132 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS 



erly, dismiss it as an "accident." As another example, consider how in 

 the early 19th century Prout called attention to a relation (among 

 chemical atomic weights) which, aside from a few notable excep- 

 tions, seemed too frequently approximated to be dismissed as an 

 "accident." No generally convincing theoretic explanation of this re- 

 lation ha\dng been given by the end of the century, most scientists 

 were then inclined to dismiss it. Today, having acquired a theoretic 

 interpretation, the relation is again deemed of some significance. 

 Following is an even more striking illustration of the influence of 

 theories on the appraisal of laws that seem to hang on the borderline 

 between significance and happenstance. 



The Bode-Titus law. In 1772 Titus announced the disco\'ery of a 

 relation among die orbital radii of the six planets then known. The 

 nature of this relation is displayed in tlie accompanying table, in 

 which the radial distances are expressed in tenths of an astronomical 



A series term -\- 4 = Total Observed orbital radius 



unit. The near equality of the numbers in die second and third col- 

 umns is amply impressive. Is it significant? Bode, who thought it 

 might be, set out to discover an as yet unobserved planet which, ac- 

 cording to the relation, should be found between Mars and Jupiter. 

 And to be sure Ceres and, subsequently, a multitude of other aster- 

 oids (presumed to be the fragments of an extinct planet) were found, 

 by various astronomers, in precisely the region predicted by the re- 

 lation. This, taken together with the somewhat earlier discovery of 

 Uranus (which has an orbital radius of 192, within 2% of that pre- 

 dicted by the relation) seemed to place the Bode-Titus law beyond 

 all doubt. 



Subsequently the tide turned. Two outer planets, Neptune and 

 Pluto, were found with orbital radii diverging 20% and 100%, respec- 



