—the average being found by adding together the two lines and dividing the sum by two. It need hardly, however, be pointed out that the result so arrived at could not be true unless the number of persons in each class was exactly the same. A man who had invested in the Great Western Railway £900 which yielded him two per cent., and £100 in the South Western which paid him six, might say, on Mr. Mayhew’s principle, that he had invested £1000 at 4 per cent; but he would soon find out that he would have to receive only £24 for his yearly dividend instead of £40—£2.8 percent. instead of £4. {27} Mr. Mann calculates that without in the least interfering with juvenile labour, and without questioning the discretion of parents who kept children between the ages of 3 and 5 and 12 and 15 at home, there ought to have been more than three million children at school in 1851. It would be easy to show that this estimate is based upon nothing better than a series of blunders and bad guesses, but there is a much shorter mode of dealing with it. The children of the middle and upper classes do not remain under professional instructors at home or at school for a longer average period than six years. Now, the total number of children in 1851 between the ages of 4 and 10 was 2,484,866, or 13.8 per cent. of the entire population. The number actually on the school books was 2,200,000, or 12.2 per cent. So that either all the children in the country were at school, but the average time was one-eighth too short; or the average time was of the right length, but the number of scholars was one-eighth too few. The truth, of course, lay somewhere between these two alternatives. Since 1851 considerable progress has no doubt been made; but it unfortunately turns out that the effect of improved machinery is not to improve the general education, but merely to shorten the time allotted to schooling. It is found that if by better modes of tuition a child can be made sooner to acquire what its parents think sufficient for it to know, it is only so much the sooner taken away. It would therefore be vain to expect that the school per centage will ever be much higher than it was in 1851—at least, until the middle classes raise their own standard. Of the children on the schoolbooks in 1851, the per centage of actual daily attendants was 83—91 for the private, and 79 for the public scholar. In America, where the schools are wholly free, the per centage was still less. In Massachusetts, for example, it was only 75. In other words, the attendance in England and Wales in 1851 was 1,826,000 daily. If the 2,200,000 had all been private scholars, it would have been 2,002,000. On the other hand if there had been 2,400,000 free scholars, it would only have been 1,800,000. These figures will speak for themselves.