through the deepest layer of atmosphere there) and must he taken account of, even with rude observing apparatus. Refraction had been studied by Ptolemy and more deeply by Alhazen and Roger Bacon. Twilight, the scattering of the rays of the sun from the particles of dust and the like in the upper atmosphere, was investigated by Peter Nonius (1492–1577) a voluminous writer on astronomical matters.
All that was known in astronomy was familiar to Regiomontanus, and during his seven years' residence in Italy his relations were with the best instructed savants of Rome, who were then concerned with projects for improving and correcting the calendar. When Copernicus went to Italy in 1496 the best traditions of all Europe had spread throughout its universities and he was, therefore, familiar with all that his predecessors had accomplished.
A passage from the 'Principles of Astronomy' of Gemma Frisius (died 1558) is worth translation, since it fixes an important date and describes methods of determining longitudes and latitudes which are used to-day. He says: "People are beginning to make use of little clocks that are called watches. They are not too heavy to be carried about; they will run nearly twenty-four hours, and even longer if you aid them a bit; they afford a very easy method of determining longitude. Before starting on a journey, set your watch carefully to the local time of the country you are leaving; take pains that the watch doesn't stop on the road; when you have gone twenty leagues, for instance, determine the local time of the place where you are, with an astrolabe; compare this with the time by your watch, and you will have the difference of longitude." The latitude of the place can be had by measuring the altitude of the pole-star. Watches, which were invented about 1525, varied several minutes a day, and the portable astrolabes of the time could hardly give the altitude so close as 10′; but the methods were correct, and are those to-day employed in using the chronometer and the sextant.
Mention must be made of Peter Bienewitz, otherwise Peter Apianus (born 1495, died 1552), who expounded the Ptolemaic system in a great volume—Astronomicum Cæsareum (1540). Apianus was the first to observe the sun through colored glasses. The astronomers of Bagdad had observed an eclipse, when the sun was low, by its reflection in water, and Reinhold had proposed to project the solar image on a card in a camera obscura, a method which was used by the astronomers of Galileo's time. His best contribution to astronomy was the discovery that the tails of comets are generally directed away from the sun, a remark independently made by Fracastor.
Comets in his day were usually supposed to be atmospheric phenomena. Why this connection between them and the sun? Why should the sun, and not the earth, control their forms? The comet of 1472 had been studied by Regiomontanus and its course among the
