sivi INTRODUCTORY DISCOURSE OF THE 



yet lighter than water, and which, without any heating, tako fire upon being exposed to the air, ami, by 

 burning, form the. substance so abounding in saltpetre aud iu the ashes of burnt wood : tlicse, surely, aro 

 things to excite the wouder of any reflecting mind nay, of any one but little accustomed to reflect. Aud 

 yet these are trifling when compared to the prodigies which Astronomy opens to our view : the enormous 

 masses of the heavenly bodies ; their immense distances ; their countless numbers, aud their motions, whose 

 swiftness mocks the uttermost eflbrts of the imagination. 



Akin to the pleasure of contemplating new and extraordinary truths, is the gratification of a moro 

 learned curiosity, by tracing resemblances and relations between things, which, to common apprehension, 

 eccm widely difl'creut. Mathematical science, to thinking minds, affords this pleasure iu a high degree. It 

 is agreeable to know that the three angles of every triangle, whatever bo its size, howsoever its sides may 

 be inclined to each other, aro always, of necessity, when taken together, the same- in amount : that any 

 regular kind ol figure whatever, upon the one side of a right-angled triangle, is equal to the two figures of 

 the same kind upon the two other sides, whatever bo the size of the triangle : that the properties of an oval 

 curve are extremely similar to those of a curve which appears tho least like it of any, consisting of two 

 branches of infinite extent, with their backs turned to each other. To trace such unexpected resemblances 

 is, indeed, tho object of all philosophy ; and experimental science, in particular, is occupied with such 

 investigations, giving us general views, and enabling us to explain the appearances of nature; that is, to 

 show how one appearance is connected with another. But we are now considering only the gratification 

 derived from learning these things. It is surely a satisfaction, for instance, to know that the same thing, 

 or motion, or whatever it is, which causes the sensation of heat, causes also fluidity, and expands bodies in 

 all directions; that electricity, the light which is seen on the back of a cat when slightly rubbed on a frosty 

 evening, is the very same matter with tho lightning of the clouds ; that plants breathe like ourselves, but 

 differently by day and by night ; that the air which burns in our lamps enables a balloon to mount, aud 

 causes the globules of the dust of plants to rise, float through the air, and continue their race iu a word, is 

 the immediate cause of vegetation. Nothing can at first view appear less like, or less likely to be caused by 

 the same thing, than the processes of burning and of breathing the rust of metals and burning an acid 

 and rust the influence of a plant on the air it grows in by night, and of an animal on tho same air at any 

 time, nay, and of a body burning in that air; aud yet all these are the same operation. It is an undeniable 

 fact, that the very same thing which makes the fire burn, makes metals rust, forms acids, and enables plants 

 and animals to breathe ; that these operations, so unlike to common eyes, when examined by the light of 

 science, are the same tho rusting of metals the formation of acids the burning of inflammable bodies 

 the breathing of animals and the growth of plants by night. To know this is a positive gratification. Is 

 it not pleasing to find the same substance in various situations extremely unlike each other ; to meet with 

 fixed air as the produce of burning, of breathing, and of vegetation : to find that it is the choke-damp of 

 mines, the bad air iu the grotto at Naples, the cause of death in neglecting brewers' vats, and of tho brisk 

 and acid flavour of Seltzer and other mineral springs ? Nothing can bo less like than the working of a vast 

 (team-engine of the old construction, aud the crawling of a fly upon the window. Yet we find that these 

 two operations are performed by the same means, the weight of tho atmosphere, and that a sea-horse climbs 

 the ice-hills by no other power. Can anything be more strange to contemplate ? Is there, in all tho fairy- 

 tales that ever were fancied, anything moro calculated to arrest the attention and to occupy and to gratify 

 the mind, than this most unexpected resemblance between things so unlike to tho eyes of ordinary 

 beholders ? What more pleasing occupation than to see uncovered and bared before our eyes the very 

 instrument and the process by which Nature works? Then we raise our views to tho structure of the 

 heavens ; and are again gratified by tracing accurate, but most unexpected resemblances. Is it not iu the 

 highest degree interesting to find, that tho power which keeps this earth in its shape, and in its path, 

 wheeling upon its axis and round the sun, extends over all the other worlds that compose tho universe, and 

 gives to each its proper place and motion ; that this same power keeps the moon in her path round our 

 earth, and our earth in its path round the sun, and each planet in its path ; that the same power causes the 

 tides upon our globe, and the peculiar form of the globe itself; and that, after all, it is tho same power 

 which makes a stone fall to the ground ? To learn these things, and to reflect upon them, occupies the 

 faculties, fills the mind, and produces certain as well as pure gratification. 



But if the knowledge of tho doctrines unfolded by science be pleasing, so is tho being able to trace the 

 steps by which those doctrines are investigated, and their truth demonstrated : indeed, you cannot be said, 

 in any sense of the word, to have learnt them, or to know them, if you have not so studied them as to per- 

 ceive how they are proved. Without this you never can expect to remember them long, or to understand 

 them accurately ; and that would of itself be reason enough for examining closely the grounds they rest ou. 

 But there is the highest gratification of all, iu being able to see distinctly those grounds, so as to be satisfied 

 that a belief in the doctrines is well founded. Hence to follow a demonstration of a grand mathematical 

 truth to perceive how clearly and how inevitably one step succeeds another, aud how the whole steps lead 

 to the conclusion to observe how certainly and unerringly the reasoning 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, 



