VOL, LXXXV.] PHILOSOPHICAL TRANSACTIONS. 641 



rections for the chord angles have been added to, or taken from them, and the 

 remaining angle or angles considered as erroneous. In the case of one angle 

 being supposed right, and the other two wrong, the errors have been considered 

 equal between the latter, unless the sum of the angles round the horizon at one 

 of the stations has indicated that either the whole, or the greatest part of the 

 excess or defect, was due to a particular angle. Also, when any triangle has 

 been found in excess or defect, and all the angles have appeared to be determined 

 with equal accuracy, the corrections for the reduction to the angles formed by 

 the chords have been first applied and then the errors considered equal. 



What is called the spherical excess in the 5th column, is computed according 

 to the rule, p. 171, Philos. Trans, vol. 80. These excesses above 180° would of 

 course be exactly the same as the respective sums of the differences in the 4th 

 column, if both were not obtained from approximating rules. It is almost un- 

 necessary to remark that no computations have been attempted with the chords 

 of the sides of the lesser triangles in the principal series. 



The account then gives the calculation for the triangles which connect the 

 base of departure on Hounslow Heath with that of verification on Salisbury 

 Plain, being bounded by the sides connecting the stations, Hanger Hill, St. 

 Ann's Hill, Bagshot Heath, Highclere, Beacon Hill, and Four Mile-stone on 

 the north ; and on the south side, by those connecting the stations Dean Hill, 

 Butser Hill, Hind Head, Leith Hill, and Banstead. After which is given the 

 length of the base of verification deduced from that on Hounslow Heath, and 

 the foregoing triangles. The base on Hounslow Heath is 27404.2 feet, which, 

 with the first 4 triangles, give 76688 feet for the mean distance of St. Ann's 

 Hill and Banstead. That mean distance, with the 5, 6, 7, 10, 11, 12, 13, 

 16, and 17th triangles, will give 36574.7 feet for the base of verification. If 

 the computation be made with the 8 and Qth triangles also, and the mean 

 distance taken between Hind Head and Bagshot, the base will be 36574.3. 

 And those mean distances of St. Ann's Hill and Banstead, and Hind Head and 

 Bagshot, with the 14th and 15th triangles, excluding the l6th and 17th, will pro- 

 duce 36574.6, and 36574.9 respectively. Lastly, if the computations are carried 

 directly from one base to the other, independent of the mean distances and the 

 14th and 15th triangles, the greatest and least results will be 36574.8, and 

 36573.8, the mean being 36574.3 feet, or about an inch short of the measure- 

 ment. 



Of the several ways by which the base of verification, or distance between 

 Beacon Hill and Old Sarum is deduced, the first seems to have the preference, 

 because the angles of the 6th and 7th triangles appear to have been observed very 

 correctly. The results from the 14th and 15th triangles cannot be considered 

 as very conclusive, because the angle at Highclere is so acute that a trifling 



VOL. XVII, 4 N 



