The foot-rule of the carpenter not only gives him the standard of a foot measure, which he could not exactly ascertain by any experience, or any mental process, but it is also a scale of the proportions of an inch, or several inches, to a foot, and of the parts of an inch to an inch. What a quantity of calculations, and of dividing by compasses, does this little instrument save the carpenter, besides ensuring a much greater degree of accuracy in all his operations! The common rules of arithmetic, which almost every boy in England now learns, are parts of a great invention for saving mental labour. The higher branches of mathematics, of which science arithmetic is a portion, are also inventions for saving labour, and for doing what could never be done without these inventions. There are instruments, and very curious ones, for lessening the labour of all arithmetical calculations; and tables, that is, the results of certain calculations, which are of practical use, are constructed for the same purpose. When we buy a joint of meat, we often see the butcher turn to a little book, before he tells us how much a certain number of pounds and ounces amounts to, at a certain price per pound. This book is his 'Ready Reckoner,' and a very useful book it is to him; for it enables him to despatch his customers in half the time that he would otherwise require, and thus to save himself a great deal of labour, and a great deal of inaccuracy. The inventions for saving mental labour, in calculations of arithmetic, have been carried so far, that Mr. Babbage had almost perfected a calculating machine, which not only did its work of calculation without the possibility of error, but absolutely was to arrange printing types of figures, in a frame, so that no error could be produced in copying the calculations before they are printed. We mention this curious machine, to show how far science may go in diminishing mental labour, and ensuring accuracy. The want of government funds prevented its completion. To all who read this book it is no difficulty to count a hundred; and most know the relation which a hundred bears to a thousand, and a thousand bears to a million. Most are able, also, to read off those numbers, or parts of those numbers, when they see them marked down in figures. There are many uncivilized people in the world who cannot count twenty. They have no idea whatever of numbers, beyond perhaps as far as the number of their fingers, or their fingers and their toes. How have we obtained this great superiority over these poor savages? Because science has been at work, for many centuries, to diminish the amount of our mental labour, by teaching us the easiest modes of calculation. And how did we learn these modes? We learnt them from our schoolmasters.