J, I ir 



if ;i man, balanced in a common pair of *c;ii*'s, pi :.-.> upw.'K 

 n>e;ms of a rod, against any point of tlio beam, except that from which 

 the scale is suspended, he will preponderate. 



;{. In a compound lever, where one is made to turn another, there is 

 an equilibrium, when W I P II the product of all the arms taken alter- 

 nately, beginning with that to which the power is applied : the product 

 of all the other arms, 



4. Any weights will keep each other in equilibrio on the arms of a 

 straight lever, when the products, which arise from multiplying each 

 xveight by its distance from the fulcrum, are equal on each side of the 

 fulcrum. 



Cor. 1. If in the above Propositions we would allow for the weight of 

 the lever itself, we must suppose its weight to be united iu the centre of 

 gravity, and to act there as a third force added to the power or the 

 weight, according to the side of the fulcrum on which it is placed. 



Cor. 2. If the weights do not act perpendicularly to the arms of Ihc 

 lever, we must for the distances substitute the perpendiculars, (see Art. 

 2.) 



Cor. 3. Let A D be the common "F C "P O D 



steelyard, whose fulcrum is C, and i *~~T\ *~ ~~* j 



let the moveable weight P, when 



placed at E, keep the lever at rest ; O W OP 



then when W and P are suspended upon the lever, a^id the whole r<. 

 mains at rest, WXAC PXDC-|- PXEC^PXDE; .*. W 

 varies as E D ; the graduation must .'. begin from E, and if P when 

 placed at F support a weight of one pound at A, take FG, GD, &c, 

 equal to one another and to E F ; and when P is placed at G it will sup- 

 port two pounds ; and when at D it will 'support three pounds, &c, 



LIFE Annuities. See Annuities Life. 



LIFE Assurances. See Annuities. 



LIGHT, Phenomena of. 



Light, propagation of. 



1. In a free medium the force and intensity of light, which propagates 

 itself in rays emanating from the same point, are inversely as the squares 

 of the distances from that point. 



Prob. Having given the position of two lights of known intensities, 

 to determine the nature and equation of the surface, of which every 

 point shall be equally illuminated by the two lights. 



Let A and B be the two point" at which the lights are placed, m and n 

 1G3 . K 



