MEMOIR OF DELAMBRE. 129 
globe. To Delambre and Mechain was confided the task of measuring an are 
of the meridian from Dunkirk as far as Barcelona—a vast undertaking, whose 
character, progress, and difficulties it is impossible here to detail. Suffice it to 
say, that its success was principally due to Delambre; he has written its his- 
tory, and it is to his works we must resort if we would acquire a just and 
accurate knowledge of the care which it exacted and the results which it 
produced. 
To trace this meridional line of more than two hundred leagues in length, 
and actually to measure it in its whole extent, is what could never have been 
proposed : it is the office of geometry to supply the place of immediate measure- 
ment. But what a multitude of obstacles does the execution present! The 
temperature of the air and of solid bodies is continually changing; the atmos- 
phere, whose state is so variable, deflects light from a direct course ; the unequal 
height of the points to be observed, the difficulty of selecting, placing, and 
maintaining signals, all conspire against the exactness of results, which may 
be varied also by the attraction of mountains and influenced by inequalities in 
the figure or mass of the globe. Physics, astronomy, and mathematical analysis 
must combine their lights to dissipate these causes of uncertainty and error, 
and to enable the operator to distinguish among the various species of proof 
that which is applicable to his immediate object. 
We must restrict ourselves here to citing one remarkable instance of verifi- 
cation which occurred in comparing the two bases of Perpignan and Melun, 
each in extent about three leagues. Delambre had taken the length of both by 
actual measurement. Now, one only of these measurements was necessary, for 
the two bases being comprised in a common chain of consecutive triangles, the 
one could be deduced from the other by calculation. Having submitted the 
operations to this singular proof, the more decisive from the fact that the twe 
bases are about two hundred and ‘twenty leagues distant from one another, it 
was found that there was not the difference of the third of a metre between the 
result of the calculation and that of the measurement. Thus was determined, 
by a trigonometrical operation, a line of about three leagues in length from a 
distance of more than two hundred leagues, and the error was less than a foot, 
that is to say, the thirty-sixth thousandth part of the line calculated. I will 
not say that Delambre was surprised at this coincidence; but he was at least 
highly gratified, for it was the result alike of his own assiduity and of the 
astonishing accuracy of the instruments. Those used for the measurement of 
angles, as well as for taking astronomical observations, were the repeating circles 
of Borda, whose advantage especially consists in the distribution of any one 
error over a multitude of observations. ‘The process adopted for measuring the 
bases, which is likewise due to the same great physicist, consists in the right 
application of a measure formed of platina, which serves at the same time as a 
measure and a thermometer. 
Thus far we have spoken only of difficulties incident to geodesic operations 
in general, but‘the conductors of the grand work we are considering were often 
impeded by obstacles of a different nature. Their progress was beset not only 
with keen anxieties, but injurious suspicions and personal annoyance. Mechain, 
who has left us a great number of highly valuable observations, was subjected 
to quite a long imprisonment, and suffered much from the effects of unremitting 
fatigue. ‘The principal operation, however, was finished, and, as he had always 
designed, Mechain wished to carry the measurement as far as the Balearic 
islands, but died in a foreign land before the results of his painful labors were 
laid before the public. Delambre, to whose share shad fallen a much more ex- 
tensive portion of the work, collected all the elements of it, and published them 
in a leading work which must be regarded as one of the noblest monuments 
of science. He had quitted Paris in the last days of the month of June, 
1792. It is easy to judge how little favorable the political condition of France 
98 
