130 



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 alsd 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 1 st of January 1 802 : 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 be an ellipsoid, with the 

 ratio of its axis as 229 to 230, it should be 10 fathoms less. On 

 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 attended 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 different 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 di- 

 stances from their respective places of observation are given in the 

 Philosophical Transactions for 1 800 ; which, it is asserted, cannot 



