NEW STARS. 151 



stratum, is about equal to that distance which, on. a general 

 average, corresponds to the light of a star of the ninth 01 

 tenth magnitude, and certainly does not exceed that corre 

 sponding to the eleventh."* Where, from the peculiar nature 

 of individual problems, measurements and the direct evi- 

 dence of the senses fail, we see but dimly those results which 

 intellectual contemplation, urged forward by an intuitive im- 

 pulse, is ever striving to attain. 



IV. 



NEW STARS AND STARS THAT HAVE VANISHED. VARIABLE STARS, 

 WHOSE RECURRING PERIODS HAVE BEEN DETERMINED. VARIA- 

 TIONS IN THE INTENSITY OF THE LIGHT OF STARS WHOSE PERI- 

 ODICITY IS AS YET UNINVESTIGATED. 



New Stars. The appearance of hitherto unseen stars in 

 the vault of heaven, especially the sudden appearance of 

 strongly-scintillating stars of the first magnitude, is an oc- 

 currence in the realms of space which has ever excited as- 

 tonishment. This astonishment is the greater, in proportion 

 as such an event as the sudden manifestation of what was 

 before invisible, but which nevertheless is supposed to have 

 previously existed, is one of the very rarest phenomena in 

 nature. While, in the three centuries from 1500 to 1800, 

 as many as forty-two comets, visible to the naked eye, have 

 appeared to the inhabitants of the northern hemisphere 

 on an average, fourteen in every hundred years only eight 

 new stars have been observed throughout the same period. 

 The rarity of the latter becomes still more striking when 

 we extend our consideration to yet longer periods. From 

 the completion of the Alphonsine Tables, an important epoch 

 in the history of astronomy, down to the time of William 

 Herschel that is, from 1252 to 1800 the number of visi- 

 ble comets is estimated at about sixty-three, while that of 

 new stars does not amount to more than nine. Consequent- 

 ly, for the period during which, in the civilized countries of 

 Europe, we may depend on possessing a tolerably correct 

 enumeration of both, the proportion of new stars to comets 

 visible to the naked eye is as one to seven. We shall pres- 

 ently show that if from the tailless comets we separate the 

 new stars which, according to the records of Ma-tuan-lin, 



* Observations at the Cape, $ 315. 



