EXP 



EXP 



EXPERIMENTU.M crude, a capital, 

 leading, or decisive experiment; thus 

 termed, either on account of its being like 

 a cross or direction post, placed in the 

 meeting of several roads, guiding men to 

 the true knowledge of the nature of that 

 thing they are inquiring after ; or, on ac- 

 count of its being a kind of torture, 

 whereby the nature of the thing is, as it 

 were, extorted by force. 



EXPIRATION, in physic, that part of 

 respiration, whereby the air is expelled 

 or driven out of the lungs. See Par- 



EXPLOSION, in natural philosophy, a 

 sudden and violent expansion of an ae- 

 rial or other elastic fluid, by which it in- 

 stantly throws off any obsiacle that hap- 

 pens to be in the way, sometimes with in- 

 credible force, and in such a manner as 

 to produce the most astonishing effects. 

 It differs from expansion in this, that the 

 latter is a gradual and continued power, 

 acting uniformly for some time ; whereas 

 the former is always sudden, and only of 

 momentary duration. The expansions of 

 solid bodies do not terminate in violent 

 explosions, on account of their slowness, 

 and the small space through which the 

 metal, or other expanding substance, 

 moves. Thus wedges of dry wood dri- 

 ven into stone, and wetted, will cleave 

 the most solid blocks, but they never 

 throw the parts to any distance, as is the 

 case with gunpowder ; but the expansion 

 of elastic fluids will burst solid substan- 

 ces, and throw the fragments a great way 

 oft': for this two reasons have been as- 

 signed : 1. The immense velocity with 

 which aerial fluids expand, when sud- 

 denly affected with high degrees of heat : 

 and 2. The great celerity wiih which they 

 acquire heal, and are affected by it. As 

 an example, air, when heated as much as 

 iron, when brought to a white heat, is ex- 

 panded to four times its bulk ; but the 

 metal itself will not be expanded the 

 500th part of the space. In the case of 

 gunpowder, which is well known as an 

 explosive substance, the velocity with 

 which the flame moves is estimated at 

 7000 feet in a second. Hence the im- 

 pulse of the fluid is inconceivably great, 

 and the obstacles on which it strikes are 

 hurried off with vast velocity, viz. at the 

 rate of 27 miles per minute. The velo- 

 city of the bullet is also promoted by the 

 sudden propagation of the heat through 

 the whole body of air, as soon as it is ex- 

 tricated from the materials of which the 

 gunpowder is made, so that it strikes at 



once. Hence it has been inferred, that 

 explosion depends first on the quantity of 

 elasiic fluid to be expanded : secondly, 

 on the velocity it acquires by a certain __ 

 degree of heat : and, thirdly, on the ce- 

 lerity with which the degree of heat af- 

 fects the whole expansive fluid. 



EXPONEN T, in algeoru, is a number 

 placed over any power, or involved quan- 

 tity, to shew to what height the root is 

 raised : thus, 2 is the exponent of x^ uul 

 4 the exponent of x* } or xxxx. The 

 rule for dividing powers of the same quan- 

 ty is, to sabstract the exponents, and 

 make the difference the exponent of the 

 quotient : if, therefore, a lesser power is 

 divided by a greater, the exponent of the 

 quotient must, by this rule, t>e negative : 



a4 a^ 1 



thus, =a4= 6 =a-2. But ,, = ; 

 a 6 a 6 a* ' 



and hence MS expressed by a 1 , with a 

 negative exponent. It is also obvious, that 



rrra 1 1 =a; but = 1, and there- 

 a a 



fore a = 1. After the same manner, 



= a 1 ; - = a "" 3 = a 3 ; so that the 

 aaa 



,1111 

 quantities, a, I, , -. &c. may 



b< expressed thus, a 1 , a, a 1 , a*, a 3, 

 a*, 8tc. These are called the negative 

 powers of a, which have negative expo- 

 nents ; but they are at the same time po- 



sitive powers of or ai 



EXPONENT of a ratio, is the quotient 

 arising from the division of the antece- 

 dent by the consequent : thus, in the ra- 

 tio of 5 to 4, the exponent is !$ ; but the 

 .exponent of 4: 5, is |. If the consequent 

 be unity, the antecedent itself is the ex- 

 ponent of the ratio : thus the exponent of 

 the ratio 4 : 1 is 4. Wherefore the ex- 

 ponent of a ratio is to unity as the ante- 

 cedent is to the consequent. Although 

 the quotient of the division of the antece- 

 dent by the consequent is usually taken 

 for the exponent of a ratio, yet in reality 

 the exponent of a ratio ougnt to be a lo- 

 garithm. And this seems to be more 

 agreeable to Euclid's definition of dupli- 

 cate and triplicate ratios, in his fifth book. 

 For 1, 3, 9, are continual proportionals ; 

 now if 1. be the exponent of the ratio of 1 

 to 3, and 3 or * the exponent of the ratio 

 of 3 to 9 ; and !|. the exponent of the ra- 





