Comparatively few small reflectors have been made or used in the United States, although the climatic conditions here are more favorable than in England, where the reflector originated and has been very fully developed. The explanation may lie in our smaller number of non-professional active astronomers who are steadily at observational work, and can therefore use reflectors to the best advantage. The relative advantages of refractors and reflectors have long been a matter of acrimonious dispute. In fact, more of the genuine _odium theologicum_ has gone into the consideration of this matter than usually attaches to differences in scientific opinion. A good many misunderstandings have been due to the fact that until recently few observers were practically familiar with both instruments, and the professional astronomer was a little inclined to look on the reflector as fit only for amateurs. The comparison is somewhat clarified at present by the fact that the old speculum metal reflector has passed out of use, and the case now stands as between the ordinary refracting telescope such as has just been described, and the silver-on-glass reflector discussed immediately thereafter. The facts in the case are comparatively simple. Of two telescopes having the same clear aperture, one a reflector and the other a refractor, each assumed to be thoroughly well figured, as it can be in fact today, the theoretical resolving power is the same, for this is determined merely by the aperture, so that the only possible difference between the two would be in the residual imperfection in the performance of the refractor due to its not being perfectly achromatic. This difference is substantially a negligible one for many, but not all, purposes. Likewise, the general definition of the pair, assuming first-class workmanship, would be equal. Of the two, the single surface of the mirror is somewhat more difficult to figure with the necessary precision than is any single surface of the refractor, but reflectors can be, and are, given so perfect a parabolic figure that the image is in no wise inferior to that produced by the best refractors, and the two types of telescopes will stand under favorable circumstances the same proportional magnifying powers. The mirror is much more seriously affected by changes of temperature and by flexure than is the objective, since in the former case the successive surfaces of the two lenses in the achromatic combination to a considerable extent compensate each other’s slight changes of curvature, which act only by still slighter changes of refraction, while the mirror surface stands alone and any change in curvature produces double the defect on the reflected ray.