Page:Proceedings of the Royal Society of London Vol 1.djvu/150

Rh the angles of a number of triangles observed near the north end of the arc; the calculations of the sides of a series of triangles extend— ing from Dunnose to Clifton; and. from these data, a calculation of the meridional distance between Dunnose and Clifton. Then come the observations with the zenith sector at Dunnose, Clifton, and Arbury Hill, near Daventry, a point almost in the middle of the arc, which was chosen with a View to ascertain how far the obser- vations at the terminations would agree with others made for ﬁnding the value of its parts. A few additional observations made at the Royal Observatory are also given. serving to demonstrate the pre- cision of the former ones, and the accuracy of the instrument.

Next follow the extensive and laborious calculations by which, in order to assimilate the numerous observations made at different times, they are all reduced, from the respective days on which they were made to the lst of January 1802 : the equations here introduced are those for aberration, nutation, semi-annual solar equation, pre- cession, and refraction.

The general conclusions deduced from this ample stock of obser- vations and calculations are, that the whole arc, subtending an angle of 2° 50' 23", measures 1,036,337 feet; so that the length of a de- gree on the meridian, in latitude 52° 2' 20”, is = 60'820 fathoms. This degree, at the latitude of Arbury Hill, is found to be 42 fathoms longer; whereas, admitting the earth to he an ellipsoid, with the ratio of its axis as 229 to 230, it should be 10 fathoms less. 0n maturely weighing all the causes that may have occasioned this de- viation, it is thought most likely that, owing to different attractive forces, which increase as we proceed northward, the plumb-line of the sector has been drawn somewhat towards the south at each of the stations,—a circumstance that must be carefully atte'nded to in the prosecution of this survey, whenever the zenith sector is to be used. It is observed in general, that meridional observations carried on in insular countries are not so likely to afford just conclusions, with regard to the diﬁerent lengths of the degrees, as the same operations if conducted in places very remote from deep seas.

Adverting, lastly, to the operations of the French astronomers who have measured the arc of the meridian between Paris and Barcelona, Which distance was found = 3,527,921 English feet, this, combined with the arc lately measured, gives the whole meridional distance between Clifton and Barcelona, being 12° 5’ 42" '79, something more than the thirtieth part of the whole circumference of the globe, = 4,411,968 feet. According to this determination, the mean length of a degree of the meridian, in latitude 47° 24', will be = 60.795 fathoms; and in the latitude 51° 9', the degree will measure 60,825 fathoms.

In an Appendix are subjoined the latitudes and longitudes of those places intersected in the surveys of Essex, Suffolk, &c. whose distances from their respective places of observation are given in the Philosophical Transactions for 1800; which, it is asserted, cannot