the terminating point 6 on the line F G, and move the rule, parallel, to the angle 5, finding the point D on the base E H, from which point draw a line to 6, the process then being complete. The line D 6 thus drawn, leaves the same area of lake to the left, that there is of land to the right. (Fig. 5.) Any figure may be calculated upon the same principle ceed in like manner with that portion of the figure to the left of the perpendicular line, throwing it into two triangles. (Fig. 6.) CONVENIENT RULES FOR CORRECTING THE COURSE OF RANDOM LINES, WHEN THE CORRECTION DOES NOT EXCEED 200 LINKS TO EACH MILE. RULE FOR HALF A MILE, OR FORTY CHAINS. From the number of links to be corrected in that distance, subtract one-seventh; the difference will be the number of minutes of a degree required for the correction of the course. Example. Number of links to be corrected, 42-6= 36' answer. RULE FOR ONE MILE, OR EIGHTY CHAINS. From half of the number of links to be corrected in that distance, subtract one-seventh, the difference will be the number of minutes of a degree required for the correction of the course. Example. Number of links to be corrected, 70 ÷ 2 = 35—5= 30' answer. RULE FOR THREE MILES. Divide the whole number of links to be corrected by seven; the quotient will be the number of minutes of a degree required for the correction of the course. Example. Number of links to be corrected, 297 ÷ 7 = 423' an swer. RULE FOR SIX MILES. Divide one-half of the number of links to be corrected by seven; the quotient will be the number of minutes required for the correction of the course. Example. Number of links to be corrected, 370 ÷ 2 = 185÷7= 263' answer.* The distances given for corrections in the above examples, are those for which corrections are generally made in the survey of the public lands, and the calculation for the course of the corrected line can generally be mentally made by the surveyor, while he is occupied in adjusting his instrument. *The above rules are close approximations. TABLE VI. Showing the Difference of Latitude and Departure in running 80 chains, at any course from 1 to 60 minutes. VARIATION OF THE NEEDLE. 1. The angle which the magnetic meridian makes with the true meridian, at any place on the surface of the earth, is called the variation of the needle at that place, and is east or west, according as the north end of the needle lies on the east or west side of the true meridian. 2. The variation is different at different places, and even at the same place it does not remain constant for any length of time. The variation is ascertained by comparing the magnetic with the true meridian. 3. If we suppose a line to be traced through those points on the surface of the earth, where the needle points directly north, such a line is called the line of no variation. At all places lying on the east of this line, the variation of the needle is west; at all places lying on the west of it, the variation is east. 4. The public is much indebted to Professor Loomis for the valuable results of many observations and much scientific research on the dip and variation of the needle, contained in the 39th and 42d volumes of Silliman's Journal. The variation at each place was ascertained for the year 1840; and by a comparison of previous observations and the application of known formulas, the annual motion, or change in variation, at each place, was also ascertained, and both are contained in the tables which follow. 5. If the annual motion was correctly found, and continues uniform, the variation at any subsequent period can be ascertained by simply multiplying the annual motion by the number of years, and adding the product, in the algebraic sense, to the variation in 1840. It will be observed that all variations west are designated by the plus sign; and all variations east, by the minus sign. The annual motions being all west, have all the plus sign. 6. Our first object will be to mark the line, as it was in 1840, of no variation. For this purpose we shall make a table of places lying near this line. At the point whose latitude is 40° 53', longitude 80° 13', the variation of the needle was nothing in the year 1840, and the direction of the line of no variation, traced north, was N. 24° 35' west. The line of no variation, prolonged, passed a little to the east at Cleveland, in Ohio-the variation there being 19' east. Detroit lay still further to the west of this line, the variation there being 1° 56' east; and Mackinaw still further to the west, as the variation at that place was 2° 08′ east. The course of the line of no variation, prolonged southerly, was S. 24° 35′ E. Marietta, Ohio, was west of this line the variation there being 1° 24' east. Charlottesville, in Virginia, was a little to the east of it—the variation there being 19' west; while Charleston, in South Carolina, was on the west- the variation there being 2° 44' east. From these results, it will be easy to see about where the line of no variation is traced in our own country. 7. We shall give two additional tables: |