Dr. S. L. Dana on the Manufacture of Sulphuric Acid, 115 



2. When QOy is a circle, the points T and V coincide in 

 a nodal point n, where the two sheets of the wave surface cross 

 each other. At this point there are an infinite number of 

 tangent planes, for OQ and Qq are now indeterminate. The 

 same refracted ray O n may therefore be derived from any 

 one of an infinite number of incident rays, and its polariza- 

 tion will differ accordingly; for the vibrations are in the line 

 n S drawn from the node to the foot of the perpendicular OS 

 on the tangent plane. The ray On, however, is always ac- 

 companied by another, but variable, refracted ray. 



The three lines OP, Oq, OS, are at right angles to each 

 other, and the first two of them are confined, as before, to 

 given planes. For O^ is in the plane of the circle QOq; and 

 OP being perpendicular to the tangent plane at Q must lie in 

 a given plane. These given planes are parallel to two prin- 

 cipal tangent planes passing through n and touching the cir- 

 cle and ellipse that compose the wave section in the plane 

 of the nodes : whence it is easy to see that every nodal tangent 

 plane intersects the two principal tangent planes in lines that 

 are constantly at right angles; for these lines are parallel to 

 OP and Oq. 



The examination of both cases is completed by the follow- 

 ing theorem: — 



When three right lines at right angles to each other pass 

 through a fixed point, in such a manner that two of them are 

 confined to given planes, the plane of these two, in all its po- 

 sitions, touches the surface of a cone whose sections parallel 

 to the given planes are parabolas; while the third right line 

 describes another cone, whose sections parallel to the same 

 planes are circles. 



The application is obvious. We see that the curve of con- 

 tact in the first case is a circle. The points S in the second 

 case are also in a circle. 



XXIV. On the Manufacture of Sulphuric Acid, and on the White 

 Crystalline Substance which is formed during that Process. By 

 S. L. Dana, M.D. 



To Richard Phillips, Esq. 

 Dear Sir, 

 [" SEND you the remarks on the manufacture of oil of vitriol, 

 -*- which I had the pleasure of reading to you in your labora- 

 tory this morning. I made the observations in the winter of 

 1831, at the laboratory of the Newton Chymical Company 

 near Boston, in the United States of America. I had not at 

 that time met with Dr. Henry's analysis of the white solid 



Q2 



