VOL. XLI.] PHILOSOPHICAL TRANSACTIONS. 515 



A Rule for Jinding the meridional Parts to any Spheroid, with the same Exact- 

 ness as in a Sphere. By Colin Mac Laurin, F. R. S. N° 451, p. 808. 



It was demonstrated long since, that in a sphere the nautical meridian line 

 is a scale of logarithmic tangents of the half complements of the latitudes. The 

 same may be computed with no less exactness to any spheroid by the following 

 rule. 



Let the semidiameter of the equator be to the distance of the focus of the 

 generating ellipse from the centre, as m to i. Let A represent the latitude for 

 which the meridional parts are required, s the sine of this latitude, the radius 



being unit ; find the ark b, whose sine is — ; take the logarithmic tangent of 



half the complement of b from the common tables; subtract this logarithmic 

 tangent from 10.000000, or the logarithmic tangent of 45°; multiply the re- 

 mainder by '■ ^^ &c. and the product subtracted from the meridional 



parts in the sphere, computed in the usual manner for the latitude a, will give 

 the meridional parts expressed in minutes, for the same latitude in the spheroid, 

 provided it is oblate. When the spheroid is oblong, the difference of the me- 

 ridional parts in the sphere and spheroid for the same latitude, is then deter- 

 mined by a circular ark ; but it is not necessary to describe this case at present. 

 Example. — If mm : 1 : : 1000 : 22, then the greatest difference of the meri- 

 dional parts in the sphere and spheroid, is 76.O929 minutes. In other cases it 

 is found by multiplying the remainder above mentioned by II74.078. 



The Parabolic Orbit for the Comet of 1 739, observed by Signor Eustachio Za- 

 notti at Bologna. N° 461, p. 8O9. 



The motion in its own proper orbit was retrograde. 



The perihelion was in 55 5° 1 1' 



The descending node in y 25 18 



The perihelion from the node 69 53 



The comet was in the perihelion June .... 9"* g** 59™ 



descending node July 1 8 4 57 



The perihelion of the comet's orbit was within the sphere of the orbit of 

 Venus, and without that of the orbit of Mercury ; being distant from the sun 

 0.69614 parts of the earth's mean distance from the sun. The plane of the 

 orbit was inclined to the plane of the ecliptic in an angle of 53° 25'. The di- 

 urnal mean motion, according as it is interpreted by Dr. Halley in his Elements 

 of cometical Astronomy, was l'' 5707. 1 



3 u 2 



