Examples For Practice In The Use Of Seven Figure Logarithms

Examples for Practice in the Use of Seven-Figure Logarithms

From the Preface. CONSIDERABLE practice is required by most students before they acquire the accuracy which is absolutely necessary in the use of logarithms. According to my experience, mistakes are more frequently made by taking out a wrong logarithm than by blundering in the arithmetic. It would seem therefore that a student should always be expected to take out himself all the logarithms, whether of numbers or of Trigonometrical Functions, which are needed in the solution of any question; and that the practice, which has been so common, of supplying him with all these in addition to the data should be abandoned. It is mainly with the wish of bringing about this result that 1 have put together the accompanying collection of examples. As the answers are given in each case, this little book is the result of a very considerable amount of work. I have taken all pains to secure accuracy, but cannot hope to have completely succeeded, and shall be grateful to anyone who will point out to me any mistakes I may have made. I have given what may be thought a disproportionate number of examples of the calculation of the parts of a tetrahedron when the lengths of its edges are given. This was done, chiefly because I am convinced that no other kind of examples so soon teaches the habitual accuracy which ought to be attained, but also to some extent to give examples for the use of those who have occasion for practice in the solution of Spherical Triangles. In the calculation of each tetrahedron is involved the obtaining all the parts of four Spherical Triangles, and this has induced me, after considerable hesitation, to abstain from giving explicit examples for such solutions. I have principally, but not exclusively, used Chambers' Mathematical Tables in my working out of these examples. Of course the seventh significant place in numbers, and the second decimal place in seconds of angles, are not absolutely to be relied upon. If this book should be used with tables of six or five-figure logarithms, the corresponding number of places should be struck off my results, the usual correction being made when necessary in the remaining final figure.

Examples for Practice in the Use of Seven-Figure Logarithms

From the Preface.CONSIDERABLE practice is required by most students before they acquire the accuracy which is absolutely necessary in the use of logarithms. According to my experience, mistakes are more frequently made by taking out a wrong logarithm than by blundering in the arithmetic. It would seem therefore that a student should always be expected to take out himself all the logarithms, whether of numbers or of Trigonometrical Functions, which are needed in the solution of any question; and that the practice, which has been so common, of supplying him with all these in addition to the data should be abandoned. It is mainly with the wish of bringing about this result that 1 have put together the accompanying collection of examples. As the answers are given in each case, this little book is the result of a very considerable amount of work. I have taken all pains to secure accuracy, but cannot hope to have completely succeeded, and shall be grateful to anyone who will point out to me any mistakes I may have made. I have given what may be thought a disproportionate number of examples of the calculation of the parts of a tetrahedron when the lengths of its edges are given. This was done, chiefly because I am convinced that no other kind of examples so soon teaches the habitual accuracy which ought to be attained, but also to some extent to give examples for the use of those who have occasion for practice in the solution of Spherical Triangles. In the calculation of each tetrahedron is involved the obtaining all the parts of four Spherical Triangles, and this has induced me, after considerable hesitation, to abstain from giving explicit examples for such solutions. I have principally, but not exclusively, used Chambers' Mathematical Tables in my working out of these examples. Of course the seventh significant place in numbers, and the second decimal place in seconds of angles, are not absolutely to be relied upon. If this book should be used with tables of six or five-figure logarithms, the corresponding number of places should be struck off my results, the usual correction being made when necessary in the remaining final figure.

Examples for Practice in the Use of Seven-figure Logarithms