No. 50.] 341 
which yet remains unprovided for, I apprehend is comparatively incon- 
siderable. La Place measures these effects by the temperature of the 
air, and observes that this hypothesis very nearly satisfies the observa- 
tions that have hitherto been made. The agreement of my results, 
w^here courses of observations v^^ere taken, intimates v^ith w^hat degree 
of approximation I have corrected for the changes of the v^eather. This 
agreement is particularly worthy of remark in relation to Long lake, 
where the observations were protracted in time, and the weather sin- 
gularly variable. But notwithstanding all this, I am free to admit, that 
these corrections are still less perfect than could be desired. 
The theodolite is above the need of eulogium from any one ; but, 
like every other human invention, it has its proper capabilities and de- 
fects. An indispensable condition to the accuracy of angular measure- 
ments, is the exact determination of a base line, a work which requires 
that skill, variety of dehcate instruments, time, and means, which, in 
this country, are not generally at the command of a single individual. 
Triangulations embracing great extent, have been executed with asto- 
nishing precision, and the results of similar measurements, properly 
conducted, are entitled to the utmost confidence. On the contrary, the 
angular determinations of high mountains have been comparatively 
vague. One cause for this difference, consists in the great distances 
at which mountains are generally observed, and the consequent small- 
ness of the angles of elevation. In this respect, a condition is almost 
necessarily violated, which was scrupulously satisfied in the surveys 
just referred to. 
The chief source of error in mountain measurements, and one which 
distinguishes it from horizontal ones, is refraction. This diflliculty, 
growing out of the condition of the air, and independent, therefore, of 
the instrument, is analagous to the one which the barometrical method 
is exposed to, with this difference in favor of the latter, that the at- 
mospheric changes going on at both stations may be detected and com- 
pared. 
Refraction differs, in different countries and at different times, from 
one fourteenth to one-eighth of the distance, reckoned in minutes. Such 
being the uncertainty as to the true path of light in low and familiar 
regions, it must be particularly difficult to follow it with precision 
through mediums of changing relations, and elevated tracts compara- 
tively unknown. Refraction, too, depends not only upon the affections 
