290 THE PRINCIPLES OF SCIENCE. [CHAP. 



found preferable to take a shorter interval, rather than 

 incur the risk of greater instrumental errors in the earlier 

 observations. 



It is obvious that many of the slower changes of the 

 heavenly bodies must require the lapse of large intervals 

 of time to render their amount perceptible. Hipparchus 

 could not possibly have discovered the smaller inequalities 

 of the heavenly motions, because there were no previous 

 observations of sufficient age or exactness to exhibit them. 

 And just as the observations of Hipparchus formed the 

 starting-point for subsequent comparisons, so a large part 

 of the labour of present astronomers is directed to record- 

 ing the present state of the heavens so exactly, that future 

 generations of astronomers may detect changes, which 

 cannot possibly become known in the present age. 



The principle of repetition was very ingeniously em- 

 ployed in an instrument first proposed by Mayer in 1767, 

 and carried into practice in the Repeating Circle of Borda. 

 The exact measurement of angles is indispensable, not 

 only in astronomy but also in trigonometrical surveys, and 

 the highest skill in the mechanical execution of the gradu- 

 ated circle and telescope will not prevent terminal errors 

 of considerable amount. If instead of one telescope, the 

 circle be provided with two similar telescopes, these may 

 be alternately directed to two distant points, say the 

 marks in a trigonometrical survey, so that the circle shall 

 be turned through any multiple of the angle subtended 

 by those marks, before the amount of the angular revolu- 

 tion is read off upon the graduated circle. Theoretically 

 speaking, all error arising from imperfect graduation might 

 thus be indefinitely reduced, being divided by the number 

 of repetitions. In practice, the advantage of the invention 

 is not found to be very great, probably because a certain 

 error is introduced at each observation in the changing 

 and fixing of the telescopes. It is moreover inapplicable 

 to moving objects like the heavenly bodies, so that its use 

 is confined to important trigonometrical surveys. 



The pendulum is the most perfect of all instruments, 

 chiefly because it admits of almost endless repetition. 

 Since the force of gravity never ceases, one swing of the 

 pendulum is no sooner ended than the other is begun, 

 so that the juxtaposition of successive units is absolutely 



