COMETS. 



17 



Table III. On the Elliptical Motion of Comets. — Continued. 



Dist. 

 900 

 901 

 902 

 903 

 904 

 905 

 906 



Time. 



Dist. 



Time. 



Dist. 



923 



924 

 925 

 926 

 927 

 928 

 929 



Time. 

 325639 



Dist. 

 .934 



Time. 



Dist. 



Time. 



Dist. 

 956 



Time. 



Dist. 



Time. 

 384992 

 386728 

 388493 

 390288 

 3921 14 

 393972 

 395865 



Dist. 



978 



979 

 980 

 981 

 982 

 983 

 984 



Time. 



Dist.| Time. 



302091 



303C47 

 •04011 

 304980 

 305954 

 306933 

 3079*9 



912 

 Q\3 

 914 

 915 

 916 

 917 

 918 



313957 



338267 



9*5 



352079 



367460 



967 

 968 

 969 

 970 



971 

 972 

 973 



405921 

 408069 

 410270 

 412527 

 414845 

 417231 

 419687 



989433353 



314984 

 316018 

 3170.59 

 318107 

 319161 

 320223 



326745 

 327859 

 32898! 

 330111 

 331250 

 332397^ 



.935 



936 

 937 

 938 

 .939 

 940 



339470 

 340681 

 341904 

 343137 

 344378 

 345635 



946 

 947 

 948 

 949 

 950 

 951 



353404 

 354744 

 356097 

 357463 

 358843 

 360253 



957 

 958 



959 

 960 

 961 

 963 



368956 

 370451 

 371981 

 373530 

 375099 

 37669] 



990 

 991 

 992 

 993 

 994 

 995 



436444 

 439696 

 443135 

 446799 

 450737 

 155022 



907 

 908 

 909 

 910 



9 ; l 

 912 



30891'' 

 309907 

 310910 

 31199 

 312Q34 

 313957 



919 

 920 

 921 

 922 

 923 



321291 

 322369 

 323430 

 324541 

 325639 



930 

 931 

 932 

 933 

 934 



833553 



334717 

 33589! 

 337074 

 SS8267 



941 



912 

 943 

 941 

 945 



346900 

 348177 

 349466 

 350766 

 352079 



952 

 953 

 954 

 955 

 956 



361668 

 363089 

 364530 

 265999 

 367460 



96, 

 964 

 965 

 966 

 967 



378303 

 379939 

 38 1 600 

 383289 

 384992 



974 

 975 

 976 

 977 

 978 



397795 

 399763 

 401771 

 403824 

 105921 



985 

 986 

 987 

 988 

 989 



422226 

 424850 

 427569 

 430386 

 433353 



996 

 997 

 998 

 999 

 1000 



459763 

 465148 

 471539 

 479872 

 500000 



1 



EXPLANATION OF THE TABLES. 

 Table I. 



The use of this Table is to find the course of a comet, 

 whose perihelion distance is equal to the radius of the 

 earth's orbit. The first column contains the number of 

 days since the comet passed its perihelion ; — the second 

 column contains the true anomaly of the comet, reckon- 

 ed from the perihelion ; — and the third column, the dif- 

 ferences. 



In order to adapt the Table to other parabolic orbits 

 of any form, let the radius of the earth's -orbit zz 1 , and 

 the perihelion distance of the new orbit =r x. Then if 

 we multiply the number of days since the comet passed 



its perihelion in the first column by x., and enter the 

 Table with this new number of days, we shall find in 

 the opposite column the true anomaly corresponding to 

 the given orbit 



On the contrary, if we wish to find from the given 

 time after the passage of the perihelion, the time in the 

 '1 able, and from this the true anomaly, we must divide. 



X 

 the given time by x 1 , in order to obtain the time in the 



Table. 



Example. — If we suppose the perihelion distance of 

 a comet to be 0.5835 = x, and that its true anomaly is 

 required 49 days, 18 hours, 55' and 16" after its passage 

 of the perihelion, . Then reducing the hours and minutes, 

 &c. to decimals of a day, we shall have. 



49.78837 ,,,„„„ , 



— 4 !- = 111.7034.day9, . 



(0.5835)^" 



which may be found by logarithms in the following 



manner: 



Leg. of the perihelion distance 0.5835 . . . 9.7660409 



Half of this logarithm 9.3830204 



Three halves of the log. of the perihel. dis- 

 tance 9.6490613 



Which being subtracted from 49.78837 days 1.6971279 



There remains the log. of 111.7034 days . . 2.0480666 

 With 111.7034 days enter Table I. and correspond- 



\OL. VII, FART I. 



ing to it will be found 90° 38' 57".4, the true anomaly 

 of the comet 49.78837 days before and after its passage, 

 of the perihelion. 



Table IL 



The second Table is computed for the parabolic or- Explana» 

 bit of a comet whose perihelion distance is == 0, or '' OI .\ of ir , 

 whose orbit is a straight line. The first column con- e ** 



tains the distances; the second and fourth the time, and 

 the third the differences. 



This Table is of very general use for all parabolic 

 orbits, and serves to find the time in which a comet 

 describes a given arch, when we know only the three 

 sides of a triangle formed by lines drawn from the sun 

 to the two extremities of the arch. One of these sides 

 is the chord of the arch which we shall call c, and the 

 other two sides which may be called a and b, are the 

 radii vectors, or the distances of the comet from the sun. 

 With these numbers find the values of 



a + b + c 



= vt 



a A c 



— = n 



2 



With these values of m and n enter Table II. and 

 take out the time from the second and fourth columns, 

 and the difference of the times thus found is the time in 

 which the comet would describe the given arch of a pa-, 

 rabola. 



Example. — Let a = 1 ; b = 1 ; c = 2.2361, then 



m = - — = 2.61 805 which gives 



in the Table 116.084 days, 



a A- b — c 



n r= — — 



2 



in the Table . 6.467 days 



= 0.38195 which gives 



109.617 days 



Hence the time in which the arch c is described is 

 109.6117 days, or 109 days, 14 hours, 48'. 



In this Table the cubes of the numbers in the first 

 column are proportional to the squares of the numbers 

 in the second and fourth. 



