MR. HUDSON’S HOURLY OBSERVATIONS ON THE BAROMETER. 
579 
hour of the mean day, a total mean of the whole of the observations made 
during the given period, has then been obtained, and each mean hourly quan- 
tity being referred to it, the hourly variations from this general mean have 
been determined. These hourly results are detailed in eleven Tables. 
In the first five sets of fifteen days’ observations the instruments were regis- 
tered as nearly at the exact hour as was found to be practicable, and as few of 
the observations were omitted to be taken as circumstances would allow. The 
mean times of observation are therefore given in these five sets ; and where an 
hour has passed unobserved, the place of a real observation has been supplied 
by a mean quantity derived from the two nearest observations. I have reason 
to believe, from a variety of trials which I have made, that when the interval 
of time elapsed is short, and the omission of an observation occurs only occa- 
sionally, and without periodical recurrence, that this mode of supplying the 
vacancy, not by an arbitrary quantity but a derived mean, is by far the simplest 
and best, and less injurious to the result than that of allowing the vacancy to 
remain unoccupied *. In the Tables the amount of such interpolations is stated ; 
and from the number of the observations, and the small extent of possible error 
which could be made, it is probable that the mean result is little, if at all, 
different from that which an entirely unbroken series of observations during 
these five periods would have given. In the remaining three sets, the obser- 
vations were made in every instance at the complete hour, and without the 
omission of a single observation. — The corrections have been applied to the 
mean results of the observations. Those of the Standard Barometer have been 
corrected for the relative superficial capacities of the cistern and the tube, for 
the constant amount of capillary depression ( — '004), and for temperature. The 
Mountain Barometer, in addition to these, (the capillary depression being as- 
sumed as = -—*044) has been corrected for its brass continuous scale. The 
Reduction Tables for the English Barometer, drawn up and published under 
the direction of Professor Schumacher, first in his Sammlung von Hiilfstafeln, 
and afterwards, with the brass scale referred, at Mr. Baily’s suggestion, to 
* In the former case, the error is limited by the small extent of the hourly oscillation ; in the latter, 
it extends to the mean daily variation at the particular hour for the given period. This daily mean, 
so widely remote in general from the single hourly observation, is, in effect, by this last process, made 
the substitute of it, — the mean of any set of quantities being equal to the mean of such quantities in- 
creased in number by the addition of the former mean. 
