“The improved mode of using the theodolite referred to above consisted in making it do the work of a repeating circle; and thus I was enabled, with respect to each of the principal angles, to obtain the mean of perhaps twenty measurements. I may here mention that the fact of this contrivance happened, on a subsequent occasion, to do me good service. Some years afterwards, being in London, I wished to visit the Royal Observatory, and procuring a letter of introduction to Captain Kater, then a member of the Board of Longitude, I applied to him for an order. With all the politeness that can attend a negative, he told me that the Astronomer Royal (Mr. Pond) had been so much interrupted of late as to deprecate any further issue of orders save in cases of absolute necessity. As some consolation, however, he offered to show me his own apparatus; which, I need not say, I examined with great interest. In the course of conversation I mentioned my new device, when, turning to me with a look of great pleasure, he told me that he had hit upon the same improvement himself. Before I left he sat down and wrote the order; of which I did not fail to make use. I may add that at a later period he visited the school, subsequently placed a son under our care, and continued till death to honour me with his friendship. “To return to the survey, I give a second extract from my Journal:— “‘_June 23rd, 1819._—This day I completed the calculations for the trigonometrical survey of Birmingham, and some parts of the adjoining country. “‘After completing the survey of the town, I thought it desirable to extend it for the purpose of verifying the admeasurement of the base, by computing the length of two lines which were measured by Colonel Mudge. These are the distance [the respective distances] of Wolverhampton and Wednesbury spires from a station at Bar beacon. Colonel Mudge has left no mark to show the situation of his station; he describes it indeed, but not with very great precision. He says in his report, ‘The station is thirty yards north of the plantation.’ I have supposed his description to be exactly correct, that is, that the station was placed directly north of the centre of the plantation, and thirty yards from the nearest part of the clump of trees. If this be correct the station would stand fifty-six yards directly north of the flagstaff, and this I have supposed to be its situation. “‘The distance of Wolverhampton spire from the station at Bar beacon, Colonel Mudge gives at 48,345 feet. This, reduced to the distance from the flagstaff, gives 48,355 feet.