88 



LECTURES 



2. The difference of latitude at its extremities, or what is the same 

 thing, the angle made between the plumb-lines, must be determined. 



3. The length of the arc in miles, or parts of miles, must be deter- 

 mined. 



By the aid of a few simple diagrams I can readily indicate to you 

 how these results are obtained. 



1. To run a true north and south line we have only to direct the 

 telescope of a transit instrument on a theodolite to the north star when 

 it is directly above or heloio the pole, and then, the axis being hori- 

 zontal, sight to some well defined object situated to the north and to 

 another at the south. The line passing through these points and con- 

 tinued by sighting to new objects will be the line required. The 

 time, which occurs twice in every twenty-four hours, when the north 

 star is so situated, is easily known from the Nautical Almanac. This 

 is the readiest method of fixing the line. But if the Nautical Almanac 

 is not on hand, the same result is obtained by so placing the instru- 

 ment that the time between the upper and lower transits of a circum- 

 polar star passing through the western portion of its revolution shall 

 be the same as that in passing from the lower transit through the 

 eastern portion of its revolution to the upper. 



2. To find the angle made be- 

 tween the plumb-line, let a and 

 5, fig. 1, represent the arc of the 

 meridian ; C the centre of the 

 earth ; Z and Z' the zeniths of 

 the two extremities of the line. 

 It is required to find the angle 

 a G h. This will be the diff'er- 

 ence in latitude between the two 

 stations. But it is most easily 

 obtained by observing the zenith 

 distance of any star in the vicinity 

 of the zenith as it passes the me- 

 ridian. Thus Z a s' would be the 

 zenith distance of the star at a, 

 and Z' h s' the zenith distance at l. The difference between these 

 two is the required angle at C. In practice this element is obtained 

 very readily and with great precision. 



3. By far the most difficult part of the work is to measure the exact 

 distance between the two points a and h. This is best done by a 

 system of triangles. Thus, in fig. 2, suppose A and B to be the 

 extremities of the meridian line, and D E F Gr and H to be prominent 

 points of the country at such elevations as to be visible the one from 

 the other. Commencing the operation at A, a line A D, of several 

 miles in extent, lying along a level plain, if such can be found, is 

 selected and accurately measured. This is called a base or base line, 

 and the utmost refinement of methods is required for its measurement. 

 The base line having been measured, we place an instrument, adapted 

 to the measurement of horizontal and vertical angles, (usually a 

 large theodolite,) at A, and measure the horizontal angle DAE, 



Ma J 



