shew how much more advantageous a machine must be which, with 

 little less steadiness than a transit instrument, is capable of identify- 

 ing the minute stars which are sometimes used as objects of com- 

 parison, to the accuracy of a few seconds. It is true that from the 

 oblique and variable stress to which the polar axis of such an instru- 

 ment is exposed, and the unequal effect of temperature on its sup- 

 ports, it cannot have the precision of a large Vertical Circle ; but 

 leaving to such the almost differential researches connected with 

 parallax and aberration, much remains to be filled up, before we 

 can say that we are acquainted with the Heavens. To accomplish 

 this, with the assistance of a standard catalogue, the machines 

 which we are considering are fully adequate ; and it is surprising 

 when we consider how many of them are in the hands of amateurs 

 that so few results have been obtained by their means : except the 

 Armagh instrument, and that which Mr. South uses with such zeal 

 and ability, none that I know of seem to have contributed any ad- 

 dition to Science. But it must be owned that their use presents 

 certain difficulties; the calculation of refraction and parallax is con- 

 siderably involved, and these corrections affect both declination and 

 right ascension ; the adjustments are more numerous and complex 

 than in vertical instruments^ and much more easily disturbed ; and 

 the absolute impossibility of using a plumb-line for the verifications 

 is unfavorable to accuracy. The refraction apparatus of Ramsden 

 is commonly annexed to them, but it cannot be employed with any 

 regard to the permanence of the coUimation. Some of these in- 

 conveniencies I think I have been able to obviate; and in offer- 

 ing the formulae which I use to the notice of the Academy, if I can 

 induce any person who possesses an equatorial, to take it from its 

 ,pase, and avail himself of its powers, I shall be well rewarded : 



