230 Length of a Degree of the Terrestrial Meridian. 



14. After what we have said of the superiority of the method 



founded upon lunar observations, it might be expected that we should 



1 

 adopt oTTc^nH for °^ j but we are not assured that a sufficient number 



of observations have yet been applied, to entitle this value to be re- 

 ceived ; besides, we are deterred by the opinion of Dr. Bowditch, 

 than whose opinion none commands greater deference from all who 

 are acquainted with the splendid monument, which the American 

 mathematician has recently erected to his ovv'n genius, in his transla- 

 tion of the Mecanique Celeste ; a translation for which one ought to 

 be the more grateful, since, with the help of the translator's numer- 

 ous addenda, it is comparatively easy to understand the modus ope- 

 randi of treating the great questions of physical science embodied in 

 the original work of the immortal Laplace. From an elaborate ex- 

 amination of the figure of the earth, Dr. Bowditch concludes that 



1 

 ^TT^ measures the oblateness more nearly than any other fraction, 



and that the corresponding value of the semi-equatorial diameter is 

 3963 miles, and the semi-polar diameter 3950 miles very nearly. 

 These values for a and a, being placed in formula (4) will give us 



68.70859375 miles 



L = ; -■ — 71" . A Ar^g^oon rT- (5). From this WO havc Calculated 



1 — sm.^-^' ^".006033256 ^ ' 



the following table, in which columns A contain the latitudes, and 



columns B the lengths of the corresponding degrees, having their 



middle points at the latitudes given in the table ; the latitudes being 



expressed in degrees, and the values of L in English miles. 



Table of the Length of the Degrees of the Terrestrial Meridian. 



B 



miles 

 68.708594 

 68.708825 

 68.709437 

 68.710484 

 68.711682 

 68.713809 

 68.716079 

 68.718762 

 68.721828 

 68.725£-;4 

 68.729254 

 68.733508 

 68.738175 

 68.743206 

 68.748651 

 68.754413 



B 



miles. 

 68.754413 

 68.760571 

 68.767079 

 68.773936 

 68.781143 

 68.788651; 

 68.796492 

 68.804867J 

 88.8131271 

 68.821841 

 68.830873 

 68.840030 

 68.849762 

 68.859079 

 68.868762 

 68.879873 



I miles. 

 30:68.879873 j45 



3168.890333 46 



32,68.900952 47 



33 68.911889 48 



34'S8.915936 49 



35:68.934127 50 



3668.945492 51 



37168.956968 52 



38 168. 9685.56 

 39,68.980238 

 4068.992048 

 41169.003921 

 4269.015841 

 4369.019492 

 4469.039825 

 45'69.051873 



B 



miles. 

 69.051873 

 69.063873 

 39.075889 

 39.087905 

 39.098250 

 69.111968 

 69.123619 

 59.135317 

 89.146968 

 69.158492 

 69.169889 

 S9.181174 

 )9.192032 

 59.203206 

 !39. 213984 

 J9.224539 



Al B 

 o miles. 

 6069.224539, 

 6169.234905: 

 6269.2450631 

 63[69. 254951 

 64:69.263220 

 65169.272619; 



69.284145 

 69.291984 

 69.300556 

 69.308771 1 

 69.316492 

 69.324349 

 69.331629 

 69.338587; 

 69.345177! 

 75169.351413! 



B 

 miles. 

 69.351413 

 69.357302 

 69.362809 

 69.367936 

 69.372651 

 69.377000 

 69.380936 

 69.384492 

 69.387635 

 69.390371 

 69.392683 

 69.394556 

 69.396048 

 69.396889 

 89 1 69.397746 

 90 '69.397594 



