206 GEOLOGY OF THE SECOND DISTRICT. 



base, connected with Iiis acknowledged skill in his profession, furnishes abundant evidence 

 that strict topographical accuracy was not his object. 



Between what limits, then, may the trigonometrical result be depended upon? Mr. John- 

 son has deprived his measurement of a requisite essential to confidence as an exact operation, 

 in leaving us totally ignorant of the position in space of his point of observation, of the dis- 

 tance that he actually used, and of the number and values of the angles that he observed. 

 His estimate of distance, on the authority of the old survey 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 anticipate, in a country where the lands were almost absolutely valueless, and 

 where numerous obstacles, such as local attractions, ponds and mountains, opposed the exe- 

 cution of a survey with even an approximation to accuracy. 



Suppose now, that the angles were observed from a point near the University, at an eleva- 

 tion of SCO feet above tide ; that the distance of the peak from this station falls between 

 thirty-five and forty-five miles ; and that its elevation above tide, according to the trigonome- 

 trical measurement, is 4907 feet. These hypotheses are sufficiently exact to answer our 

 purpose, and from all that appears in Mr. Johnson's description of his method, 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 remainder of the elevation, the third part. 

 These three portions, in the order above named, assuming the distance to be thirty-five miles, 

 are 360, 817 and 3730 feet. All things else being equal, correct now a supposable error in 

 distance of five miles, calling it forty instead of thirty-five. The first part of the elevation 

 remains constant; the second part, varying as the square of the distance, is 1067 feet; and 

 the third part, varying in the simple ratio of the distance, is 4263 feet. The total elevation 

 based on this last hypothesis of distance, is 5690 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 five miles, induces an error of elevation of 783 feet. 



To show what error in Mr. Johnson's estiiuates would produce identity 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 + (Z 



-:r- + ;,~^-- + 360 — 4907 = 442. 



o do 



This gives the requisite distance d, equal to 37-8 miles. Supposing, therefore, an error in 

 distance of only 2 miles and 8 tenths, a supposition not only jjossible but probable, our results 

 would become identical. 



As I have not learned the distance that Mr. Johnson actually used, it is proper to remark, 

 that if we should assume the distances 40 and 45, instead of 35 and 40, our conclusions 

 would not differ so much from those above, as to vitiate the argument. Using these latter 



