PLEASURES OF SCIENCE. \\^ J T "$& I T Y 



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solid part, the earth or water, be removed, for then it 

 of air bounded by four walls or hedges ; but suppose the* 1 

 hedges were removed, and a mark only left at each corner, still it would 

 be true that the space enclosed or bounded by the lines supposed to be 

 drawn between the four marks was 10,000 square yards in size. But 

 the marks need not be there ; you only want them while measuring one 

 side; if they were gone, it would be equally true that the lines, sup- 

 posed to be drawn from the places where the marks had been, enclose 

 1 0,000 square yards of air. But if there were no air, and consequently 

 a mere void, or empty space, it would be equally true that this space 

 is of the size you had found it to be by measuring the distance of one 

 point from another, of one of the space's corners or angles from another, 

 and then multiplying that distance by itself. In the same way it would 

 be true, that if the space were circular, its size, compared with another 

 circular space of half its diameter, would be four times larger ; of one 

 third its diameter, nine times larger, and of one fourth sixteen times, 

 and so on always in proportion to the squares of the diameters ; and 

 that the length of the circumference, the number of feet or yards in the 

 line round the surface, would be twice the length of a circle whose dia- 

 meter was one half, thrice the circumference of one whose diameter was 

 one third, four times the circumference of one whose diameter was one 

 fourth, and so on, in the simple proportion of the diameters. There- 

 fore every property which is proved to belong to figures belongs to 

 them without the smallest relation to bodies or matter of any kind, 

 although we generally see figures in connection with bodies ; but all 

 those properties would be equally true, if no such thing as matter or 

 bodies existed ; and the same may be said of the properties of number, 

 the other great branch of the mathematics. When we speak of twice 

 two, and say it makes four, we affirm this without thinking of two 

 horses, or two balls, or two trees ; but two of any thing and every thing 

 equally. Nay, this branch of mathematics may be said to apply still 

 more extensively than even the other ; for it has no relation to space, 

 which geometry has ; and, therefore, it is applicable to cases where 

 figure and size are wholly out of the question. Thus you can speak 

 of two dreams, or two ideas, or two minds, and can calculate respect- 

 ing them just as you would respecting so many bodies; and the pro- 

 perties you find belonging to numbers, will belong to those numbers 

 when applied to things that have no outward or visible or perceivable 

 existence, and cannot even be said to be in any particular place, just as 

 much as the same numbers applied to actual bodies which maybe seen 

 and touched. 



It is quite otherwise with the science which we are now going to 

 consider, Natural Philosophy. This teaches the nature and proper- 

 ties of actually existing substances, their motions, their connections 

 with each other, and their influence on one another. It is sometimes 

 also called Physics,' from the Greek word signifying Nature, though 

 that Greek word is more frequently, in common speech, confined to one 

 particular branch of the science, concerning the bodily health. 



We have, mentioned one distinction between Mathematics and Natu- 

 ral Philosophy, that the former does not depend on the nature and 

 existence of bodies, which the latter entirely does. Another distinc- 



