L 



0?i the different llieories of Arches, p'aulls, o^c. 3S9 



actions, that each must be augmented according to its po- 

 sition ; the second must he niHde more heavy than the first, 

 the third than the second, and so on until the last, which 

 must be infinitely heavy, because it does not make any eflort 

 to fall. 



To rt-nder this subject practically more intelligible, we 

 have only to consider, that every vaussoir except the last, in 

 Jetting anoiher vaussoir fall, must itself rise, and that it re- 

 sists this elevation to the extent of the weight which it it- 

 self exerts to fall ; and that only the last vaussoir on each 

 side can let another fall, without itself risintr. as it has only 

 to slide along its horizontal bed : as a finite weight has not 

 any power of resistance to a horizontal motion, every thing 

 being considered lubricous; we must conceive the last vaus- 

 soir to be infinitely heavy, to made any lateral resistance. 



An arch * may stand immediately on the earth, which is 

 its base, or be sustained by a wall or abutment pier: in 

 both cases the joint effort of the parts is communicated to 

 the base, which is its foundation, as if it were one and the 

 same body continued. 



Curves used in arches are of three characters: 1st, Arcs 

 of circles, wherein the height must always be equal, or less 

 than half the width ; in the first case the tangent at the 

 springing will be vertical. The curtate cvcloid is applica- 

 ble in all the conditions of the circle, and the tangent at 

 the springing may be vertical. 2d, The arcs of ellipses, 

 whose widths may bear any proportion to their heights, 

 and the tangent at the springing may be vertical. 3d, The 

 catenaria, the parabola, the hyperbola, &c. whose spans 

 may bear any proportions to their heights, but whose tan- 

 gent at the springing cannot be vertical. 



The natural consequence from these data seems to be, 

 that when the given height of an arch exceeds half the width, 



• The arch has been considered as a curve, infinitely thin, uniform 

 throughout, and composed of an infinite number of joints j and the inquiry 

 has been lo determine the weight which may be placed upon each joint, in 

 a direction perpendicular to ihe horizon, so that it may retain its position. 

 In lliis way of considerinjj the subject, the pleasing analogy between the 

 chain and the arch, as applied in a popular experiment, together with the 

 happy adaptation of the modern analysis to detei mine forniuTai for universal 

 practice, have, in the eleyant display of the means, blinded the inquirers as 

 to the end, and as to the absolute properticB of the arch itself. It liven hag 

 jppearetl to men of other habits, that if such an hypothesis were applica- 

 ble, it must be subseijuent to the determination of the arch, or the curve of 

 infinite joints, which must at all events be determined on the principle of 

 the wedge, or a collection of bodies butting on each other ; the lower being 

 an inclined plaiic to the superior; and then the weight, however suj-p-neil to 

 bear on the arch, must be determined in reUtion to this pieviouii-iuvehti- 

 ijation. 



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