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VOL. LXXVII.] PHILOSOPHICAL TRANSACTIONS. 



from Hounslow-heath to the neighbourhood of Dover; but the contrivance and 

 construction of an instrument, new of its kind, proposed to be made use of, 

 and more particularly the nicety of its division, by which it is hoped the angles 

 may be determined to a degree of precision hitherto unexampled, have required 

 much more time than Mr. Ramsden himself at first imagined. Without mean- 

 ing to disappoint, this ingenious artist was perhaps in the outset too remiss and 

 dilatory, and accidents having happened when the workmanship was already far 

 advanced, which he could not foresee or prevent, the execution has thus been 

 greatly retarded. However, since the instrument may at present be considered 

 as nearly finished, such parts as yet remain to be perfected being only of the 

 smaller kind, we may fairly conclude, that early in the ensuing summer, or as 

 soon as the weather in this country will permit, the trigonometrical operation 

 may be begun. In this state of things, I have therefore judged 

 that it might be proper to lay before the Society a short sketch of 

 the mode proposed to be followed in fulfilling his Majesty's com- 

 mands, accompanied by a very slight general map of the country, 

 only collected from the common surveys, but still sufficient to 

 show nearly the disposition of the triangles that will be used in 

 forming the junctions between the meridians of the two Obser- 

 vatories. 



In every series of triangles, where each angle is to be actually 

 observ^ed with the same instrument, they should, as near as the 

 circumstances will permit, be equilateral: for were it possible to 

 choose the stations in such a manner as that each angle should be 

 exactly 60 degrees, the half number of triangles in the series, mul- 

 tiplied by the length of one side, would, as in the annexed figure, 

 give at once the total distance; not only the sides of the scale or 

 ladder would be perfectly parallel, but the diagonal steps, marking 

 the progress from one extremity to the other, would be alternately 

 so throughout the whole length. The first side is supposed to be 

 found by the measurement of a base h, of about half its length; 

 and the last side to be verified by such another base r at the op- 

 posite extremity. In any particular case, where only '2 angles of a 

 triangle can be actually observed, these should be as near as possible each 45°. 

 At any rate their sum should not differ much from 90°; for the less the com- 

 puted angle differs from 90°, the less chance there will be of any considerable 

 error in the intersection. 



Romney-marsh, from its levelness, as well as other advantageous circumstances 

 attending its situation, seeming to aflfbrd the best base of verification for the last 

 triangle, I have given the series the shortest direction from Hounslow-heath to 



VOL. XVI. 1 1 



