RES 



IIES 



amounts to _.?_ of the same quantity; 

 whence in a velocity of 1065 feet in 1'', 

 (the medium of 1180 and 950) the resist- 

 ing power of the air is augmented in no 

 greater proportion than of 11 to 7; where- 

 as in greater degrees of velocity, as before, 

 it amounted very near the ratio of 3 to 1. 



That this resisting* power of the air to 

 swift motions is very sensibly increased 

 beyond what Sir Isaac's theory for slow 

 motions makes it, seems hence to be evi- 

 dent. It being-, as has been said, in mus- 

 ket, or cannon shot, with their full charge 

 of powder, nearly three times the quantity 

 assigned by that theory. 



The resistance of a bullet of three 

 quarters of an inch diameter, moving in 

 air with a velocity of 1670 feet in 1", 

 amounting, as we said, to 10/6. the resist- 

 ance of a cannon ball of 24/6. fired with 

 its full charge of powder, and thereby 

 moving with a velocity of 1650 feet in 1", 

 may hence be determined. For the velo- 

 city of the cannon ball being nearly the 

 same as the musket-bullet, and its sur- 

 face above 54 times greater, it follows, 

 that the resistance on the cannon ball will 

 amount to more than 540/6. which is 

 nearer 23 times its own weight. And from 

 hence it appears how rash and erroneous 

 the opinion of those is, who neglect the 

 consideration of the resistance of the air 

 as of no importance in the doctrine of 

 projectiles. See Robins's Tracts; Hut- 

 ton's Dictionary, article RESISTANCE. 



RESOLUTION, or SOLUTION, in ma- 

 thematics, is an orderly enumeration of 

 several things to be done, to obtain what 

 is required in a problem. 



RESOLUTION, in algebra, or algebrai- 

 cal resolution, is of two kinds ; the one 

 practised in numerical problems, the other 

 in geometrical ones. 



in resolving a numerical problem alge- 

 braically, the method is this : First, the 

 given quantities arc distinguished from 

 those that are sought ; and the former 

 denoted by the initial letters of the alpha- 

 bet, but the latter by the last letters. 2. 

 Then as many equations are formed as 

 there are unknown quantities. If that 

 cannot be done from the proposition or 

 data, the problem is indeterminate : and 

 certain arbitrary assumptions must be 

 made to supply the defect, and which can 

 satisfy the question. When the equations 

 are not contained in the problem itself, 

 they are to be found by particular theo- 

 rems concerning equations, ratios, pro- 

 portions, &,c. Since, in an equation, the 

 known and unknown quantities are mix- 

 ed together, they must be separated in 



such a manner that the unknown remain 

 alone on one side, and the known 

 ones on the other. This reduction, or 

 separation, is made by addition, subtrac- 

 tion, multiplication, division, extraction of 

 roots, and raising of powers ; resolving 

 every kind of combination of the quanti- 

 ties by their counter or reverse ones, and 

 performing the same operation on all the 

 quantities, or terms on both sides of the 

 equation, that the equality may still be 

 preserved. 



To resolve a geometrical problem alge- 

 braically. The same sort of operations 

 are to be performed as in the former arti- 

 cle : besides several others, that depend 

 upon the nature of the diagram, and geo- 

 metrical properties. As, 1. The thing 

 required or proposed, must be supposed 

 done, the diagram being drawn or con- 

 structed in all its parts, both known and 

 unknown. 2. We must then examine 

 the geometrical relations which the lines 

 of the figure have among themselves, 

 without regarding whether they are 

 known or unknown, to find what equa- 

 tions arise from those relations for finding 

 the unknown quantities. 3 It is often 

 necessary to form similar triangles and 

 rectangles, sometimes by producing of 

 lines, or drawing parallels and perpendi- 

 culars, and forming equal angles, &c. ; 

 till equations can be formed from them, 

 including both the known and unknown 

 quantities. 



RESOLUTION, in chemistry, &c. the 

 redaction of a mixed body into its com- 

 ponent parts, or first principles, by a pro- 

 per analysis. The resolution of bodies is 

 effected by divers operations, as distilla- 

 tion, sublimation, fermentation, precipi- 

 tation, &c. See DISTILLATION, SUB* 

 LIMATION, &c. 



Some logicians use the term resolution 

 for what is more usually called analysis, 

 or the analytic method. 



RESOLUTION of forces, or of motion, is 

 the resolving or dividing of any one force 

 or motion into several others, in other 

 directions, but which, taken together, 

 shall have the same effect as the single 

 one ; and it is the reverse of the compo- 

 sition of forces or motions. 



RESPIRATION, in animal economy. 

 The absolute necessity of respiration, or 

 of something analogous, is known to eve- 

 ry one ; and few are ignorant that in man, 

 and hut blooded animals, the organ by 

 which respiration is performed is the 

 lungs. Now respiration consists in draw- 

 ing a certain quantity of air into the lungs, 

 and throwing it out again alternately. 



