No person will deny that the highest degree of attainable accuracy is an object to be desired, and it is generally found that the last advances towards precision require a greater devotion of time, labour, and expense, than those which precede them. The first steps in the path of discovery, and the first approximate measures, are those which add most to the existing knowledge of mankind. The extreme accuracy required in some of our modern inquiries has, in some respects, had an unfortunate influence, by favouring the opinion, that no experiments are valuable, unless the measures are most minute, and the accordance amongst them most perfect. It may, perhaps, be of some use to show, that even with large instruments, and most practised observers, this is but rarely the case. The following extract is taken from a representation made by the present Astronomer-Royal, to the Council of the Royal Society, on the advantages to be derived from the employment of two mural circles:— "That by observing, with two instruments, the same objects at the same time, and in the same manner, we should be able to estimate how much of that OCCASIONAL DISCORDANCE FROM THE MEAN, which attends EVEN THE MOST CAREFUL OBSERVATIONS, ought to be attributed to irregularity of refraction, and how much to THE IMPERFECTIONS OF INSTRUMENTS."