486 THE PKINCIPLES OF SCIENCE. [CHAP 



10,000 possible trials. If the precision of our measure- 

 ments is increased, so that the one-thousandth part of a 

 degree can be appreciated, our trials may be increased 

 tenfold. The probability of connection will be proportional 

 to the accuracy of our measurements. 



When we can vary the quantity of a cause at will it 

 is easy to discover whether a certain effect is due to that 

 cause or not. We can then make as many irregular 

 changes as we like, and it is quite incredible that the 

 supposed effect should by chance go through exactly the 

 corresponding series of changes except by dependence. 

 If we have a bell ringing in vacuo, the sound increases as 

 we let in the air, and it decreases again as we exhaust the 

 air. Tyndall's singing flames evidently obeyed the direc- 

 tions of his own voice ; and Faraday when he discovered 

 the relation of magnetism and light found that, by making 

 or breaking or reversing the current of the electro-magnet, 

 he had complete command over a ray of light, proving 

 beyond all reasonable doubt the dependence of cause and 

 effect. In such cases it is the perfect coincidence in time 

 between the change in the effect and that in the cause 

 which raises a high improbability of casual coincidence. 



It is by a simple case of variation that we infer the 

 existence of a material connection between two bodies 

 moving with exactly equal velocity, such as the locomo- 

 tive engine and the train which follows it. Elaborate ob- 

 servations were requisite before astronomers could all be 

 convinced that the red hydrogen flames seen during solar 

 eclipses belonged to the sun, and not to the moon's atmo- 

 sphere as Flamsteed assumed. As early as 1706, Stannyan 

 noticed a blood-red streak in an eclipse which he witnessed 

 at Berne, and he asserted that it belonged to the sun ; 

 but his opinion was not finally established until photo- 

 graphs of the eclipse in 1 860, taken by Mr. De la Eue, 

 shewed that the moon's dark body gradually covered the 

 red prominences on one side, and uncovered those on the 

 other ; in short, that these prominences moved precisely as 

 the sun moved, and not as the moon moved. 



Even when we have no means of accurately measuring 

 the variable quantities we may yet be convinced of their 

 connection, if one always varies perceptibty at the same 

 time as the other. Fatigue increases with exertion ; 



