AN IMPORTANT part in the teaching of any technical subject, in higher educational establishments as well as schools, is experience in the solution of problems. As well as providing practice in the methods of computation, it enables the teacher to follow the students' progress both in comprehension and application of theory. The literature of astronomy is badly lacking in this respect, both in quantity and range of topics; and in fact the author is aware of the existence of only one textbook devoted to exercises in astronomy. This is "Astronomical Problems" (Astronomicheskii zadachi), a textbook for young people by Professor N. P. Kamenschikov, published in 1923. This textbook is intended for use in universities, teachers' training colleges, and in school college preparatory or sixth forms. The syllabus covered by all three types of institution is much the same, the differences lying in the depth rather than the field of learning. For this reason the material in each chapter is divided into two sections. The first section is elementary. The second section is more difficult, set approximately at the level of the teachers' training colleges. In each section the problems are grouped into sub-topics, and set in order of increasing difficulty. In every chapter the problems are preceded by a summary of the theory and the formulae to be exercised, under headings I and II, applying to sections I and II, respectively. Problems are presented, requiring both exact and approximate solutions, so that on occasion the same data may be repeated with varying degrees of accuracy. We have presented two, and exceptionally three, examples of the most typical problems, so that the teacher may use one or more for demonstration, leaving a similar exercise for the student. vii Vlll PREFACE However, the author realizes that students become frustrated if presented with the same problem, under different formulations (e.g. Nos. 29 and 30), and the teacher is asked to note that this occurs in a number of places in the book. In the preparation of this book, the author used the books referred to in the first Russian Edition of this work. As many of the problems are unoriginal, or "natural", the source of a problem is given only in those cases where the problem seemed unusual. Many of the problems and exercises were devised by the author, but only about 300 of these (marked with an asterisk*) appear to be unique in the literature. Ninety per cent of the problems borrowed by the author were originally published without answers.