atcr. ii.] DISSERTATION SECOND. 75 



science were discovered at the expense of so much labour 

 and patience, or with the exertion of more ingenuity and 

 invention in imagining and combining observations. These 

 discoveries were all made before Bacon wrote, but he is 

 silent concerning them ; for the want of mathematical know- 

 ledge concealed from his view some of the most splendid 

 and interesting parts of science. 



Astronomy is full of such collective instances, and af- 

 fords them, indeed, of the second and third order, that is 

 to say, two or three times generalized. The astronomer 

 observes nothing but that a certain luminous disk, or per- 

 haps merely a luminous point, is in a certain position, in 

 respect of the planes of the meridian and the horizon, at a 

 certain moment of time. By comparing a number of such 

 observations, he finds that this luminous point moves in a 

 certain plane, with a certain velocity, and performs a revo- 

 lution in a certain time. Thus, the periodick time of a 

 planet is itself a collective fact, or a single fact expressing 

 the result of many hundred observations. This holds 

 with respect to each planet, and with respect to each ele- 

 ment, as it is called, of the planet's orbit, every one of 

 which is a general fact, expressing the result of an indefi- 

 nite number of particulars. This holds still more remark- 

 ably of the inferences which extend to the distances of the 

 planet from the earth, or from the sun. The laws of Kep- 

 ler are therefore collective facts of the second, or even a 

 higher order ; or such as comprehend a great number of 

 general facts, each of which is itself a general fact, includ- 

 ing many particulars. It is much to the credit of astrono- 

 ?ny, that, in all this process, no degree of truth or certain- 

 ty is sacrificed ; and that the same demonstrative evidence 

 is preserved from the lowest to the highest point. No- 

 thing but the use of mathematical reasoning could secure 

 this advantage to any of the sciences. 



