LONGITUDE OF McGILL OBSEEVATORY. 



141 



his iustriiment offered peculiar facilities for investigation, was the examination of the 

 law of the variation of the personal equation of the observer, due to the varying velocity 

 and direction of the motion of the star with respect to the threads. His discussion of 

 the material so far obtained has led to the conclusion, which he puts forward simply as a 

 plausible inference, to be held tentatively for future investigation that the personal 

 equation of the observer is a function of the velocity of the star in a direction perpendic- 

 ular to the thread, and that this relation may be expressed by : 



E = a (sec ô sec p) 

 in which a is a constant and jt) is the position angle of the thread. The exponent k, in all 

 the observations thus far examined, appears to be in the neighborhood of one-half, and 

 corresponds to the provisional working hypothesis 



E = a ■y sec tf sec p. 



The interpretation of this expression is that the personal equation in transit observations 

 varies inversely as the square root of the velocity of the star across the thread. In the case of meri- 

 dian observations p = o and the relation becomes 



E = a x^ sec 6. 



It will not escape attention that there are evidences in the present scries of observa- 

 tions, both at Cambridge and at Montreal, of systematic deviations between the values of 

 the clock error depending upon the declination of the star observed. At Montreal, the 

 illumination was not entirely symmetrical for different altitudes. At Cambridge, the 

 source of error most likely to occur, was that due either to a variation in the collimatiou 

 through a movement of the prism in the cube or to the flexure of the instrument. No 

 decisive evidences of error from these causes have been found. It seems probable, there- 

 fore, that the discordances noted, may be in some way connected with the question of 

 variable personal equation. 



As an illustration of the method of reduction described on pp. 137-139, the observations 

 of June 4 are selected. By subtracting the equations for the time stars of each group from 

 the equations for the separate polar stars, and dividing by the co-efficient of c, we find : 



Time. 



Group I. 



Group II. 



Group II.' 



Group III. 



f 13.4 U.C. 



i 13.4 L.C 



g 13.9 L.C. 



X 17.0 i.e. 



0= +0.74 — 1.11a + c 



— .12 + .48a— c 



— .19 + .48a — c 

 ^ .25 + .57a — c 



0= + 0.55— .91a + c 



— .22 + .60o— c 



— .29 + .59a — c 



— .32 + .65a — c 



0= +0.55— .910+ c 



— .23 + .60a — c 



— .30 + .59a — 



— .32 + .65a— p 



0= +0.52— .81a + c 



— .28 + .67a — c 



— .34 + .67a — c 



— .36 + .70a — c 



r 14.2 u.c. 



i 14.9 U.C. 



g 15. S U.C.i 



3 16.2 U.C. 



0=+1.20— .98a — cl 0= +1.10- 

 +1.09— 1.06a— c + .95- 

 + 1.19— .98a— r +1.09- 

 + 1.17 — 1.0.3a— r +1.04- 



L 14.3 i.e. , — .58 + .42a + c 



.68 + 



.H8a — cl- 

 .92a — c '. 

 .SRa — . 

 .90a— r. 

 .53a + c . 



+ 1.04— .78a— c 



+ .78— .80a— -c 



+ 1.03— .79a — r 



+ .95— .SOa — c 



— .81 + .66a + c 



