150 THE ROYAL SOCIETY OF CANADA 



stration of its utility can be made without an extended analysis and 

 further consideration of a large number of tides in the light of the 

 special requirements of hydrographers. The results illustrated in 

 Fig. 4 alone appear to have justified the work; they are most suggestive 

 and apparently fît the particular difficulty which led to these pro- 

 jection experiments, but it is apparent that in the development of the 

 technique and practical directions for analysing estuary tidal curves 

 in this manner, and in the possible association of the new constants 

 with some physical factors, most of the work remains to be done. 



§4. The Projection Apparatus. The apparatus which was as- 

 sembled for these tests was of a very simple character. The main part 

 of the apparatus, shown in Fig. 7, was constructed from part of the 

 framework and stand designed for an adjustable mirror. The rotation 

 of the supporting stand as a whole gave the angle 6, while the inclin- 

 ation of the frame about its axis which was fixed in direction with 

 reference both to the frame and its stand, gave the angle </>. In an 

 improved instrument, the size of the frame should be increased and 

 its solid parts should be reduced to minimum dimensions in order to 

 avoid the shadows which interfere seriously when the angles of pro- 

 jection are large. 



Behind the tilting frame lies the "projection plane" or "plane 

 of reference," which is parallel to, and will receive the same projec- 

 tions as the imaginary "initial plane." It is conveniently made with 

 a plate of glass, to which paper may be stuck ready for the tracing of 

 the projected shadows. 



An ordinary magic lantern is suitable for the production of the 

 beam of light, but a large and very good lens must be employed in 

 order to get a satisfactory parallel beam giving sharp definition to 

 the shadows. In our case the objective of a large telescope was used, 

 in such a way that the various parts of any given figure could in turn 

 be projected by the central part of the beam. 



The graphs were cut out of thin, stiff cardboard, and held in 

 place by drawing pins and thin metal supporting strips as shown in 

 the photograph. 



A telescope and distant mirror were also tried instead of the 

 beam from the lantern, but the accuracy obtained in tracing the 

 curves by this method was inferior, and the process very tedious in 

 comparison. 



In conclusion the writers desire to express their thanks and to 

 record their indebtedness to Dr. Dawson, who suggested the problem, 

 and who has very kindly written the introduction (§1.) to these notes. 



