Objects, Advantages, And Pleasures Of Science.

OBJECTS , ADVANTAGES , AND PLEASURES OF SCIENCE .

( Continued from - page 54 . ) II . DIFFERENCE BETWEEN MATHEMATICAL AND PHYSICAL TRUTHS . 'foil perceive , if you reflect a little , that the science which we have been considering ,

in both its branches , has nothing to do with matter ; that is to say , it does not at all depend upon the properties or even , upon the existence of any bodies or substances whatever . The distance of one point or place from another is a straight

line , and whatever is proved to be true respecting this line , as for instance , its proportion to other lines of the same kind , and its inclination towards them , what we call the angles it makes with them , would be equally true whether there were

anything in those places , at those two points , or not . So if you find the number of yards in a square field , by measuring one side , 100 yards , and then , multiplying that by itself , which makes the whole area 10 , 000 square yards , this is equally true

whatever the field is , whether corn or grass , or rock , or water ; it is equally true if the solid part , the earth or water , be removed , for then it will be a field of air bounded by four walls or hedges ; but the walls or hedges were removed

suppose , and a mark only left at each corner , still it would be true that the space inclosed 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 gotre it would be equally true that the lines supposed to be drawn from the places where the marks had been , inclose

10 , 000 square yards of air . But if there were no air , aud 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 anotherof one of the space ' s

, corners or angles from another , and then multip lying 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 ofvone 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 diameter 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 . Therefore

, 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 are accustomed only to 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 we assert it concerning two of anything and every thing equally . Nay , this branch of mathematics may be said to ajiply still more extensively than even

the other ; for it has no relation to space , which geometry has , and , therefore , it is apjilicable to jilaces 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 respecting

them just as you would respecting so many bodies ; and the properties you find belonging to numbers , will belong to those numbers when ajiplied to things that have no outward or visible or perceivable existenceand cannot even be said to be

, in any particular jilace , just as much as the same numbers applied to actual bodies which may be seen and touched .

It is quite otherwise with the science of Natural Philosophy . This teaches the nature and properties of actually existing substances , their motions , their connections with each other , and their influence on one another . It is sometimes also called Physicsfrom the Greek word signifing

, y Nature , though that word is more frequently , in common speech , confined to one particular branch of the science , that which treats of the bodily health .