The object of this note is to show how various problems commonly occurring in Elementary Trigonometry may be classified as particular cases of trigonometric survey. The general case may be stated first, and certain well-known particular cases appended.

The instrument is an ordinary dry and wet bulb hygrometer adapted to give a direct

reading of the percentage humidity. I, I are pointers set at the dry and wet bulb readings by means of pieces sliding on the rods A, B and joined together by a link C, which actuates by a slot the scale F (movable in the vertical) on which the percentage humidity is read at the pointer D.

In this note the formula

is illustrated for a few curves.

The following method of proof of the identity,

where A, B, C are the angles of a triangle, was proposed in an examination paper, and it has been suggested to me that it might be of interest to teachers. It is rather easier than that given on p. 344 of “New Trigonometry for Schools” by Lock and Child.

I have sometimes been laughed at when I have ventured the opinion that University students of mathematics ought to do original work in mathematics as part (and an important part) of their degree work. But this will not prevent me from maintaining that original work should be done by every scholar in a junior class of geometry. Of course in one sense this is a mere platitude, for every “problem” and “rider” requires for its solution original work on the part of the scholar. He or she that would solve a geometrical problem must “intend the mind continually” on it, like Sir Isaac Newton, and acquire the faculty of trying different points of view till the right one is found. For him or her, at any rate, the Pragmatists' test of truth is appropriate. He asks of every hypothesis “will it work?” and finds the answer by actual trial.