yOL. LXXXV.] PHILOSOPHICAL TRANSACTIONS. 637 



angle, or rather the fractional part of a half degree, was measured by the 

 micrometer, the wire of which was brought from the centre of the glass to 

 bisect the black line, and was either added to, or subtracted from, the former 

 quantity, as the angle described by the telescope fell short of, or exceeded, that 

 formed by the hypotenuse and the plane of the horizon. By this method, all 

 the angles of elevation and depression were taken. And we consider it as pro- 

 bable that they are within a quarter of a minute of the truth ; since the instru- 

 ment was capable of being used with great accuracy, the arch having been 

 divided by one of Mr. Ramsden's best workmen, and the value of one, or any 

 number of revolutions of the micrometer-screw, had been accurately ob- 

 tained. 



After as many points as were judged necessary had been fixed in the true 

 direction, by the means described, and the chains compared with each otiier, 

 the mensuration was begun, and continued without much interruption for 7 

 weeks, when it was finished with that part of the 366th chain, which terminated 

 its apparent length. On the first favourable opportunity, subsequent to this 

 conclusion of the measurement, the chains a and b were compared with each 

 other, when it was found that the wear of the former, by the constant use of 

 it, was only 1 division of the micrometer-head, or -^-oth of an inch. The 

 smallness of this quantity in the measurement of a base of such great length, was 

 doubtless owing to the pivots, and pivot holes of the joints being smoothed, and 

 as it were polished, in the operation on Hounslov; Heath ; and it may also be 

 adduced as some proof, that the joints had not rusted while the chains remained 

 in the Tower; but to prevent this, care had been taken to deposit them in a 

 dry place, being afterwards frequently examined and oiled. Then follows the 

 table containing the particulars of this operation. The first column showing 

 the number of hypotenuses; the 2d, that of the chains in each hypotenuse; 

 the 3d, the observed angles of elevation or depression given to the nearest 10''; 

 the 4th and 5th, the perpendiculars answering to the elevations and depressions ; 

 the 6th, the reduction of the hypotenuses to the horizontal lines, or the versed 

 sines of the elevations and depressions to the hypotenuses as radii; the 7th and 

 8th, the perpendicular distance between the termination and beginning of any 

 two hypotenuses when a new direction was commenced above or below. 



Reduction of the Base measured on Salisbuiy Plain, to the Temperature of 62°. 



The overplus of the 366tU chain was measured by Mr. Rainsden, and found to be 9-939 Feet, 

 feet; therefore the apparent length of the base was 36590.06'l 



By the measurement in the Duke of Marlborough's riding-house, the chain a was found 

 to exceed 100 feet in the temperature of 54°, by 0.11425 inches; to which adding half 



the wear, namely, -^ inch, we get — feet for the excess of the chain's length 



above 100 feet; therefore — x 365.9 chains = 3.542 feet, is the correction for 



