52 Memoir upon living and fossil Elephants. 



In order to find the angle subtended by any number of 

 degrees, we have only to nmltiplv the constant part of the 

 formula corresponding to that number in the table by AB, 

 or the angle subtended by the whole field. Thus ifAB is 

 30 minutes, as it happens to be in the micrometer which I 

 have constructed, the angle subtended by 1 degree of the 

 scale will be 30' x '009 = 16| seconds, and the angle sub- 

 tended by 40 degrees v;ill be 30' x '342 = 10^ Xb-Q" ', and 

 by making the calculation it will be found that as the angle 

 to be measured increases, the accuracy of the scale also in- 

 creases ; for when the arch is only 1 or 2 degrees, a variation 

 of 1 degree produces a variation of about 16 seconds in the 

 angle ; whereas when the arch is between 1 70 and 1 SO, the 

 variation of a degree does not produce a change much more 

 than one second in the angle. This is a most important 

 advantage in the circular scale, as in Cavallo's micrometer 

 a limit is necessarily put to the size of the divisions. 



It 15 obvious, from an inspection of fig. 1 , that there is no 

 occasion for turning the circular micrometer round its axis^ 

 becatise the divided circumference lies in every possible di- 

 rection. In fig. 2., foi^ example, if the object has the direc- 

 tion ah it will be measured by the arch aol, and if it lie* 

 in the line cd it will be measured by the arch crd. 



In the circular micrometer which I have been in the habit 

 of using, AB, or the diameter of the field of view, is exactly 

 half an inch, the diameter of the brass tube in which it is 

 fixed is one inch, the length of the tube half an inch, and 

 the degrees of the divided circumference ^^th of an inch. 



I am, sir. 

 Your obedient humble servant, 



Edinburgh, David Brewster, 



September 1, 1807. 



X. Additional Memoir upon living and fossil Elephants, 

 . By M. CuviKR. 



[Continued from vol. xxviii. p. 366.] 



X HAVE endeavoured to represent this progress of dentition 

 in the figures of my Plates (III and IV) of elephants. 



Plate 



