EXPLANATION AND USE OF THE TABLES.

TABLE A.

For Correcting Gunter's Chains of 100 Links.

In the use of chains, they are found to stretch and unless this quantity is most carefully observed daily by comparison with a standard, all the measurements made will be erroneous and in defect in proportion as the chain is too long. This Table, therefore, gives the equivalent in links to be added for every inch from one to eleven.

Suppose a chain to have stretched 4 inches;-then for every 10 chains measured, in the column of links opposite 10 and under the heading of 4 inches, will be found 5.051 the number of links to be added, to bring the chains to their proper standard length,-and vice versâ for chains too short the same quantity will be deducted.

TABLE B.

For reducing Chains to the Decimal parts of a mile.

This Table is useful in the protraction of the co-ordinate distances for general maps on the Geographical scale. For plotting the latitude and departure points from the first station in the series as given in the main Circuit Traverse, the distances require to be divided by 80 for the convenience of scale. By the Table this is avoided and the chance of error, by frequent small divisions, obviated. Thus :

To obtain the value of 345 chains in miles and decimals, look for the even tens and hundreds (340) in the top lines of the Table, and for the odd chains (5) in the left hand column, at the intersection of these two columns will be found 4.3125 the number of miles sought.

TABLE C.

Showing the length of a degree, minute and second of Latitude and Longitude, for every degree of the Quadrant, the compression of the earth being assumed 04.

This Table, (extracted from Boileau's Traverse Tables) is calculated by the Formulæ xliii, page 116, of Mr. F. Baily's Astronomical Tables and Formulæ ; the compression of the earth at the poles being assumed, and the mean degree of latitude taken at 364547 feet. The first ten degrees of latitude and

longitude, and afterwards every fifth degree, were computed by the Formulæ, the intermediate degrees being filled in by interpolation, by differences carried out as far as such could be done. The degrees of latitude are calculated for the latitudes of their middle points: for instance, the degree in the Table on a line with the number 27, in the first column, is that degree which extends from latitude 26° 30' to latitude 27° 30', and in like manner of the rest. The degrees of longitude are computed for the parallels of latitude expressed by the numbers in the same line in the column designated "distance from the equator."

The use of this Table is to convert the Tabular traverses expressed in units of linear measure into their equivalent values of latitude and longitude in arc: i. e. in degrees, minutes, etc. for that part of the earth's surface to which the traverses belong. For a further description of the use of this Table, see pages 362, 363, etc.

TABLE D.

For converting Chains and Links into Feet and Decimals
of Feet.

It frequently happens that measurements made in one denomination require to be converted into their equivalents of another denomination, for instance, route surveys are generally measured with instruments registering yards or feet; and circumstances may occur, and do frequently happen, where instruments cannot be readily procured, which induce the necessity of making all measurements of every kind in one or other of the above denominations. Land surveys are, however, generally made in Gunter's measure or in links, the 1000th part of a furlong; and this is the most convenient of all measures for determining the acreage of any extent of surface; but for geographical purposes the standard unit being the English foot, those measurements are most convenient which are made in this denomination, the length of degrees of latitude and longitude being most frequently expressed in tables in feet also. The arrangement of this table (taken from Boileau's Traverse Tables) requires no explanation.

There being two significant figures in the number of chains, the first denoting tens, the second units, the equivalents must be taken out for each separately. Enter the column of chains corresponding to the significant figures in the first part of the table, where it is an exact decimal multiple of that number, or in the first or second part of the table, according as the number of links is more or less than 50. When the whole distance is less than 10 chains, the first part of the equivalent value is found in the same column under the number of chains and in a line with the number of links in the column so designated; the last part of the equivalent is found in the column headed deci

d

mals of feet, of which there is one for each part of the table. The decimal parts are taken out as whole numbers, removing the decimal point in the equivalent number as many places as it is removed in the original. Given the length of a line in a survey 47,25-6 links required its equivalent in feet and decimals.

This Table from the Nautical Almanac of 1826, is computed upon principles explained by DR. YOUNG in the Philosophical Transactions for 1819; and it appears to agree more perfectly with the latest observations than any other table that has been published. The formula employed is

; r being the fraction, v the sine of the altitude, and s the

The apparent altitude being found in the first column, the second shows the refraction when the barometer stands at 30 inches, which is its mean height on the level of the sea, and the thermometer at 50° of Fahrenheit. The third column contains the difference to be subtracted or added for every minute of altitude, reckoned from the nearest number in the first column. The fourth shows the number of seconds to be added for every inch that the height of the barometer exceeds 30, or to be subtracted for each inch that it wants of 30: and the last contains the number of seconds to be subtracted for each degree that the thermometer stands above 50°, or to be added for each degree that its height wants of 50°.

If great accuracy be required, we must also deduct from the observed height of the barometer 003 i. for each degree that the thermometer near it is above 50°, and add an equal quantity for an equal depression. In fact, however, the table, as it now stands, is found to require the temperature to be estimated from the height of the thermometer within; and if we employed the height of the thermometer without, which would be more consistent with the theory it would probably be necessary to suppose the standard temperature of the table 48° only, instead of 50°.