Red Triangle

“ Thus by every device that resourcefulness [106] and experience could suggest the workers of the Y.M.C.A. in France ministered to the comfort of the men who were so bravely sustaining that terrible onslaught. The organisation of the Red Triangle is the embodied goodwill of the British people towards its beloved army. An emergency like the one in the spring of 1918 was just the time when the services of the Red Triangle were most sorely needed by our soldiers. ”

“ So far as I can see, there is no clue whatever beyond the Red Triangle, which, as yet, I cannot understand. The strangling points to the murder being committed by a powerful man, certainly, and it is a form of crime that may have been perpetrated silently. But beyond that I can see nothing. The apparent motivelessness of the thing makes the mystery all the darker, and the circumstances we are acquainted with, instead of helping us, seem to complicate the puzzle.
"What was it that Denson feared when he left those diamonds behind him, when he might have carried them away? ”

“ Then this Denson is found dead that same night disguised in the clothes of a labourer, in a most conspicuous spot in London—the last place in the world one would expect a murderer to select for depositing his victim's body, for it is evidently not the place where the murder was committed. More, on the forehead there is this extraordinary impressed mark of a Red Triangle. Now, what can all that mean? Robbery, perhaps one thinks. But the body isn't robbed! ”

“ The figures of the Red Triangle are colossal, and yet figures by themselves fail to give an adequate idea of the magnitude of the work, and for obvious reasons it is impossible to make those statistics complete. ”

“ And I tell you, Brett, I believe that it was only the being informed of this fact that prevented Mayes from trying some of his hypnotic tricks on the bank manager; in which case there would have been a big bank robbery—perhaps something worse in addition."
"Murder?"
"Murder with a tourniquet, perhaps—perhaps with some other weapon; but, at any rate, probably with the Red Triangle. You know, of course—indeed I told you, I think—that in most cases—not all—it is necessary to get the subject's consent to the first exercise of hypnotism on him. ”

“ The Romance of the Red Triangle is a twenty-four hours a day romance, for many of its centres never close their doors. When we are comfortably sleeping at night and in the early hours of the morning, Y.M.C.A. workers are hard at work on motor patrol conveying leave men from station to station or hut to hut, and others are on foot meeting the men and guiding them to their destination. Alighting from the Edinburgh train at Leeds very early one morning, it was raining and a young Scottish trooper [34] stepped down to the platform from the adjoining compartment. ”

“ The way the movement has grown and is growing still is nothing short of a romance, and the following pages tell the story of service [18] rendered under the sign of the Red Triangle to the men of His Majesty's Forces, irrespective of class, creed, or party, in England and north of the Border, in Wales and Ireland, on every battle-front and in every base; amongst men of every colour and creed who are serving under our great Flag—the Flag that stands for Freedom. ”

“ The oranges came from Italy, and the chocolate was made by Americans in French or Swiss factories taken over by the Y. M. C. A. Trench supplies are never sold; these are "specials," gifts to those who for days at a time must bear the body and nerve destroying ordeal of the most advanced places. No man who has not seen the faces of the men and heard their "Thank yous" can appreciate what these trench trips of the Red Triangle mean to the soldiers of the Republic. ”

“ But though there may be some connection between the triangle and the substances representing the three natural kingdoms, it gives nothing practical—nothing to go on."
Martin Hewitt had been closely examining the marks on the paper, and now he answered, "I'm not so sure of that, though, Plummer. I think at least that it gives us another conjecture. I should guess that the man you want, as well as being acquainted with the use of the tourniquet, has at some time travelled in, or to, China." ”

“ When you hit upon the right one and leave it about, you'll start seeing things sooner or later. But your chances are small. It is not an isosceles triangle, but a scalene. The original pentagram was a very rough effort, far from symmetrical, and only by a fluke did it contain this dangerous triangle.
"How did I discover all this? It began with my investigation of the haunting of a cottage in Norfolk. I connected the phenomena with a small glass prism which had been lying about the place (the former occupant was a spectroscopist—until he went mad and was put away) . ”

“ It is a common custom to refer to the usual complication between one man and two ladies, or one lady and two men, or a lady and a man and a nobleman, or—well, any of those problems—as the triangle. But they are never unqualified triangles. They are always isosceles—never equilateral. So, upon the coming of Nevada Warren, she and Gilbert and Barbara Ross lined up into such a figurative triangle; and of that triangle Barbara formed the hypotenuse. ”

“ Can a triangular harmony form the substance of the elements? Is fire, as Plato affirms, an acute triangle, and light and heat properties of this triangle? Air and water, are they rectangular and equilateral triangles? Is the form of the terrestrial element a square, because, being the least perfect of all the four elements, it recedes as much as possible from a triangle without losing its essence? Do the male and female embrace only to complete the triangle of generation? These platonic ideas have two very different [334] aspects. ”

“ The triangle is much more common as a decorative motive than the circle or the rectangle, variety being brought about by the difference in length of the sides. The hourglass formed by two triangles with one angle of each united is common. The quail’s-head design, or triangle [34] having two parallel marks on an extension at one angle, is not as common as on Little Colorado pottery and that from the Gila valley.
As in all ceramics from the San Juan area, the stepped figures are most abundant. ”

“ Then, with my compass at E, I sight another line at an angle of sixty degrees from my last. I am making what is called an equilateral triangle; that is, a triangle with equal sides and equal angles. Each angle must measure sixty degrees. With two angles and one side, we can always get the other two sides; and the other angle will be where those two sides meet. They will meet at C. Now, since the sides are of equal length, the distance from D to C is the same as from D to E,—that is, four rods and thirty links, just the distance we wish to go; C, then, is the place for your corner stake. ”

“ And the wife stares at the old man, and then at the blond organist. And the blond organist stares at the mother of his beautiful children, and then at the bearded interloper. And they all stare at each other and feel very embarrassed.
The story is familiar to you? Well, perhaps so. It is the story of the eternal triangle, the most useful [82] pattern of geometrical forms in the construction of a romantic pattern.
Heigho! the trouble with human triangles is that they are never equilateral. Two sides together are invariably greater than the third side. ”

“ I removed and destroyed one of those common triangular shelf brackets, and got the credit for exorcising the spirits! Do you know why Burlham Rectory is still known as 'the most haunted house in Britain'? Because I couldn't get permission to attack a beam completing a triangle of one of the gables!
"I tell you, you've only got to look around any of these 'haunted' houses, and know what you're looking for, and you'll find the cause of the trouble sooner or later. It may be a fortuitous triangle of scratches on the wall, a coat-hanger, or even the side of a pepper-pot! But it's always there. ”

“ The Triangle
Beneath Andromeda. Three lines compose
The Triangle. On two sides measured equal,
The third side less. It is not difficult
To be discerned. More luminous than many.
Frothingham's Aratos.
The Triangle is an asterism of considerable antiquity, and was evidently more noticed by the ancients than by us. ”

“ Now for a little puzzle in triangular numbers.
Sandy McAllister, of Aberdeen, practised strict domestic economy, and was anxious to train his good wife in his own habits of thrift. He told her last New Year's Eve that when she had saved so many sovereigns that she could lay them all out on the table so as to form a perfect square, or a perfect triangle, or two triangles, or three triangles, just as he might choose to ask he would add five pounds to her treasure. ”

“ Calculation of Triangulation.
The surface of Great Britain and Ireland is uniformly covered by triangulation, of which the sides are of various lengths from 10 to 111 miles. The largest triangle has one angle at Snowdon in Wales, another on Slieve Donard in Ireland, and a third at Scaw Fell in Cumberland; each side is over a hundred miles and the spherical excess is 64′′. The more ordinary method of triangulation is, however, that of chains of triangles, in the direction of the meridian and perpendicular thereto. ”

“ In a case therefore like the present, where the base of our isosceles triangle is to the other two sides as eight units to twelve thousand, it is impossible not to perceive that it behoves us to be singularly diffident as to the conclusion at which we have arrived, or rather it behoves us to take for granted that we are not unlikely to fall into the most important error. We have satisfied ourselves that the sides of the triangle including the apex, do not form an angle, till they have arrived at the extent of ninety-five millions of miles. ”

“ I direct it in like manner to the end of the base E, and then the light it receives is in the direction of the side of the triangle FE ; I turn it then to the same distant signal G. Therefore, by these observations, I have really and truly got, by the theodolite, the measure of the two angles of the triangle at E and F. Now, that is sufficient. Every person who has a knowledge of trigonometry, knows that if we have got the measures of the side EF, and of these two angles, we are able, either to construct the triangle on paper, or to determine, by calculation, the whole of its parts. ”

“ But the whole secret really lies in just one triangle of that figure. The surface size is irrelevant, and the rest of the pentagram frame redundant. It's the angles of that one triangle which are important. Fashion a triangle with its three angles of sizes I could give you (though an error amounting to a second will suffice to make it impotent) and you will have a triangle of terror indeed. ”

“ He turned round from his window. “Triangle?” He looked at my glass of punch, and then at me. “Go easy with the Bombo,” he repeated.
“Bombo?” I echoed. “You call this Bombo? You don’t know how remarkable that is, but that’s because you don’t know Aunt Carola, who is very remarkable, too. Well, never mind her now. Point is, it’s always a triangle.”
“I haven’t a doubt of it,” he replied.
“There you’re right. And so was your uncle. He knew. Triangle.” Here I found myself nodding portentously at John, and beating the table with my finger very solemnly. ”

“ Does nothing depend on the nature of the subject itself? "That two sides of a triangle," says Mr Whewell, "are greater than the third, is a universal and necessary geometrical truth; it is true of all triangles; it is true in such a way that the contrary cannot be conceived. Experience could not prove such a proposition." Experience is allowed to prove it of this or that triangle, but not as an inseparable property of a triangle. ”

“ Of course, all the men must be used on every occasion.
137.—A STUDY IN THRIFT.
Certain numbers are called triangular, because if they are taken to represent counters or coins they may be laid out on the table so as to form triangles. The number 1 is always regarded as triangular, just as 1 is a square and a cube number. Place one counter on the table—that is, the first triangular number. Now place two more counters beneath it, and you have a triangle of three counters; therefore 3 is triangular. Next place a row of three more counters, and you have a triangle of six counters ”

“ The natural supposition must be that some one had surveyed the triangle A F B and computed its area correctly as about fifty square rods. The mere recording of this area is sufficient evidence that the triangle A F B had been surveyed in 1816, and this is sufficient proof that mound B E stood just as it stands today and was considered in Mr. Lewis’s day as one of the embankments of Fort Necessity. ”

“ Sometimes the sides of the triangles are many miles in length, and when Arago connected the coast of Valencia in Spain with the Balearic Islands, one of the sides measured 422,555 toises.
When one side and two angles of any triangle are known, the other sides and angle maybe found; by taking, therefore, a side of one of the known triangles for a new base, and by measuring the angles adjacent to the base, new triangles can be successively formed along the whole length of the arc; and since every straight line in the network of triangles is known, the length of the arc can be easily determined. ”