3830.^ 
On the Longitude of Benares. 
131 
selves to determine any intermediate expansions, our views having been re- 
stricted to the enquiry, how far the different tliermometric scales differ 
amongst themselves. But to give a clearer idea of the results, we have added 
a column, exhibiting the temperature which each substance would indicate, on 
the supposition that the expansion is uniform. These temperatures are such as 
would be indicated by thermometers constructed of each of these substances. 
TABLE 4. 
Tempera- 
ture, as 
shewn by 
an air ther- 
mometer- 
Mean ex- 
pansion of 
iron. 
Tempera- 
ture, as 
shewn by a 
thermome- 
ter of iron. 
Mean ex- 
pansion 
of brass. 
Tempera- 
ture, as 
shewn by a 
thermome- 
ter of brass. 
Mean ex- 
pansion 
of plati- 
na. 
Tempera- 
ture, as 
shewn by a 
thermome- 
ter of platina 
100° 
300 
i 
23 2 o<J 
2 7 0 o 
100° 
372,6 
r343(j 
1 77 oo 
100° 
328,8 
377oo 
3(i3uo 
100 
311,6 
These results, compared with those Ave had previously obtained for glass, 
prove, contrary to the general opinion, that the expansion of solids, referred to an 
air thermometer, increases with the temperature, and in a ratio different for each 
substance. 
We think we have attained, in this enquiry, all the accuracy that can be looked 
for in such delicate operations, and our readers may assure themselves of this, 
by comparing the numbers we have given for the first 100°, with those obtained 
by 1\T. M. Lavoisier and Laplace. We will add but one remark, which is, that in 
attempting to determine the direct expansion of solids, any little uncertainty in 
the result is tripled in reducing the linear expansion to that of the volume. But 
our experiments give us, at once, the expansion in volume : whatever the error be, 
therefore, of our experiments, it is not multiplied in the results. 
IV. — On the Longitude of Benares, as determined by a series of Lunar 
Transits. 
Of all the methods of finding the Longitude, derived from the Moon’s position in 
her orbit, at a given instant, it must be allowed that the observation of her tran- 
sit over the meridian, promises, on .shore, the best chances of accuracy; both 
in regard to the steadiness and delicacy of the instruments which may be em- 
ployed, the almost simultaneous correction of the time, the simplicity of the cal- 
culation, and the frequent repetitions which (in this climate at least) may be com- 
manded. For comparative observations, under meridians not far asunder, it affords 
the further advantage of rendering us independent of the errors of theLunarTables. 
Still, however, there mast be always a limit of accuracy in the slow motion of the 
moon itself: as she performs only a twenty-fifth part of a revolution in a day, any 
error in the noting of the time of her passage will be magnified twenty-five fold in 
the resulting longitude ; and if, therefore, a quarter of a second in time be assumed 
as a probable error of observation, the limit of accuracy, in the longitude deduced, 
will be six seconds in time, or a mile and a half in space. 
But this is no great amount ; nay, — twice as much would be still considerably 
within the limits of error of other methods of determination, such as the eclipses 
of Jupiter’s Satellites; where differences of 20 and 30 seconds in time, or seven 
and eight miles, are by no means avoidable. 
In the year 1827, I had, for a short time, an opportunity of judging of the 
practical facilities of this method ; for, with a transit telescope of small power, by 
no means a superior instrument, I found no difficulty in obtaining results agreeing 
among theraseh'es within one mile, and seldom more than three miles at variance 
under unfavorable circumstances. 
I was fortunate also in enjoying the co-operation of the Observatory at the Sur- 
veyor General’s office, which enabled me to check any errors arising from the Lunar 
Tables. I deferred, however, at the time, the publication of the results, hoping that 
an opportunity of continuing them would have occurred. 
That I should, at this late period, seek to rescue the observations from oblivion, 
is due to the kindness and patience of a military friend, well known as an indefa- 
tigable calculator and astronomer, who has taken the trouble to recalculate, with 
