64 Refusions on theitew Planets 



diftant from that body 4 + [ a ~ . 3 ] : or, if we exprefs, as 



profeflbr Wiirm has done*, the meari diftance of the firft 

 planet by a, the difference between the diftance of the firft 

 and fecond by b, and the mean diftance of the earth from 

 the fun by J, the mean diflance of the «'^ planet from the 



fun will be = a + ( a ~ ib\i 



This law is founded on tio known theory^ at lead it has 

 never yet been demonftrated mathnjiatically;, and is merely 

 deduced empirically frotn imalcgical coiiclujions. In no fai- 

 ence have the powers of the human mind, merelv by mathe- 

 matical reafoning and the acutenefs of geometrical refleftion, 

 produced fo many, fo certain, and fo pure truths as in aftro- 

 iiomy. When we confuicr the inimenfity and exalted nature 

 of the objefts on which this fcience is employed, and the 

 infignificance of man and his tcrreflrial habitation, together 

 with the endlefs variely and concatenation of the celedial 

 phenomena, which all take place in confcquence of one 

 general very fimple law of nature, that of gravity, diffufcd 

 throughout the whole creation ; and when wc refleiht what 

 abftrufe mathematical formula; and methods muft be invented 

 to fubje£l thefe fo varioufly combined phicnomena to cal- 

 culation, and to obtain a uniform and continual correfpond- 

 ence of thele calculations with what a6lunllv takes place in 

 the heavens, it muft be acknowledged, that no fcience does 

 more honour to the himian genius; that in no fcience have 

 more difcoveries been made ?/ ^r/orz; and that no fcience is 

 founded on more incontrovertible proofs than the exalted 

 fcience of aftronomyf . 



The mathematical aflronomcrs, for there are fome who 

 are not fo, do not readily adopt any thing that cannot be 

 mathematically proved. However great, therefore, might be 

 the probabilitv that the above-mentioned relation, in regard 

 to the didance.- of the planets, taking it at leaft as an ap- 

 proximation, exifted in nature, there were aflronomcrs who 

 doubted the confequences of this undemonftrated law, and 

 the exiftence of an invifible planet between Mars and Jupiter, 



"^ Berlin Aftron. J,-'hre Buchc, 1790, p. 168. 



•f- I^a Hdce, that cinineur analvft) in tlie preface to his excellent work, . 

 ipe.iking of the prot;rei\ ot the modern chcmiiiry, iayj ; Et ce i)e fera qu'au 

 moment oi les loix dc;, M(hniti:<; cliimiqiics IcVdn't fnffi(":imment obiervces, 

 pour y .ippliquer r"analyfe, ciue cettq fcience (lachiinie) aiira Ic degrc de per- 

 fc<',tion auquci rHltroiioinie s'cft clevce par la cJecouvcrtc de la gravitation 

 univei-lllle. Ibfotu du Moiivtment et u'e la Fi^iiw cUiptKiuc U<-i Pla»tles, 



It 



