"We will now, for our non-calculating reader, put the matter in another way. We see that a circle-squarer can advance, with the utmost confidence, the assertion that when the diameter is 1,000, the circumference is accurately 3,125: the mathematician declaring that it is a trifle more than 3,141-1/2. If the squarer be right, the mathematician has erred by about a 200th part of the whole: or has not kept his accounts right by about 10s. in every 100l. Of course, if he set out with such an error he will accumulate blunder upon blunder. Now, if there be a process in which {111} close knowledge of the circle is requisite, it is in the prediction of the moon's place--say, as to the time of passing the meridian at Greenwich--on a given day. We cannot give the least idea of the complication of details: but common sense will tell us that if a mathematician cannot find his way round the circle without a relative error four times as big as a stockbroker's commission, he must needs be dreadfully out in his attempt to predict the time of passage of the moon. Now, what is the fact? His error is less than a second of time, and the moon takes 27 days odd to revolve. That is to say, setting out with 10s. in 100l. of error in his circumference, he gets within the fifth part of a farthing in 100l. in predicting the moon's transit. Now we cannot think that the respect in which mathematical science is held is great enough--though we find it not small--to make this go down. That respect is founded upon a notion that right ends are got by right means: it will hardly be credited that the truth can be got to farthings out of data which are wrong by shillings. Even the celebrated Hamilton[207] of Edinburgh, who held that in mathematics there was no way of going wrong, was fully impressed with the belief that this was because error was avoided from the beginning. He never went so far as to say that a mathematician who begins wrong must end right somehow.