292 THE PRINCIPLES OF SCIENCE. [CHAP. 



in observing the motion of waves in water. If the canal 

 in which the experiments are made be short, say twenty 

 feet long, the waves will pass through it so rapidly that 

 an observation of one length, as practised by Walker, will 

 be subject to much terminal error, even when the observer 

 is very skilful. But it is a result of the undulatory theory 

 that a wave is unaltered, and loses no time by com- 

 plete reflection, so that it may be allowed to travel back- 

 wards and forwards in the same canal, and its motion, say 

 through sixty lengths, or 1200 feet, may be observed with 

 the same accuracy as in a canal 1200 feet long, with the 

 advantage of greater uniformity in the condition of the 

 canal and water. 1 It is always desirable, if possible, to 

 bring an experiment into a small compass, so that it 

 may be well under command, and yet we may often 

 by repetition enjoy at the same time the advantage of 

 extensive trial 



One reason of the great accuracy of weighing with a 

 good balance is the fact, that weights placed in the same 

 scale are naturally added together without the slightest 

 error. There is no difficulty in the precise juxtaposition 

 of two grams, but the juxtaposition of two metre mea- 

 sures can only be effected with tolerable accuracy, by the 

 use of microscopes and many precautions. Hence, the 

 extreme trouble and cost attaching to the exact measure- 

 ment of fv base line for a survey, the risk of error entering 

 at every 'juxtaposition of the measuring bars, and inde- 

 fatigable attention to all the requisite precautions being 

 necessary throughout the operation, 



Measurements by Natural Coincidence. 



In certain cases a peculiar conjunction of circumstances 

 enables us to dispense more or less with instrumental 

 aids, and to obtain very exact numerical results in the 

 simplest manner. The mere fact, for instance, that no 

 human being has ever seen a different face of the moon 

 from that familiar to us, conclusively proves that the 

 period of rotation of the moon on its own axis is equal 



1 Airy, On Tides and Waves, Encyclopaedia Metropolitans, p. 345. 

 Scott Russell, British Association Report, 1837, p. 432. 



