[page] 317

The Convexity of Water

Sir,—I should hardly have thought it worth while to answer Mr Carpenter's letter in your last had you not invited me to do so, as the question of my verbal accuracy is one quite beside the main Issue.

    In Mr Carpenter's "Objections," 8, 9, and 10 (see Field, March 26), he speaks of there being "a rise" shown from the point of observation to the central signal, and argues that, if so, the point of observation must be in a depression or "circular concavity." Here then "a rise" is used in the surveyor's sense of "rise above the level of the point of observation," and I replied that I had not used the word "rise" (of course meaning in the same sense) in connection with these experiments. It is, therefore, quite beside the question for Mr Carpenter to quote me as saying that the middle signal would be seen "rising" above the others. His own diagrams show that it did so; but at the same time it "fell" below the point of observation (as every surveyor will tell him) by its being seen below the cross hair in the level telescope, allowing of course for the inverted image.

    The fallacies in the remainder of Mr Carpenter's letter have been so ably refuted (by anticipation) by your correspondent Mr J. Tanner, that I need say no more about them. I would ask Mr Carpenter, however, to state, for the information of your readers, whether the universally-accepted and only known method of deciding whether three distant points are in a straight line is true or false. That method is to place the eye (whether aided by a telescope or not) at or behind one of the extreme points, and see whether the other two or all three coincide, the nearer hiding or covering the more distant. If so, they are in a straight line. Every carpenter who looks along the edge of a floor board, every surveyor who runs his base lines across the country, every builder who sets out a long wall, uses this method. Does Mr Carpenter say they are all wrong, and that every line thus set out is a crooked or curved line? If so, let him prove this elementary point by experiment and diagrams, and thus found a totally new and hitherto unimagined geometry. If, on the contrary he admits that lines so set out are straight, then the middle and end signal which did not so coincide when seen from the other end signal could not be in a straight line, or there would be two diverging straight lines terminating in the same points, and inclosing a space!

    Mr C. has confounded actual with apparent equi-distance in the field of view of a telescope, between which there is no connection, as Mr Tanner's diagrams show. If Mr Carpenter will not try any such simple experiment as I proposed in my last, I must decline to spend any more time in refuting arguments founded on total ignorance alike of facts and of geometrical principles.

    The "men of common sense" to whom Mr C. so confidently appeals are very slow in coming forward. The solitary individual he so triumphantly quotes against me (Mr Westlake) now confesses to an oversight, and cruelly deserts him. Mr Hampden, in his letter to me, continually appeals to "public opinion" as being against the fairness of your verdict. It has, however, now clearly spoken through your widely-circulated columns, and, unless he can prove that letters on the other side have been refused insertion, he would do well, as a man of honour and of sense, to bow to its decision.