MERIDIAN MEASUREMENT. The deter mination of the form and size of the earth from the measurement of a meridional are has been a favorite problem with mathematicians from the earliest times, but, up to the middle of the eigh teenth century their operations were not carried on with exactness sufficient to render their con clusions of much value. Since that time, how ever, geodesy has progressed so rapidly, owing to the invention of more accurate instruments and the discovery of new methods, that the measure ment of the meridian can now be performed with very high precision. The modus operandi is as follows: Two stations, having nearly the same longitude, are chosen; their latitude and longi tude are accurately determined (the error of a single second in latitude introduces it consider able error into the result), and the direction of the meridian to be measured ascertained ; then a base line is measured with the greatest accuracy, as an error here generally becomes increased at every subsequent step; and then, by the method known as triangulation (q.v.), the length of the arc of the meridian contained between the paral leis of latitude of the two stations is ascertained.
As the previously found latitudes of its two ex tremities give the number of degrees it contains, the average length of a degree of this arc can . be at once determined; and also, on certain as as to the earth's form, the length of ci the whole meridional ciremnference of the earth. This operation of meridian measurement has been performed at different times on a great many arcs lying between latitude 6ti° and latitude 38° S., and the results show a steady though irregular increase in the length of the degree of latitude as the latitude increases. On the sup position that the law of increase holds good to the poles, the length of every tenth degree of latitude up to 70° is as follows: This table is calculated on the theory that the earth is not spherical, ns in that ease the length of n11 degrees of latitude would he alike. but of a more or less spheroidal form. that is. having its curvature becoming less and less as we go from the extremity of its greater or equa torial diameter to the lesser or polar axis. Sec EARTH DECREE OF LATITUDE.