ON THE GENERAL DIFFUSION OF KNOWLEDGE. 



perceive, how every step of the demonstration 

 proceeds with unerring certainty, and leads the 

 mind to perceive the truth of the conclusion to 

 which it leads, with as high a degree of demon 

 strative evidence as that 3 added to 6 make 9, 

 or that 5 multiplied by 4 make 20. In like 

 manner, when it is clearly demonstrated by ma 

 thematical reasoning, that &quot; the three angles of 

 every triangle, whatever be its size or the incli 

 nation of its sides, are exactly equal to two right 

 angles, or 180 degrees,&quot; and that &quot; the sides of 

 a plane triangle are to one another as the sines 

 of the angles opposite to them,&quot; the utility and 

 importance of these truths may not at first view 

 be appreciated, however convincing the evi 

 dence from which the conclusions are deduced. 

 But when the student comes to know that on 

 these demonstrated properties of a triangle de 

 pends the mode of measuring the height of 

 mountains, and the breadth of rivers, of deter 

 mining the circumference of the earth, the dis 

 tance of the sun and moon, the magnitudes of 

 the planets, and the dimensions of the solar sys 

 tem, it cannot but afford a positive gratification 

 to perceive the important bearings of such truths, 

 and that the astronomer, when he announces his 

 sublime deductions respecting the sizes and dis 

 tances of the heavenly bodies, does not rest on 

 vague conceptions, but on observations con 

 ducted with the nicest accuracy, and on calcu 

 lations founded on principles susceptible of the 

 strictest demonstration. 



&quot; To follow a demonstration of a grand ma 

 thematical truth,&quot; says a powerful and enlight 

 ened writer, &quot; to perceive how clearly and how 

 inevitably one step succeeds another, and how 

 the whole steps lead to the conclusion, to ob 

 serve how certainly and unerringly the reason 

 ing goes on from things perfectly self-evident, 

 and by the smallest addition at each step, every 

 one being as easily taken after the one before as 

 the first step of all was, and yet the result being 

 something, not only far from self-evident, but so 

 general and strange, that you can hardly believe 

 it to be true, and are only convinced of it by 

 going over the whole reasoning, this operation 

 of the understanding, to those who so exercise 

 themselves, always affords the highest delight,&quot; 



It is likewise a source of enjoyment to con 

 template the experiments by which the doctrines 

 of science are supported, and the reasonings and 

 deductions founded on experimental investiga 

 tions. When a person is told that the atmos- 

 [here presses on every part of the surface of the 

 earth with a force equal to two thousand one 

 hundred and sixty pounds on every square foot, 

 it must surely be gratifying to behold a column 

 of water supported in a glass tube, open at the 

 ower end, and a square bottle connected with 

 an air-pump, broken to pieces by the direct pres- 



the height of the mountains in the moon, when the 

 ength 10 their shadows is known. 



sure of the atmosphere, and from a comparison 

 of the weight of mercury suspended in a tube 

 with the diameter of its bore, to be able to cal 

 culate the atmospherical pressure on the body 

 of a man, or even on the whole earth. When 

 he is told that one ingredient of atmospheric air 

 is the principle of flame, is it not curious and 

 highly interesting to behold a piece of iron burn 

 ing in this gas, throwing out brilliant sparks of 

 white flame, and illuminating a large ha.1 with a 

 dazzling lustre ? and when he is informed that 

 fixed air is the heaviest of the gases, and de 

 structive to flame and animal life, is it not gra 

 tifying to perceive this invisible fluid poured from 

 one vessel to another, and when poured on the 

 flame of a candle that it instantly extinguishes 

 it ? Many of the deductions of natural science 

 are so wonderful, and so unlike every thing we 

 should have previously conceived, that to the un 

 tutored mind they appear almost incredible, and 

 little short of unfounded and extravagant asser 

 tions. When such a one is told that &quot; any 

 quantity of liquid, however small, will counter 

 poise any quantity, however great,&quot; that the 

 rubbing of a glass cylinder against a cushion 

 will produce the effect of setting fire to spirits 

 of wine, or of bursting a bladder of air at the 

 distance of a hundred feet from the machine 

 that the galvanic agency will produce a violent 

 and uncommon effect upon the nervous and mus 

 cular system and that in certain vegetable in- 

 fusions, myriads of animals of various forms, 

 may be seen a thousand times less than the 

 smallest visible point such assertions are apt 

 to stagger his belief as improbable and extrava 

 gant. But when he actually sees in the first 

 case, a large hogshead that would hold above a 

 hundred gallons, filled with water, and a long 

 tube whose bore is not half an inch in diameter, 

 firmly inserted into its top, and a small quantity 

 of water scarcely exceeding a quart, poured into 

 the tube and then beholds the top rapidly 

 swelling, and in a few moments, the whole cask 

 burst to pieces, and the water scattered in every 

 direction, or in the second case, when he sees 

 alcohol suddenly taking fire, and a bladder filled 

 with oxygen and hydrogen gas, exploding with a 

 tremendous report, merely by the turning of the 

 electrical machine at the other end of a long 

 hall, and the interposition of a wire, or, when 

 in the third case, he sees a person drink a glass 

 of porter which has a wire around it connected 

 with a galvanic battery, and at a certain stage 

 of the operation, receive a tremendous concus 

 sion, which makes him start and roar like a 

 madman, or, in the last case, when he looks 

 through a powerful microscope, and perceives 

 hundreds of mites like so many young pigs, 

 clambering among rocks of cheese, and thou 

 sands of fishes in a drop of water such experi 

 mental illustrations of the truths of science, can 

 not fail to prove highly satisfactory, and to atlbrd 



