111. On a flagstaff consisting of an upright pole (6 feet of which is underground) is a cross-yard 24 feet long; the latter is fixed at a distance of one-third of the length of the visible part of the pole from the top; passing from the top of the pole to the ends of the yard are ropes, forming stays whose falls or ends reach to the ground on either side of the pole, and it is found that these falls just reach the base of the pole. The total length of rope in the aforesaid stays is 40 feet. Supposing that the top diameter of the pole is one-third of that at the extreme base, and that the whole length of rope used is 54,177 times the base diameter of the pole, what would the pole cost at 1 penny per 100 cubic inches? TEACHER--“Your writing is fairly good, but how do you account for making so many mistakes in your spelling?” SCHOLAR--“Please, ma’am, I had chilblains on my hand?” 112. Put down 4 marks (| | | |), and then require a person to put 5 more marks and make 10. “KEEP YOUR HAIR ON.” 113. Supposing there are more persons in the world than anyone has hairs on his head, there must be at least two persons who have the same number of hairs on the head to a hair. Explain this. 114. Show what is wrong in the following:-- 8-8 = 2-2, dividing both these equals by 2-2 the result must be equal; 8-8 divided by 2-2 = 4, and 2-2 divided by 2-2 = 1, therefore, since the quotients of equals divided by equals must be equal, 4 must be equal to 1. “GLAD TIDINGS.” Many will be surprised to hear that there is Scriptural authority for advertising. Advertising not only has Scriptural authority, but it is of very respectable antiquity as well. If you will look in Numbers XXIV., 14, you will find Balaam saying “Come now, and I will advertise,” and Boaz says in Ruth IV., 4, “And I thought to advertise.” OPTICAL ILLUSIONS. Illusions of the Eye are numberless, and afford a wide field for experiment. Some people are left-eyed, others right-eyed, and very few use both eyes equally. It is impossible to tell how far they really do deceive us unless they have been tested in the proper manner. For instance, if you ask anyone to what height a bell-topper would reach if placed on the floor against the wall, nine times out of ten the height guessed will be half as much again as the real height of the hat. Everyone seems to _over_-estimate the proper height. [Illustration] Another favourite illusion is to ask a person to mark on the wall a height from the floor which would represent the length of a horse’s head: here the majority guess far too little--for a horse’s head is much longer than most people imagine, ranging from 25 to 34 inches. In a recent experiment 5 persons out of 6 _under_-estimated the proper height. [Illustration] Here are two triangles. Which is the one whose centre is the better indicated? (It looks like A, but it is B). [Illustration]