Royal Society of Edinburgh. 141 



experiaienting as to the best mode of feeding them, at least two 

 feline animals : that one be fed in the manner now practised at the 

 Society's Gardens, viz. with one full meal daily, and that the other 

 be fed twice a day with one half the quantity of flesh now given for 

 a meal ; that notes be made of the circumstances of the animals at 

 the time of commencing the experiment, of the quantity of food 

 taken daily by each, of the times of feeding, and of the results; 

 and that reports thereon be made monthly during the continuance 

 of the experiment : that to render the results of the experiment 

 more conclusive it be tried on the greatest number of any one spe- 

 cies that the state of the Society's collection will permit : and that, 

 so far as the collection will allow, similar experiments, varying only 

 according to circumstances, be tried on animals of other carnivorous 

 genera. 



ROYAL SOCIETY OF EDINBURGH. 



Dec. 19. — A paper on Sp/(e?ica/ Loci, by T.S. Davies, Esq. F.R.S.E. 

 F.R.A.S. was read. The earliest attempts to investigate the proper- 

 ties of figures traced on the surface of the sphere were made 

 in consequence of the celebrated challenge of Viviani to the ana- 

 lysts of his day, to find a portion of the sphere which admitted of 

 accurate quadrature. The processes generally employed by those who 

 attempted its solution consisted in impressing the orthogonal projec- 

 tion on the plane of the equator, and combining this with the coiie- 

 sponding value of the vertical ordinate, to obtain an integrable expres- 

 sion for the area in question. A corresponding problem to find a line 

 traced upon a spherical surface which should be rectifiable, was also 

 proposed some time afterwards by M. Offenberg ; and though the so- 

 lution was unsuccessfully attempted by Hermann, it was solved by 

 John Bernoulli, Maupertuis, Clairault, and Mirle, in the Paris Mc- 

 vioires for 1732. About this period attention was diverted from 

 the inquiry under this aspect by the general method developed by 

 Clairault in his Analyse des Lignes Courbes, in which he proposed the 

 method now universally adopted of expressing all curves of double 

 curvature by two equations between three variables. On this princi- 

 ple all spherical curves were considered as the intersection of a sphere 

 with some other given surface : and no change of method from that 

 period to the present seems to have been contemplated by any geo- 

 meter. 



It will be recollected that the nature of the hour lines upon the an- 

 tique sun-dials has been a subject of discussion amongst astronomers 

 and geometers from the time of Commandine to our own day. De- 

 lambre returned to the incjuiry repeatedly, and to the last without 

 any satisfactory results. Mr. Cadell in the eighth volume of the Edin- 

 burgh Transactions showed by actually tracing them upon a polar 

 dial, that in that case they were sensibly curved ; and he hence in- 

 ferred that the lines on the sphere of which these were the projections 

 were not great circles. He stated also that this variation was visible 

 when Die lines which n sected the semi-diurnal arcs were traced on 

 the sphere ; but lie failed in showing tiie nature of the lines them- 

 selves. 



