The general theory embraced by some leading men of science in reference to the cause of volcanoes, is that they are the smoke pipes ot the great fire in the interior ot this earth. They believe that we are living on the top of a huge white-hot cauldron, and that the volcanoes in different parts of the world are merely vents of this internal fire. The following are the views of Prof. Silli-man, ot Yale College, on the subject embraced in a lecture recently delivered in this city : The internal heat of the earth is proved by direct experiments. A gentleman is still living in Paris, who first called the attention of geologists and philosophers to this subject. He was one of those scientific men who ac companied Napoleon to Egypt, when he went on that great expedition—mdash;lor Napoleon took with him not only the weapons of war, but he took a much more important cohort—mdash;that is, men of science, and art, and literature, able to explore and examine all the antiquities ot the most important and venerable country. A great literary work resulted from this expedi tion, which proved to the world that the in terior of the earth was in a heated state, bring ing together facts already known, in regard to mines and springs. This general principle announced, has been followed up repeatedly by very deep borings, called artesian wells. The very deep well in Paris had been worked upon for seven years, without reaching water, when Arago came forward and gave the go vernment assurance that if they would con tinue their work, and go tbrough the beds of chalk, they would, in all probability, find water. They continued their work till they got down through the chalk, when the water I rose up in a great volume of twelve feet. This water still flows there, and doubtless will continue to flow to the end of time.—mdash; This water was found to be very hot. Many other artesian wells have been made all over Europe, for various purposes, and the uniform result has been that we find the earth increas ing in heat the lower we go down. Add to this the testimony of those who work in very deep mines, and we ascertain the fact that the rate of heat increases about one degree for every fifty feet of descent; so that, if we Were to *o down two miles, we should find boiling water; and at ten miles we might reasonably expect to arrive at ignited rocks. Is all then beneath us on fire ? I am not pre pared to say, with some, that this is the case, although there is strong evidence to justiiy such a theory. Witness the geysers ot Ice land—mdash;where hot waters are gushing up from the earth age after age, and century after century. The result of all observations on springs, goes to show that they are thermal—mdash; that is, of a higher temperature. The Azores present a very important fact in example. The hot springs of Lucca, in the Apennine Mountains, are large spouting springs, of a high temperature, so copious, that they may be relied upon lor hot baths all the year round. Another case is the hot springs of Bath in England. These are the more remarka ble as there are no volcanoes in the British Islands. We know that from the time of the Romans these waters have never ceased to gush up in vast abundance. The hot springs of the Rocky Mountains are also very important, and the great salt lake in Virginia is very hot. Taking the ar tesian wells and the thermal, we have, from these sources, the best evidence of the heated temperature of the internal portion of the earth, and this is placed beyond all question by the great volcanoes in the world. And here we have decisive evidence that the heat which will melt the solid rock is not connect ed with any external cause ; for, among the cold, icy mountains, there are volcanoes bursting up to the height of 12,000 feet. In Spain and South America we find great volcanoes bursting out. The fact is, the world is on fire. It has always been on fire. It was kindled at the time of its creation, and has been burning ever since. [Dr. Antisel, of this city, recently delivered a lecture, in which the same views are de veloped ; the substance of it we will present next week; as he embraces the electrical theory, he certainly militates against the ne bular theory. Both agree as to the internal , heat, viz., that we live on the top of a furnace.