314 THE PRINCIPLES OF SCIENCE. 



cal power, a very precise instrument would be useless. 

 Measuring apparatus and mathematical theory should ad- 

 vance paripassu, and with just such precision as the theorist 

 can anticipate results, the experimentalist should be able 

 to compare them with experience. The laborious and scrupu- 

 lously accurate observations of Flamsteed, were the proper 

 complement to the intense mathemetical powers of Newton. 

 Every branch of knowledge commences with quantita- 

 tive notions of a very rude character. After we have far 

 progressed, it is often amusing to look back into the 

 infancy of the science, and contrast present with past 

 methods. At Greenwich Observatory in the present day, 

 the hundredth part of a second is not thought an in- 

 considerable portion of time. The ancient Chaldseans 

 recorded an eclipse to the nearest hour, and even the 

 early Alexandrian astronomers thought it superfluous to 

 distinguish between the edge and centre of the sun. 

 By the introduction of the astrolabe, Ptolemy and the 

 later Alexandrian astronomers could determine the places 

 of the heavenly bodies within about ten minutes of arc. 

 But little progress then ensued for thirteen centuries, 

 until Tycho Brahe made the first -great step towards 

 accuracy, not only by employing better instruments, 

 but even more by ceasing to regard an instrument 

 as correct. Tycho, in fact, determined the errors of his 

 instruments, and corrected his observations. He also took 

 notice of the effects of atmospheric refraction, and suc- 

 ceeded in attaining an accuracy often sixty times as great 

 as that of Ptolemy. Yet Tycho and Hevelius often erred 

 several minutes in the determination of a star's place, and 

 it was a great achievement of Reamer and Flamsteed to 

 reduce this error to seconds. Bradley, the modern Hip- 

 parchus, carried on the improvement, his errors in right 

 ascension being under one second of time, and those of 

 declination under four seconds of arc according to Bessel. 



