if we step 100 feet (nearly) forward, the direction of the plumb-line changes one second. If, then, we can find the distance from our observing station at N to that at S, then we can tell from that distance how much the directions of the plumb-line at N and S would be inclined if there were no mountain; and we can compare that inclination with the inclination observed by means of the Zenith Sector.
Accordingly the observations were made in exactly the same manner as the observations made for determining the figure of the earth. The Zenith Sector was carried to N, and certain stars were observed; the Zenith Sector was then carried to S, and the same stars were observed at that place. By means of these observations of the stars, the actual inclinations of the plumb-line at the two places were found. The next thing done was to carry a survey by triangulation across the mountain. This was done in the most careful way in which the best surveyors of the time could accomplish the task. The result was, that the distance between the stations was found such that, supposing that there was no mountain in the case, the inclination of the two plumb-lines ought to be 41 seconds. It was found practically from the observations by the Zenith Sector, that the inclination of the two plumb-lines actually was 53 seconds.
The difference between the two was the effect of the mountain. The mountain had pulled the plumb-line at one station in one direction, and at the other station in the opposite direction, to such a degree, that instead of the two plumb-lines making an angle of 41 seconds, they made an angle of 53 seconds; or, in other words, that the sum of the effects of the two attractions of the mountain, on opposite sides, was 12 seconds.
