VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 201 



difference may amount to. Suppose a change of 22° of Fahrenheit's ther- 

 mometer, that is, from the freezing point to the moderate air of a summer's 

 night, and a difference of an inch in the height of the barometer ; these two 

 causes both conspiring, which does not often happen, may occasion an alteration 

 of .00096th part of a second in 5, at an altitude of 20° ; but this, being less 

 than the thousandth part of a second, may safely be rejected as a quantity alto- 

 gether insensible. 



Since it may not be always convenient to view those stars at the altitude of 

 20°, it remains to see what effect different altitudes may have : let us then 

 make the most unfavourable supposition, that they may one time be seen in a 

 horizontal position, having before been seen vertical. In this case, as the 

 whole difference of refraction in a difference of 5" of altitude is no more than 

 .0111, provided they are observed not lower than 20°, and the whole difference of 

 the difference of refraction is only .0000 ; the sum .012, when both conspire, 

 not exceeding much the 100th part of a second, may still be rejected as insen- 

 sible. Let us also examine how near the horizon it may be safe to observe such 

 stars. At 10°, for instance, the refraction is 5' 14". 6; the difference for 5" is 

 .0388 ; the joint effect of the changes in the barometer and thermometer is 

 .0034 ; the sum of the whole together amounts to .0422, which is less than 

 half the 10th of a second : now this may either be taken into consideration, -or 

 such low observations may be avoided, as being by no means necessary, and but 

 ill suiting the high powers a telescope proper for this purpose ought to bear. 



The change of position of the earth's axis I consider as an unsurmountable 

 obstacle to taking the parallax of stars by the method of zenith distances : for 

 though refraction is much reduced in the zenith, this change is there no less 

 sensible than in other parts of the heavens ; but as this will always affect our 

 two stars exactly alike, we are entirely freed from this embarrassment. The 

 aberration of light can have no influence of the least consideration on our two 

 stars, as a mere inspection of the tables will show. In a whole degree, its 

 effects, when greatest, amount but to -^ of a second, and consequently in 5" 

 to no more than .0005, or the 2000th part of a second. 



Observations of the relative distance of the two stars that make up a double 

 star being thus cleared of every impediment, are capable of being continually 

 improved by every degree of perfection the telescope may acquire: we can chuse 

 stars that may be viewed sufficiently high to be clear of the vapours that swim 

 near the horizon, and consequently employ the greatest powers our instruments 

 are capable of. From experience I can also affirm, that the stars will bear a 

 much higher degree of magnifying than other celestial objects. Too much has 

 hitherto been taken for granted in optics: every natural philosopher is ready 

 enough to allow the necessity of making experiments, and tracing out the steps 



vol. xv. D D 



