300,000 cathartical compositae pills; 52,500 pounds chloroform; 583,523 vials anti-tetanous serum; 640,000 sulphonol tablets; 11,000,000 strychnine sulphate tablets; 770,000 tablets of sodium salicylate and 350 ounces of apothesin.

This and much other quantity of drugs was used in Red Cross hospitals in France and elsewhere. Appropriations of the Red Cross for hospitals within the actual fighting zones amounted to $3,102,807 this year. Hospitals behind the lines and supplies cost $5,874,392. The equipment of civil hospitals for Belgian refugees in France cost $59,962. There are more than 7,000 beds available for American wounded in and about Paris. Many thousands of beds in tents, hospitals and in temporary buildings: are right behind the advancing battle lines. There are six dis-1 pensaries and eight infirmaries at rest stations. There are eight convalescent homes for American soldiers.

At the American Red Cross laboratory, 10 Rue de Tilsitt, Paris. Assembling Burlingame units to send to the Front. The Burlingame unit is a box containing an emergency set of surgical instruments for surgeons behind the lines. July, 1918.

The Red Cross is operating eight hospitals on its own account and in connection with the army. In addition, it operates a tuberculosis sanitarium for soldiers, another similar institution for civilians and has a dozen hospitals for children in various parts of France. Then, too, it has dispensaries and diet kitchens and sixteen magnificently equipped hospital trains.

To date the Red Cross has received more than $325,000,000 from the American people in money and supplies. The service of the Red Cross is broadening daily as the number of our men overseas is increasing, as thousands are repatriated, as French and Belgian and Balkan territory is reclaimed. The Red Cross

must continue its service work for humanity. To do so it must have the united support of the American people. Accordingly it has set aside the week of December 16 to 23 for its second annual Christmas Roll Call. It is hoped that then every American will become a member of the Red Cross as a reconsecration of the people, an inspiring reassertion to mankind that in this hour of world tragedy, not to conquer but to serve is America's supreme aim.

PICRIC ACID MANUFACTURE.
By HARRY C. DOANE,
Grand Rapids.

Piorio Loid

To manufacture pioric acid, phenol, commonly cald carbello aoid, is dissolvd in sulfuric acid. These react as foliowat

PHENOL

The product of the above action is treated with nitric acid,

and the following action takes place:

It and its

Picric acid consists of bright yellow crystals.
ammonium salt (ammonium picrste) are used as explosive, mainly
in filling shells, and the acid is used as a dye.

Neither picric acid or the ammonium salt is easily exploded
on heating or by ordinary shocks. It is exploded by a violent
shook caused by the explosion of a cartridge fild with fulminate
of mercury, cald a detonator, The detonator is exploded by means
of a fuse.

SULFURIC ACID NITRIC ACID

PICRIC ACID

WATER

+

Sulfuric acid is also formd azrin, and is left over at the end of the action.

A MODEL OF SUPPLEMENTARY TRIHEDRAL ANGLES.

BY R. M. MATHEWS,
Duluth, Minn.

When the vertices of a spherical triangle are joined to the center of a sphere, a trihedral angle is determined whose face angles are measured by the sides and whose dihedral angles are measured by the angles of the spherical triangle. The two figures may be called "related." Each property of a spherical triangle implies a corresponding property in the related trihedral angle. Conversely, when a trihedral angle is placed with its vertex at the center of a sphere, its edges cut the surface in the vertices of a related spherical triangle.

Let a perpendicular be erected to each face of a trihedral angle at the vertex and on the same side as the third edge. These three new lines determine a new trihedral angle which is called "supplemental" to the first. The related spherical tri

Figure 1

Y

angles of these trihedral angles are polar triangles, and each property of one pair implies a corresponding property in the other pair.

The geometry of polar triangles is a regular part of our courses in solid geometry. The geometry of supplemental trihedral angles has been neglected until recently, when they have been introduced in some of the newer texts. The chief difficulty in studying them lies in obtaining a clear image of the relative positions of the lines and in making the perspective diagrams. I have found that one recitation devoted to planning the con

B

struction of a cardboard model is fully justified by the pupils' resulting clearness of conception and firmer grasp on the many principles used in the work.

The model consists of two main c' parts, one for each of the trihedral angles. It is evident how to construct a trihedral angle in cardboard when its three face angles are known. Convenient dimensions are 4

X

Figure 2

Χ

inches for radius of sphere (or edge) and a = 65°, b

c = 50° for the face angles of the initial figure. Each face must have extensions on it, however, to hold it in proper posi

to the thickness of the cardboard. Around 0 cut out a sector of 1-2 inch radius, to make the assembling easier, and leave small lugs at Y and Z'. In a similar fashion faces b and c are prepared and the three are assembled. It is well to mark the six corners (as X, X', etc.) with the notation indicated in Fig. 2, for guides when this part is placed in the other one.

The face angles of the second trihedral angle are supplementary to the opposite dihedral angles in the initial trihedral. We must determine these. Through a point A on edge OA pass two

Figure 4

planes, the one orthogonal to edge OB and the other to edge OC of the trihedral angle (Fig. 3). These planes intersect in a line AF which is normal to face BOC. Accordingly, triangle AFC is right angled at F and its angle C is a plane angle of the dihedral OC.

When this figure is folded out on the plane of OBC, the constructions are evident (Fig. 4). We lay out angles AOB, BOC and COA, equal to the initial angles respectively. Take OA OA1. Draw AB perpendicu

=

=

lar to OB and A,C perpendicular to OC meeting at F. Construct a right angle at F and make CA', CA1. Then angle FCA', is the plane angle of dihedral OC, and A'CA, is its supple