n of other projects. For example one major project begun in 1678-79 involved draining water from the mines in the Harz Mountains. His idea was to use wind power and water power to operate pumps. He designed many different types of windmills, pumps, gears but every one of these projects ended in failure. Leibnitz himself believed that this was because of deliberate obstruction by administrators and technicians, and the worker's fear that technological progress would cost them their jobs. In 1680 Duke Johann Friedrich died and his brother Ernst August became the new Duke. The Harz project had always been difficult and it failed by 1684. However Leibnitz had achieved important scientific results becoming one of the first people to study geology through the observations he compiled for the Harz project. During this work he formed the hypothesis that the Earth was at first molten. Another of Leibnitz's great achievements in mathematics was his development of the binary system of arithmetic. He perfected his system by 1679 but he did not publish anything until 1701 when he sent the paper Essay d'une nouvelle science des nombres to the Paris Academy to mark his election to the Academy. Another major mathematical work by Leibnitz was his work on determinants, which arose from his developing methods to solve systems of linear equations. Although he never published this work in his lifetime, he developed many different approaches to the topic with many different notations being tried out to find the one, which was most useful. An unpublished paper dated 22 January 1684 contains very satisfactory notation and results. Leibnitz continued to perfect his metaphysical system in the 1680s attempting to reduce reasoning to an algebra of thought. Leibnitz published Meditationes de Cognitione, Veritate et Ideis (Reflections on Knowledge, Truth, and Ideas) which clarified his theory of knowledge. In February 1686, Leibnitz wrote his Discours de mtaphysique...
