ordinary relative velocity. The occurrence, however, of a modified form 
of the above-mentioned hypothetical case would suffice to account for some 
of the marvellous statements of the force supposed to have been exerted by 
` sudden gusts, that force being deduced on the ratio of 42 — æ, x represent- 
ing the required force, and a the velocity, as ascertained by multiplying the 
speed of the cups by 8. 
29. Take, for instance, the great Sydney storm, already quoted in this 
paper. When the anemometer cups were travelling at the rate of 51 miles 
per hour, the accepted formula bade the observer record the wind's 
velocity as 158 miles an hour; but if my hypothesis be correct, the wind's 
velocity on that occasion may not have been more than 100 miles an hour, 
or perhaps evenless. And supposing that the precise ease suggested had 
occurred, of a suddenly doubled velocity, the theoretieal speed of the wind, 
when the cups were travelling at 51 miles per hour, would be about 102 
miles—probably somewhat less, which would represent a pressure of 52 
pounds on the square foot instead of 117 pounds as calculated—a most 
material difference. 
30. Now let us see what light Mr. Fenwick Stowe's experiments throw on 
the problem. Under my theory the heavier and larger the cups the greater 
the velocity they should indieate at the higher speed, as compared with 
lighter ones, for the simple reason that the greater weight necessarily 
would imply greater momentum. Reference to the table already quoted 
answers this question in a most decided and unmistakeable manner. It 
