ASTRONOMY. 225 



(*) II. Our second proposition is, that, whilst the pos- 

 sible laws of variation were infinite, the admissible laws, 

 or the laws compatible with the preservation of the system, 

 lay within narrow limits. If the attracting force had va- 

 ried according to any direct law of the distance, let it have 

 been what it would, great destruction and confusion would 

 have taken place. The direct simple proportion of the 

 distance would, it is true, have produced an ellipse ; but 

 the perturbing forces would have acted with so much ad- 

 vantage, as to be continually changing the dimensions of 

 the ellipse, in a manner inconsistent with our terrestrial 

 creation. For instance ; if the planet Saturn, so large and 

 so remote, had attracted the earth, both in proportion to 

 the quantity of matter contained in it, which it does ; and 

 also in any proportion to its distance, i. e. if it iiad pulled 

 the harder for being the further off, (instead of the reverse 

 of it,) it vvould have dragged the globe which we inhabit 

 out of its course, and have perplexed its motions, to a de- 

 gree incompatible with oor security, our enjoyments, and 

 probably our existence. Of the inverse laws, if the cen- 

 tripetal force had changed as the cube of the distance, or 

 in any higher proportion, that is, (for I speak to the un- 

 learned,) if, at double the distance, the attractive force had 

 been diminished to an eighth part, or to less than that, the 

 consequence would have been, that the planets, if they 

 once began to approach the sun, would have fallen into his 

 body; if they once, though by ever so little, increased 

 their distance from the centre, would for ever have receded 

 from it. The laws therefore of attraction, by which a 

 system of revolving bodies could be upheld in their motions, 

 lie within narrow limits, compared with the possible laws. 

 I much underrate the restriction, when I say, that in a 

 scale of a mile they are confined to an inch. ' All direct 

 ratios of the distance are excluded, on account of danger 

 from perturbing forces ; all reciprocal ratios, except what 

 lie beneath the cube of the distance, by the demonstrable 

 consequence, that every, the least change of distance, would, 

 under the operation of such laws, have been fatal to the 

 repose and order of the system. We do not know, that is, 

 v.'e seldom reflect, how interested we are in this matter. 

 Small irregularities may be endured ; but, changes within 

 these limits being allowed for, the permanency of our 

 ellipse is a question of life and death to our whole sensitive 

 world. 



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