Having had frequent opportunities, during my residence in France, of seeing a great many Repeating Reflecting Circles, several of which I have observed with, and having found much consistency in the results deduced from observations made with them, it occurred to me, that if I could engage Mr Troughton to execute one for me, it would be a most perfect instrument. This he accordingly did; and I trust that the observations made with it, which I am about to communicate, will perfectly justify the opinion I had formed of its precision. The instrument is only of about six inches radius, divided in gold to 20″. I have always been in the habit of choosing for latitudes 30 repetitions, when the weather would permit, divided into three series of 10 each, and reading the angle or arc run through during the series, which completely destroys every imperfection of the division, or reading. In order to determine the time, I have always found six repetitions quite sufficient to give it as correct as equal altitudes.