FAVOURABLE TO THE INVESTIGATION OF PARALLAX. 
355 
Table headed “ Difference,” should induce us to suspect the existence of a sensible 
parallax in any of the objects observed, two points are to be considered, — first, the 
amount of those changes, as compared with the probable error of the results them- 
selves ; and secondly, their direction, considered with reference to the motion of the 
earth in her orbit. 
As to the first point, it would appear, that except the change observed bear a very 
large proportion to the probable error of the determination, it may be justly treated with 
little respect, so far as the evidence to be derived from amount only be concerned. 
This conclusion is supported, first, by the great discordances between the partial 
differences, in the instances of the three stars, llSTauri, 100 Herculis, and I of H 95, 
the only objects that can be said to have been satisfactorily observed, if the delicate 
nature of the investigation be considered. 
2ndly. These discordances are the more remarkable, when we view them in connec- 
tion with the large ratios which some of the differences bear to their probable errors. 
Indeed a bare inspection of the measured angles of position given in Table I. in 
connexion with the computed weights and errors, will convince us that the differ- 
ences of the results obtained on different evenings are greater in many instances 
than those of the separate measures obtained on the same evening. This circum- 
stance, which, it is believed, is not unfrequent in observations requiring the same 
delicacy of estimation as those under consideration, renders the application of the 
calculus of probabilities embarrassing and its conclusions uncertain. It is certain, in 
fact, that in the greater number of instances given in this paper, the computed pro- 
bable errors of the results on which the parallaxes depend, form no probable crite- 
rion of the magnitude or even of the existence of parallax. The only probable ex- 
planation that can be given in such cases, where purely instrumental errors can 
scarcely have place, must arise from an unsuspected bias of the observer in the selec- 
tion of the line of direction passing through the centres of the stars, which causes an 
estimation constant on the same evening, but differing on different nights. The 
weight of each evening’s result, calculated according to the amount of discordance of 
the individual measures, may still be an adequate representative of the degree of 
dependence to be placed on it, as far as the steadiness of the atmosphere and other 
favourable circumstances are concerned ; but the probable errors of combined and 
final results, calculated on ordinary principles, will not form a good criterion of the 
accuracy of such results. Supposing, however, the bias of the observer on different 
evenings likely to be as often in excess as in defect, or not to be of the nature of a 
constant error, a better estimation of the probable error of the final means would be 
obtained by considering each evening’s set of measures as a single result without 
regard to their number, and then comparing the separate results in the usual way*. 
If the results in the present paper had been of a more positive character, a re-reduc- 
tion of some of them on this principle might have been desirable, but as the case 
stands this explanation is sufficient. It is proper to add, that I have no reason to 
* Putting^ for the probable error of 10 sets of 118 Tauri for the early period, treated as individual measures, 
andp' for the mean of the probable errors, as given in Table I., of the same sets, p 24 : 15. In the case 
of 10 sets of I of H 95 for the late period, p :y : : 11 : 9. 
