The greatest pleasure that can be obtained from the measurement of a simple crystal and the calculation of its constants is in connection with a triclinic crystal. The system has been much abused and wrongfully so. When the calculation is made in connection with a gnomonic projection it becomes a very simple problem in solid trigonometry which offers absolutely no difficulty to a student who understands the rudiments of plane trigonometry. It is true that there are spherical triangles involved; in fact there are polar spherical triangles. The only characteristic about polar triangles that one needs to know is that the angles of one polar triangle are equal to 180° minus the opposite sides of the other polar triangle. When one of these triangles is solved the other is automatically solved. When the writer started the present paper it was his intention to give a graphic solution of the constants following the classical paper of Börgstrcim and Goldschmidt,1 which served as the model of his own paper on the same subject.2 In proceeding with the work it became evident that a modification of the calculation offered many advantages in relating all the constants directly to two circle measurements so that the purpose of the present paper is to demonstrate a simple method of calculating the angular and linear constants of a triclinic crystal from measurements on the two circle goniometer.

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