The general Characteristics of the frequencyfunction of stellar movements 33 



By equations (55*) (30*) and the four first of equations (16) we have for the 

 observed membra the forms 



V B 30 = a n g 3 + a n (I - r/ 2 ) q' + a l3 (2 - 3q' + q") 

 (m V B 21 = b u q* + & 12 (1 - q") q + b n (2 - 3q> + q'») 

 1 j ^ 3 ^ 2 =c ll3 ' 3 +f 12 (l-g' 2 )g' + Cl3 (2-3 3 '+g' 3 ) 



V B 05 = d n q' s + d n (1 - g' 2 ) g' + d lt (2 - 3g' + g' 3 ) 



where the coefficients are expressed in the moments of apparent motion as follows: 

 «ii = — v 3o : 6 \\ = — v i2 : 2 



«12 = + V 20 *0 1 2 b n = + (i/o V 20 + 2a3 0 V ll) : 2 



«i3 = — V : 6 b n = — V y 0 : 2 



hi = — V 12 : 2 ^11 = — V 03 : 6 



C 12 = (*0 V 02 + 2 V0 V ll) : 2 d l»= Vi i/0 : 2 



c i3 = — ®o 2/o 2 : 2 ^13 = — //o 3 : 6 



Applying the method of least squares to (64) and letting ft, and q remain 

 undetermined we finally arrive at the forms for the unknowns 



(65*) V B ijk = flg q* + Hg (1 - g' 2 ) 5' + fl£ (1 - 32' + tf' 3 ) 



*+i + fc = 3. 



16. The corresponding equations of condition for the characteristics of the 

 fourth order may be written for each square: 

 (66) 



B 40 = a 'i ^"400 + a \ B "oio + a 's B"ooi + a i B" no + a 'b B '\os + a '.: ^"310 + a 'i B "soi + 



+ a 'gB" 0l3 + ÖS' 9 B" 031 + «'10-^220 + rt 'll ^"202 + ö 'l2^"o22 + a 'l% B '\u + 



+ «'i4- B "i2i + a'i5 B "ii2) 



A>4 = &'i*"«0 + &',B"o*0 + &' 3 ^"004 + &' 4 #"l80 + ^5 ^"l03 + '>'« ^" 3 1U + & # 7 ^" 3 01 + 

 + b '* B "oi3 + V* B '\n + h \o B '\iO + & 'll^"202 + & 'l2^"o22 + ?/ 13 ^" 2 11 + 



+"&' U B" M1 + 



fi si = e \ B '\m + c '2 B "oao + c ' 3 ß "oo4 + c 'i B "iso + c ';, B "ios + c' 6 B" 310 + c' 7 B" 301 + 



+ C ',8 B "oi3 + C' 9 #"081 + C'iO-S'mO + C 'll B "^2 + <M2 B "o22 + C ' IS B " 211 + 

 + C 'l4 5 "i21 + C 'l5^"ll2' 

 B 1S = d\ £" 400 + d', B" 040 + d', B"o04 + ^4 #" 13 0 + ^6 B ".03 + rf'e ß "s,o + <*\ S" 301 + 



+ d' 8 -B" 013 + tf" 9 £" 031 + d' 10 B" 220 + d' n £" 202 + d' V2 B" 022 +d\ s B" ni -\- 



+ ^'l4 5 "l21 + ^lö^'l^S 



B 22 = e'i-B"^ + e' 2 5" 040 + e' 3 B" 004 + e' 4 5" 130 + e' 5 B" 103 + e' 6 B" J10 + e' 7 ^" 301 + 



H~ e 's-^"oi3 + e 9-^ 031 + e ' 10 B " -I'M H~ e 'll 



-B" 202 + e' 12 B" 022 + e' 18 J8" ail + 



112 ' 



and the coefficients are expressed in the direction cosines as follows 

 (T.i = 0): 



Lunds Universitets Ârskrift. N. P. Afd. 2. Bil 11. 5 



