MINOR PLANETS DISCOVERED BY WATSON— LEUSCHNEK. 209 



The complete tabulation of the perturbations of (101) Helena, (103) Hera, and (119) 

 Althaea, is, therefore, as follows 



ndz = (ndz), + (ndz) 2 + etc + {ndz) t T—c z 



3 log r = (3 log /■), + (<} log r), + etc . - + (8 log r) t T-Cr 



dp = (£/?), + (<?/?), + etc. . . . + (*/?), T- o 



ARRANGEMENT OF THE TABLES. 



Table I gives the values of the mean anomaly g for January 0.0 of every common year, 

 and for January 1.0 of every leap year from the year of discovery to 1930, and its variations 

 for the different months and days. 



Table II gives the periodic parts of the perturbations of the mean anomaly, designated 

 by (noz)^ (ndz),, etc., for arguments 1, 2, etc., in units of 0?001 and one decimal thereof. 



Table ///gives the periodic parts of the perturbations of the radius vector, designated by 

 (8 log r) lt (3 log r),, etc., for arguments 1, 2, etc., in units of the fifth place and one decimal 

 thereof. 



Table IV gives the periodic parts of the perturbations u c<>s i multiplied by a sin 1", 

 designated by (8p) u (o^),, etc., in units of the fifth decimal place and one decimal thereof. 



Table V gives the perturbations of the mean anomaly, of the radius vector, and of the third 

 coordinate, arising from the terms to be multiplied by T, the time from the epoch expressed in 

 Julian years. These coefficients of the secular parts of the perturbations are designated by 

 (ndz) t , (8 log r) t , and (#),. 



Table VI contains the constants for the equator for the beginning of every year from the 

 date of discovery to 1930, inclusively of the logarithms of the quantities cos a and cos b and 

 cos e, by which the perturbation 8$ must be multiplied to obtain the corrections Jx, Jy, Az to 

 the heliocentric equatorial coordinates ,r, y, and z. 



DIRECTIONS FOR COMPUTING THE PERTURBATIONS n<5z, S log r=log lltl'l, and S/S. 



Let / be the epoch of the mean anomaly g , and let t be the date for which the perturba- 

 tions are to be computed. Let g' be Jupiter's mean anomaly at the date. Let g be the planet's 

 undisturbed mean anomaly at the date. For the date t take g' and g from the Tables A and I, 

 respectively. To form the argument g of the perturbations in tables II-V, apply to Table I the 

 correction J-=r— k . (See p. 203.) 



Form the necessary arguments (ig—i'g') for Tables II to V as indicated on pages 327, 338, 

 or 348. 



Express T=t—t in Julian years and decimals thereof. 



From Tables II-IV take the periodic, parts (n8z)i, (8 log r) it and (8p)f of the perturbations 

 with the arguments (ig—i'g'), in accordance with their designations on pages 327, 338, or 348. 



From Table V take the values of (noz) t , (o log r) t , and (33) t , to be multiplied by T= (t — t ) 

 in Julian years and perform the multiplication. 



Form the sums ndz, 8 log /•, and 8j3, of the periodic and secular parts of the perturbations. 



Subtract the constants c z , c r , and c^, given on pages 327, 338, or 348. 



The disturbed mean anomaly is: 



M=nz=g + n8z. 



EXAMPLE. 



As an example of the use of the tables of (101 ) Helena, (103) Hera, and (119) Althaea, we 

 shall compute the perturbations of (119) Althaea for 1907, December 2.7535, Berlin Mean Time. 



