On Calamopora in gravel deposits near Ann Arbor, Mich. 389 



have deceived many eminent mathematicians and even Newton 

 himself and Euler. But D'Alembert and Carnot have both 

 pointed out its erroneous nature. D'Alembert states the pro- 

 portion 1:— 1:: — 1:1, and observes that if —1 be less than 

 nothing, then it must be less than +1, and we should have a 

 greater number standing to a less in the same relation as a less 

 to a greater, which would be an absurdity. Therefore -1 is not 

 a less number than +1. Carnot considers this reasoning of 

 D'Alembert unanswerable, and has himself proved the same in an 

 equally ingenious manner. If —3 be less than nothing it must 

 be less than +2. But (-3)=' =9 and (+2)^=4. Therefore the 

 square of the less number would be greater than the square of 

 the greater, which is absurd.* 



Clearly, therefore, it cannot be maintained that negative num- 

 bers are less than nothing. Taken in an isolated sense, they are 

 mere mathematical abstractions, but considered m connection 

 with the operations by which they were produced, they are full 

 of significance. 



Philadelphia, Sept. 26, 1862. 



Art. XXXVL— Description of Calamopora, found in the gravel 

 ■ ' Michigan, with some introductory re- 

 irks; by Carl Eomixger, M.D. 



deposits near Ann Arbor, 



The alluvial deposits are to me at present the only accessible 

 source for palffiontological study, the nearest stratified rocks be- 

 ing 40 miles distant from my location. In passing a f avel-pit, 

 I used to feel a sort of dissatisfaction, because strata of older de- 



I hidden from my ^ 



1 have 



learned to admire the gravel exposures as a sort of a cabinet, 

 comprising the whole Paleozoic fauna. It is true, that cabinet is 

 in bad order, but fortunately its specimens are so well labelled, 

 that even the effects of a deluge could not destroy the marks, 

 and so, with care, order can be restored. The genus Calamopora 

 or Favosites is very abundantly represented and its sUicitied 

 specimens are frequently so finely preserved that to study their 

 organization, no better material could be wished lor. 



ent advanced by Cam. 

 e in the original. " Je 



S^i 



