On resuming the location of the line up the North Fork of the Smoky, on Monday last, I made the change in the line mentioned in my last report. Commencing as far back as Station three hundred and forty-five, and producing tangent to Station four hundred and thirty-eight by twenty-seven. We then bore to the left with a two degree curve and continued to Station five hundred and forty-one, leaving the line for the night. The location of the line was continued on Tuesday to Station seven hundred and nine and ninety-five hundredths, making a total distance from Sheridan of eight and nine-tenths miles. The line is an easy one for gradients; no heavy work occurs on it, but the many crossings of the stream obtained, make frequent bridges necessary. These should be of such a character as to allow a water-way of at least thirty feet, but bridges of simple construction could be used, stone of any kind being difficult to obtain. The soil is sandy and easily worked, but will make a substantial road-bed. Having received your verbal orders to run a rapid line from a point west of here on the North Fork, where that valley makes its deflection to the South, eastward to the three hundred and eighty-fifth mile post, I provided myself with ten days' supplies and rations, and on Wednesday, the sixteenth, moved up the North Fork as rapidly as the nature of the ground permitted, camping at night near the four hundred and twenty-fourth mile, on Mr. Reynold's preliminary line. Before camp was fully arranged, a heavy squall struck it, tearing down all the tents, destroying one old one used as a cook tent and injuring some of the new ones. The herd was also stampeded, but was recovered without loss. The next morning I went up the valley about ten miles and ascended the divide to take observations. I found the course of the valley here was south of west and continued four miles westward. Several large branches, with deep, broad valleys, almost as large as the main stream, came in from the North, which it would be impracticable to cross. I returned, therefore, to a point in the valley near the four hundred and thirtieth mile of Mr. Reynold's line, where ascent from the valley seemed easy, and commenced my line at Station fifteen hundred and fifty-seven by eighty-three and ascended to an upper plateau in about one and a half miles, with a grade of fifty-two and eight-tenths feet per mile. I then turned to about Magnetic east, and we held this course with some deflections northward until night. This day's work, some six miles, is extremely heavy, the first two miles averaging about forty thousand cubic yards of earthwork each. On Friday we continued the line, swinging more to the northward, as the heavy ravines and rough country forced us away from our course. Running ten miles, we found a good camping place at end of line, at night, in a large branch of the North Fork, (the same which comes in two miles west of Sheridan), where there were numerous large ponds of