1887.] W. H. P. Driver— Notes on the Assure, fyc. 251 



by means of a single variable parameter, the coordinates of the corre- 

 sponding point on the oblique trajectory may be similarly expressed. 

 The third section gives the first example where the theorem is applied 

 to the solution of Mainardi's problem. The fourth section contains the 

 next six examples ; the second example deals with a system of confocal 

 hyperbolas ; the third example considers a system of parabolas which 

 have a common principal axis, and which touch each other at their 

 common vertex ; the fourth example treats, in two different ways, of a 

 pencil of coplanar rays radiating from a point ; the fifth example is 

 about a system of circles which touch each other at a given point ; the 

 sixth example is concerned with a system of parabolas which have a 

 common focus and principal axis ; the seventh example considers the 

 case of a certain transcendental curve. The fifth and last section of 

 the paper treats of the application of the theory of Conjugate Func- 

 tions to the subject under consideration ; a new theorem is established 

 which materially simplifies the calculations in many cases, of which 

 three striking examples are given ; the eighth example treats of the 

 oblique trajectory of a tricircular sextic ; the ninth example considers 

 the inverses of a system of confocal ellipses, while the tenth example 

 deals with a transcendental curve ; the results are obtained with re- 

 markable ease by the general theorem of this paper and a judicious use 

 of conjugate functions ; but from an inspection of their very form, it is 

 clear that to have obtained the equations of these trajectories by the 

 ordinary process, would have been well-nigh impossible. Lastly, a very 

 interesting method is pointed out by which we may obtain, without any 

 difficulty, an infinite number of curves whose oblique trajectories may 

 be determined with ease by the theorems and methods of this paper.* 



The paper will be published in full in Part II, of the Journal for 

 1887. 



2. The Kudarlchot inscription of Talchshadatta. — By Dr. A. 

 EiJHRER, (with an ink impression). 



3. Couplets on coins of Jehangir. — By 0. J. Rodgers, Esq., Archae- 

 ological Survey of the Punjab. 



4. Notes on the Aboriginal tribes called Assurs, Brijias, Brihas, 

 Earias. — By W. H. P. Driver, Esq. 



* Since this paper was read, a note has been added at the end of the fifth 

 section, containing an elaborate disenssion of Mainardi's problem by means of 

 Elliptic Coordinates ; it is pointed ont that Mainardi's resnlt is really eqnivalent to 

 two solutions, of which only one is relevant to the problem, while the other is 

 wholly extraneous; this remarkable fact does not seem to have been noticed before. 



