AEROSTATIC MACHINES. J97' 



This being premifed, if a ruler be placed in the dIre6llon Method of af- 

 UB, it may be confidered as in that of the fide A B, and "g,'j"f|;^'J\/ 

 if we can fucceed in fixing a fecond ruler in fuch a manner vifual rays. 

 that the moveable index fliall carry it into the diredion R C, 

 at the inflant that the images of the two obje6ts B and C 

 are brought into one at the point L, it is evident that thefe two 

 rulers will form between them the angle B R C, and confe- 

 quently the angle BAG. 



Toaccompliflithis, let us fuppofeafortof falfe fquare, S R Q, 

 ^tuate in the plane of the inftrument, and moveable at its axis 

 on a pivot fixed at the point R, at the interfeflion of the lines 

 A R and R L ; making the angle S R Q, comprifed between 

 its arms, equal to the angle E R L, and the fide R S equal to 

 the diftance A R. If now we fuppofe that the extremity S of 

 the fide R S, is retained by a button in a groove M N, worked 

 in the moveable index, the movement of it will be communicated 

 to the falfe fquare in fuch a manner that the angle L R Q will 

 always be equal to the angle BAG, and confequently the fide, 

 R Q will be placed in the requifite diredion. 



In fa6t, (he triangle A R S being ifofceles in its form, the 

 exterior angle S R E = R A S -f A S R.= 2 RAS=B AG; 

 but S R Q being equal to E R L, if the common angle S R L 

 be taken away, there will remain the angle S R E= L R Q = 

 BAG. 



Now let us fix under each of the two rulers R L and Q R Obfervation of- 

 a fmall graduated quadrant, fufpended in fuch a manner ^ ^"^'" , 

 that it will place itfelf in the vertical plane of the fide corref- vifual rays and 

 ponding to the angle obferved; let us affix to each of th>"fe ^.^^'^ P^'^P^'^' 

 quadrants a plummet, compofed of a iUff arm moveable upon 

 a pivot, and furniflied with a nonius index and a weight, which 

 gives it a conftant tendency to atTume a vertical pofition, in 

 whalfoever fituation the fextant may be placed; finally, let 

 the whole be fo difpofed that the index of each plummet may 

 be retained at will, at ihe divifion indicated on the limb by the 

 efFedi of the fufpenfion, and this by means of a trigger, which 

 can be pulled at the exa6t infi:ant of obferving the principal 

 sngle in the points of reflexion. It is evident that the fimul- From which 

 tanepus a6lion of the two rulers and the plummets will (how plane on the 

 the three angles fought, and that nothing remains but to re- horizon are 

 dttce, by calculation, the angle B A C to the plane of the ho- "jic^ulacioru 



rizon. 



This 



