98 THE POPULAR SCIENCE MONTHLY. 



hitherto known have been expressed qualitatively, with a little allow- 

 ance for error on either side. Things which are let go fall to the 

 ground. A very observant man may know also that they fall faster 

 as they go along. But our student is shown that, after falling for one 

 second in a vacuum, a body ia going at the rate of thirty-two feet per 

 second ; that after falling for two seconds it is going twice as fast ; 

 after going two and a half seconds, two and a half times as fast. If 

 he makes the experiment, and finds a single inch per second too much 

 or too little in the rate, one of two things must have happened: either 

 the law of falling bodies has been wrongly stated, or the experiment is 

 not accurate there is some mistake. He finds reason to think that 

 the latter is always the case : the more carefully he goes to work, the 

 more of the error turns out to belong to the experiment. Again, he 

 may know that water consists of two gases, oxygen and hydrogen, 

 combined ; but he now learns that two pints of steam at a temperature 

 of 150 centigrade will always make two pints of hydrogen and one 

 pint of oxygen at the same temperature, all of them being pressed as 

 much as the atmosphere is pressed. If he makes the experiment and 

 gets rather more or less than a pint of oxygen, is the law disproved ? 

 No ; the steam was impure, or there was some mistake. Myriads of 

 analyses attest the law of combining volumes ; the more carefully they 

 are made, the more nearly they coincide with it. The aspects of the 

 faces of a crystal are connected together by a geometrical law, by 

 which, four of them being given, the rest can be found. The place of 

 a planet at a given time is calculated by the law of gravitation ; if it is 

 half a second wrong, the fault is in the instrument, the observer, the 

 clock, or the law ; now, the more observations are made, the more of 

 this fault is brought home to the instrument, the observer, and the 

 clock. It is no wonder, then, that our student, contemplating these 

 and many like instances, should be led to say : " I have been short- 

 sighted ; but I have now put on the spectacles of science which Nature 

 had prepared for my eyes ; I see that things have definite outlines, that 

 the world is ruled by exact and rigid mathematical laws ; nai ov, deoc, 

 yewfierpetc." It is our business to consider whether he is right in so 

 concluding. Is the uniformity of Nature absolutely exact, or only 

 more exact than our experiments ? 



At this point we have to make a very important distinction. There 

 are two ways in which a law may be inaccurate. The first way is 

 exemplified by that law of Galileo which I mentioned just now : that 

 a body falling in vacuo acquires equal increase in velocity in equal 

 times. No matter how many feet per second it is going, after an 

 interval of a second it will be going thirty-two more feet per second. 

 "We now know that this rate of increase is not exactly the same at 

 different heights, that it depends upon the distance of the body from 

 the centre of the earth ; so that the law is only approximate; instead 

 of the increase of velocity being exactly equal in equal times, it itself 



