Prof. Sylvester on Tactic. 45 



other by reflexion from it. The images are 

 made to overlap, and their intensity is regu- 

 lated by altering their distance from F. 



Analogous to this is the observation of 

 Brewster*. Speaking of uniting similar 

 pictures (patterns on hanging-paper) in bin- 

 ocular vision, he remarks, " The surface of it (the wall) seems 

 slightly curved. It has a silvery transparent aspect." Here the 

 images (though of the same intensity, &c.) moving with each 

 slight movement of the head induces in the mind the idea of one 

 object seen through another. 



In closing, I will remark that while many of the experiments 

 above mentioned are easily repeated, others require considerable 

 practice in this kind of observation. 



VIII. Concluding Paper on Tactic. By J. J. Sylvester, M.A., 

 F.R.S., Professor of Mathematics at the Royal Military Aca- 

 demy, Woolwich -f . 



IN my tactical paper in the May Number of the Magazine, I 

 considered the number of groupings and of types of group- 

 ings of synthemes formed out of triads of three nomes of three 

 elements each. The first example of considering the ensemble of 

 the groupings of a defined species of synthemes (each of such 

 groupings being subjected to satisfy a certain exhaustive con- 

 dition) was, as already stated, furnished by me in this Magazine, 

 April 1844. In that case the synthemes consisted of duads 

 belonging to a single nome of 6 elements, and the total number 

 of the groupings was observed to be 6, all contained in one type 

 or family. The total number of synthemes in that instance being 

 15, and there being 6 groupings of 5 synthemes each, it fol- 

 lowed that in the whole family every syn theme is met with twice 

 over ; once in one grouping, and once in another. In the case 

 treated of in my last communication to the Magazine, the total 

 number of the synthemes of the kind under consideration is 36 

 (for it may easily be shown that the number of synthemes of 

 w-nomial a-ads of n nomes of q elements each is (1.2.3. . . q) n ~ l ); 

 and as each grouping contains 9 synthemes, these 36 are distri- 

 buted without repetition between the 4 groupings of the smaller 

 of the two natural species, — a phenomenon of a kind here met 

 with for the first time in the study of syntax. If now we go on 

 (as a natural and irrepressible curiosity urges) to ascertain the 

 .groupings of the synthemes of binomial triads of the same 3 



*,The Stereoscope, p. 91. London, 1S56. 

 t Communicated by the Author. 



