DR. T. E. ROBINSON ON THE REDUCTION OE ANEMOGRAMS. 
417 
and calling V the change of 6 in the following hour, 
o e 
correction of V=y cos(\f/ — 0— •JVjx sin^V; 
supposing 0 = 0 ‘05 (and such an error is not probable) the maximum error would be 
0 m *27. This, therefore, cannot do much harm. 
3. A much more serious error may be caused by the rate of the clock which moves 
the pencils of the instrument. Suppose it a gaining one, the hour-circles on the paper 
are less than hours, and the recorded Vs belong, not to the times to which they are 
ascribed, but to periods a little in advance. The error is negligible, except for the 
hour of winding-up. There the space-curve goes beyond the last hour-circle to a 
distance equal to the rate in 24 h , and the measured V is proportionally too large. 
H + # 
If the velocity were uniform, this would be corrected by multiplying V' by where 
H is the hour-space, x its hourly increase ; but as this seldom is the case, the change 
must be allowed for by interpolation. In all cases but the last we thus obtain 
X 1 
As I never have found g greater than the second term may be neglected, and the 
coefficient scarcely differs from unity. In the last we have 
V H+a? 
n 2H + rc# 
{ 
V'x 
2H + * 
H + TlX 
+ V'X 
(n — ])#) 
"H j’ 
1 
which may be considerably less than V. The projection of the space-curve beyond the 
last hour-circle gives 24x. This excess occurred most frequently in gales from S.W., 
and was, I think, often caused by the vibration of the lofty structure which supports 
the instrument. I have not applied these corrections except in a few cases when the 
error was glaring. The winding-hour was at 9 a.m. in 1857 and 1858, at 10 a.m. in 
the other years ; and at these hours this influence might be expected ; but on comparing 
their values in Table III. with the formulae of Tables V. and VI., they seem as well 
represented as any of the others*. 
The discordances of these quantities would have been less striking had they been 
grouped as three-hourly means ; and this was my original intention, which I abandoned 
on account of a difficulty in respect of interpolation to w'hich I will refer presently. 
It is, however, necessary to remark that the numbers of Table III. are merely pro- 
bable values. A sensible proportion of the individual values is invariably negative for 
each hour ; and my first idea was to keep the positive and negative means separate. I 
tried it for January and June as extreme cases, and came to the conclusion that this 
separation would be useless. The negative values occur so constantly, that they can 
* I have given these details as they will he useful in case it he ever thought desirable to reduce the entire 
series of their anemograms, which extends from 1847 to 1870. 
MDCCCLXXV. 3 x 
