No. 50.] 
339 
records of that alpine region, is liable to an error of at least five miles. 
These surveys are notoriously imperfect — a fact that we might antici- 
pate, in a country where the lands w^ere almost absolutely valueless, 
and where numerous obstacles, such as local attractions, ponds and 
mountains, opposed the execution of a survey with even an approxima- 
tion to accuracy. 
Suppose now, that the angles were observed from a point near the 
University, at an elevation of 360 feet above tide — that the distance of 
the peak from this station falls between 35 and 45 miles — and that its 
elevation above tide, according to the trigonometrical measurement, is 
4,907 feet. These hypotheses are sufficiently exact to answer our pur- 
pose, and from all that appears in Mr. Johnson's description of his me- 
thod, the ones most favorable to his result. Imagine the elevation to 
consist of three parts ; the first part that which is intercepted between 
the levels of tide and the station at Burlington ; the second part, that 
which is intercepted between the level at Burlington, and a plane that 
touches the earth's surface at the point of observation ; and the remain- 
der of the elevation, the third part. These three portions, in the order 
above named, assuming the distance to be 35 miles, are 360, 817 and 
3,730 feet. All things else being equal, correct now a supposable er- 
ror in distance of 5 miles, calling it 40 instead of 35. The first part 
of the elevation remains constant ; the second part, varying as the square 
of the distance, is 1,067 feet, and the third part, varying in the simple ra- 
tio of the distance, is 4,263 feet. The total elevation based on this last 
hypothesis of distance, is 5,690 feet, which exceeds my measurement 
by 341 feet, and the one by Mr. Redfield and Prof. Emmons by 223. 
An error in distance, therefore, of 5 miles, induces an error of eleva- 
tion of 783 feet. 
To show wrhat error in Mr. Johnson's estimates would produce iden- 
tity in our results, we will suppose that the distance which formed the 
base of his calculations was 35 miles, and that the distance necessary 
to make our results agree, is d. The familiar principles above alluded 
to furnish the equation, 
2d^ 3730 + 6? 
-y- + — + 860 — 4907 — 442. 
This gives the requisite distance equal to 37.8 miles. Supposing, 
therefore, an error in distance of only 2 miles and 8 tenths, a supposition 
not only possible but probable, our results would become identical. 
