M'lfiretnert of a Bop on Hounflow- Heath. 42;^' 



The computed numbers in the leventh column are the 

 redudioiis * depending on the aforefaid heights, or the dif- 

 ferences between the hypothenufal diftances of 6co feet each 

 and the reduced bafe difbances. With regard to the remaining 

 cohimns of the table, or thofe towards the right hand, they 

 win be feverally fpoken to hereafter, in taking into considera- 

 tion the expanfion of metals, as determined witk great accu- 

 racy by the experiments with the pyrometer. 



Hitherto no ufe had been made of the tranfit inftrument : 

 for, in order that it might be applied to advantage, there was 

 a neceflity for laying the wheel into tiie ground at the lower 

 end of the bafe, and fo to modify the St. George's flag-ftaff 

 that, being placed in the pipe, it might be fteadily fupported 

 By braces in a true vertical pofition ; which we found, from' 

 experience, could not be effetted by ropes only. 



The wheel being accordingly laid in its place, and the other 

 precautions taken for fecuring the flag-ll:aff, which was like- 

 wife painted white, that it might be more diftindiy feen from- 



* The redudtion- in the feventh column, I have computed by the difference 

 between the fquare of the hypothenufe,. aftually imeafured, and the fqiiare of 

 the height found by the level ; and Lieut. Colonel Calderwood has done the fame 

 thing by a much fliorter method. Thus, in the annexed 



figure, CE being the hypothenufe of 6oo feet, DE the / \E 



perpendicular height obtained by levelling, DB the re- 

 dudtion required, or the difference between the hypothe- 

 nufe and true bafe j then, fubftituting the chord BE in-A 

 fteadofDE, the following analogy is obtainedj AB : BE :: 



BE* 

 BE :DB; confequently, iz DB : th'at is, the fquarc of the perpendicular 



height being divided by double the diflance, or i200 feet, the quotient is equal to 

 DB the redMftion, without fenfible error. For if DE were four feet, the greateft 

 perpendicular height in the bafe, BE the chord would only exceed it -734ot(3» which 

 would not be more than -^i-^ part of an inch. The difference between the refults, 

 by the two modes of computation, is fo trifling as not to deferve notice. 



the 





