TABLE IX.

Convergency of meridians. The second column contains the convergency, measured on the parallel, for two meridians six miles long and six miles apart, for the latitude of their middle points which is given in the first column. For other than the tabular latitudes the distance may be obtained by simple proportion. The third column contains the angle of convergency. See Diagram A, Fig. 1.

The convergency between any two meridians whose lengths are equal to their mean distances apart may be found by the following proportion: The square of the tabular meridional length (six miles) is to the square of the given length of meridians as the tabular convergency is to the convergency required.

Thus, for two meridians three miles long and three miles apart, in latitude 44°, we have: As 62 : 32:: 70. 1 links: 17.52 links, the convergency.

The convergency of equal length of meridians in the same latitude are proportional to their distance apart; thus, the convergency for five ranges (meridians 6 mls. long) in latitude 380 is, 56. 8 lks. x 5 = 2.84 chains.

TABLE IX.

Convergency of meridians six miles long and six miles apart. Also, difference of longitude for one range.

The above rules may be used to find the convergency for lengths of meridians more than 6 miles long. Take the preceding example, 5. Find from Table IX the tabular convergency for latitude 42° 49′ 36′′,equal to 67.3 links, and from the proportion, 62: 242:: 67.3 links: 1076.8 links, the convergency for two meridians 24 miles long and 24 miles apart. Then for two meridians six miles apart divide 1076.8 links by 4, the quotient, 2.69 chains, is the convergency required, which agrees closely with the result obtained by the preceding rule.

Another proportion for finding the convergency is this: The cosines of the latitudes are to each other as the lengths of the intercepted parallels.

Thus, for example 5, we have cos. 42° 39′ 12′′: cos. 43°:: 480 chs. : 477.32 chs., which proportion may be computed with natural cosines, or more expeditiously, by logarithms, as follows:

This method does not take into account the spheroidal shape of the earth, but regards it as a perfect sphere and is sufficiently exact for surveying purposes.

Columns 4 and 5 contain differences of longitude for one range in arc and time. The tabular value in last column multiplied by the number of ranges between any two points in the same latitude, gives the dif ference of their local times. Thus, for a station 20 ranges west of the standard meridian for mountain time (105° longitude), in latitude 47°, the difference in time is 30o.47 × 20=10m 98.4.