456 Astronomical Society. 
A paper was also read from Mr. Bevan on the practicability 
of determjning the difference of longitude hetween two places 
not far distant from each other, by observing flashes of lightning. 
It seems to us, however, that the mode adopted on the Con- 
tinent, by firing loose gunpowder at certain intervals, is much 
preferable. 
A paper was likewise read from M. Littrow of Vienna, point- 
ing out certain anomalies in the north polar distance of the” 
principal fixed stars. It appears that the instruments recently 
made by Reichenbach, for the observatories of Konigsberg, 
Vienna, Gottingen, &c. give the north polar distances of those 
stars greater, by 4 or 5 seconds, than the larger instruments at 
Greenwich, Dublin, Palermo, &c. This subject is one of great 
interest at the present moment: and we wait, with much im- 
patience, the publication of this memoir. 
The next and last paper was’ by Mr. Babbage, relative to a 
new invention in machinery, by which not only the usual Jo- 
garithms, but also various other mathematical and astronomical 
tables might be formed, and the types thereof set up without 
the possibility of an error throughout the whole process. This 
discovery we consider as one of the finest in modern times; and 
(like the invention of the steam-engine in its application to the 
arts) it bids fair to open a new erain science. The object, which 
Mr. Babbage had first in view, was to form an engine which 
should express any series of numbers whose first, second, third, 
&c. differences were equal to 0: and which he has completely 
effected. ‘To those who are acquainted with the method of dif- 
ferences, it will be evident that such series would embrace not 
only the common logarithms of numbers, the logarithms of sines, 
tangents, &c.; but likewise the natural sines, tangents, &c. 
whence its application to the formation of astronomical tables 
may he readily conceived. But, in the pursuit of this inquiry, 
Mr. Babbage found that many new views of the subject arose ; 
and that the engine was not confined to the expression of series 
whose ultimate differences were constant: but that it would 
form tables, not dépendent on that law; and whose differences 
~ could not be denoted by any analytical expression. | 
Since the meeting of the Society we have been favoured with 
a sight of this engine: which is very simple in its construction, 
and may be put in motion by a child. Mr. Babbage composed 
in our presence a long series of square numbers ; and likewise 
the first forty terms of the series of numbers depending on the 
formula (“*-++ 2 +41); all of which are primes, and which were 
forméd as expeditiously as a person could write them down. 
When we consider the numerous errors to which all tables are 
liable, not ouly in their original computation, but also in composing 
them 
