502 
NATURE 
[Oct. 20, 1870 
hy —hy 
derived from about 100 selected equations of the form = 
1 
is—2, when the barometer is reckoned in hundredths ef an inch 
and the velocity in miles per hour. In selecting the equations, I 
omitted all cases of abrupt change in any of the variables. 
Consequently our equation becomes 
hy — hy = 2 { Dy (12) — 2% (12) } 
+ the functions of temperature and damp. 
It may now be very reasonably asked how it is possible for the 
barometer to be affected by past and coming conditions of wind. 
Its sympathy with such considerable periods as six hours before 
and six hours after the moment of observation, cannot be 
accounted for on the hypothesis of each new phase of weather 
regularly making its first appearance high in the atmosphere, 
because, if it did so, each phase would necessarily disappear from 
above before it disappeared from the earth’s surface, and, conse- 
quently, the barometric change would invariably precede the 
change of average wind velocity, which, we have already seen, 
it does not. What, then, is the explanation of the curious phe- 
nomenon, of the barogram corresponding with the average velo- 
city of the wind, according to the system of twelve-hour 
periods ? 
The answer to this question will best be conveyed by a con- 
sideration of what we should expect-the movements of the mer- 
curial column to be if a suitab'y made barometer were plunged 
into troubled water. Its movements would not correspond 
to each ripple that passed vertically above its cistern, because 
it would be affected by all the disturbances in an area of surface 
water whose radius is a function of the depth of immer- 
sion. If it were plunged to the depth of many fathoms 
the mercury would wholly cease to oscillate, because the 
average level of the large area with which it sympathised 
would be constant, however much its surface might be 
broken up into undulations. If it were immersed to a suitable 
depth, the mercury would foretell the advent of each wave of 
exceptional size, before an exceptional height of water had arrived 
vertically above the barometer. It is easy and interesting to 
make an experiment to the same effect, by dipping a glass tube, 
open at both ends, straight into a pan of water, and disturbing 
the water with the hand. When the tube is dipped but a short 
way in, the water it encloses harmonises in its oscillations with the 
water that surrounds it, but this harmony is diminished, and the 
oscillations in the tube become more sluggish, as the tube is im- 
mersed more deeply, and at length they disappear altogether. 
In precisely the same way I believe the mercury in the barometer 
sympathises with atmospheric disturbances throughout a wide 
circle. Its height represents the average value of them at the 
moment of observation, and when a great atmospheric disturbance 
sets in, as is wont, from the westward, the barometer is affected 
some time before the arrival of the locus of greatest disturbance. 
The diameter of the circle which affects the barometer may 
admit of being determined in more than one wav, but I am not 
now concerned with its linear measurement. What I am im- 
mediately in serch of is, what the diagrams have already told 
me, that its diameter in relation to its usual rate of movement 
is such, that it is commonly twelve hours in passing over an 
observatory. 
It appears to follow that the twelve-hour period for averages 
must apply not only to the wind but to all other elements of 
atmospheric disturbance, such as temperature and damp. There- 
fore the undetermined portion of our equation will be functions 
of ¢ (12) and of @ (12). 
Without professing to decide the precise nature of those 
functions, we may be sure that it does not differ materially from 
a simple proportion, within the limits of meteorological records. 
The inferior importance of these functions makes a small error 
of still less consequence. I therefore assume the undermentioned 
portion of the equation to be 
2 {t(12) — 4, (12) + 7 fa, (12) - d, (12)} 
Calculating on the basis of the already quoted statement, that 
temperature and damp, unaided, may respectively affect the 
barometer to the amount of half an iuch, and g may both of 
them be considered equal to —1, when ¢ is reckoned in degrees 
Fahr., and dis the vapour tens‘on expressed in hundredths of 
an inch, For reasons already mentioned, I disregard the direc- 
tion of the wind, Consequently the formula becomes 
fy ~ Iig=2 {2g (12) ~ 0, (12)! + {+ (12) ~ £,(12)} + {ely (12) ~ d, (12)} 
and I now proceed to utilise it, in making a series of predictions 
for comparison with facts. 
Let 4,, 4, be separated by an interval of six hours, which I 
will distinguish by the letter 6; similarly let a represent the six 
hours that preceed /,, and c the six hours that succeed /,. 
Now the average wind velocity during the twelve-hour period 
a + 61s half the sum of the average velocity during the six-hour 
periods a and 4, 
or v,(12)=4 v (a) + v (4) } 
also v (12) =+4v(6) +0 (c)} 
—_— eo 
q (12)—v (12) = 4 { v(c) —v (a) } 
similarly for ¢ and d. 
Therefore our equation becomes 
hy ~ hy =v (0) ~ 0 (a) +4 {0 (c) -¢(a)) +4 {d(c) - d(a) | 
and j 
v (c) = hy ~ hy + 9 (a) + ${t(a) - tg 44a) —aia} 
Using this simple formula, I selected all the periods during 
which the changes of the barometer had been abrupt or other- 
wise characteristically marked, and 1 calculated the values of 
v (c) during those periods, obtaining in this way a total of 106 
predictions. Comparing these with the actual facts, I obtained 
a mean error of ten miles per hour. Next, in order to procure 
a standard whereby to ascertain the importance of this error, I ob- 
tained and took the mean of a series of differences between the 
same observed values of v (c) anda (4); in other words, I calculated 
what the mean error would be supposing it was invariably asserted 
that the average wind velocity for the next six hours would be the 
same as during the six hours just elapsed. The mean error in 
this case was only 7°7 miles per hour. This extraordinary result 
made me curious to learn whether the co-eflicients of ¢ and d 
might not be altered with advantage ; so I first made them both 
= 0, in fact, ignoring the influences of temperature and damp 
altogether. The mean error again came out ten miles per hour, 
the gains and losses due to the correction having balanced one 
another. Secondly, I made the co-efficients each = — 2, that is 
to say, I doubled the importance originally given to temperature 
and damp, and the mean error rose to 11°3 miles per hour. 
The result of all this is, that, judging by the experience of 106 
well-marked instances of change occurring at Falmouth during 
the first quarter of 1869, it is more unwise in the ratio of 
100 to 7°7 to be guided by the barometer, than to say off-hand 
that the weather will continue as it has been. Also that there 
can be no gain and may be further loss, if the wet and dry ther- 
mometers be consulted as well. 
It is, no doubt, possible that the errors I have assigned may 
he qualified in a trifling degree by other calculators. They 
may adopt periods of average and numerical co-efficients, 
somewhat differing from my own; also, their data as 
measured off from the instrumental tracings, may be more 
accurate than those that I made, but I feel satisfied there is no 
mistake in the broad truth of my results. After more tentative 
analysis than I care to describe, I believe it impossible to 
substantially improve these predictions, and the experience I 
gained from the Dublin observations makes me doubt whether 
a more extended examination would lead to different con- 
clusions. The barometer, when consulted by itself, with- 
out a knowledge of the weather at adjacent stations, can 
claim but one merit, namely, to guide us ina form of storm 
which does not occur once a year in the British Isles, of a 
fall in the mercury outstripping in an extraordinary degree 
the increasing severity of the weather ; and I believe it to be on 
account of this rare phenomenon here, and of the reports of 
sailors from hurricane latitudes, where it is much more frequent, 
that the fame of the instrument has been so widely spread. 
But for use in ordinary English gales, and still less in ordinary 
English weather, this inquiry shows the barometer to be one- 
third worse than no guide at all. It is better to base our ex- 
pectations upon what has occurred, than also to take the baro- 
meter into our counsel. We easily see the reason of this to be, 
that the theory of prediction involves many postulates, every one 
of which must be strictly fulfilled in order that the result may be 
correct. But they are only true on the average and not in the 
individual case. The area with which the barometer sympathises 
is never exactly twelve hours in passing over us ; the six-hour 
radius of that area, which has already gone by, is not an accurate 
_——_ 
