18 



Mr. W. D. Niven on the Calculation 



[May 11, 



of certain corals, the author discusses the classificatory position of the 

 vegetable form. Naming it Achlya penetrans, he suggests that it belongs 

 to a group whose life-cycle is complicated by marine and subaerial con- 

 ditions, and infers that Achlya, Saprolegnia, Botrytis, Pe?'onospora, Empu- 

 sina^ and possibly Bryopsis are so many names of the same organism 

 under these different conditions. Believing in the necessity of an arbi- 

 trary name, he prefers that of Achlya. Finally an instance of a parasite 

 resembling what is called Saproleynia ferax\ Ktz., in a littoral coral is 

 given. 



II. On the Calculation of the Trajectories of Shot.'' By W. 

 D. Niven, M.A., F.B.A.S. Communicated by J. Clerk 

 Maxwell, F.B.S., Professor of Experimental Physics in the 

 University of Cambridge. Received March 24, 1876. 



(Abstract.) 



The solution of the equations of motion of a shot is necessarily ap- 

 proximate, because the resistance cannot be expressed by a single exact 

 formula, and, moreover, there are very few formulae which are capable of 

 aifording an easy solution. The results which Hutton obtained by 

 means of the ballistic pendulum were exhibited in the shape of a simple 

 formula ; and in like manner Piobert and Didion, who also used the 

 ballistic pendulum, reduced their results, and were able to give simple 

 formulae. No one can doubt, however, that, in point of accuracy and 

 extent of information, their results are inferior to those which Mr. 

 Bashforth obtained by means of his chronograph and screens. Now 

 the formulae which Hutton and Didion gave apply only to spherical shot ; 

 and even for that kind of shot they do not agree with Mr. Bashforth's 

 results except for a limited range of velocities. Mr. Bashforth makes no 

 attempt to formulate his results, but produces them in the shape of two 

 Tables, one for spherical shot, the other for cylindrical. The nature of 

 the reductions of his experiments, and the fortunate circumstance that 

 for a large range of values of the velocity the resistance varies nearly as 

 the cube of the velocity, render it convenient to express the resistance in 

 the form ij.v^, where v is the velocity and fi a variable coefficient. In 

 fact, if cl is the diameter of the cross section of the shot in inches, and 

 W its weight in lbs,, the retardation due to resistance is 



w uooo;' 



where K is a number which is tabulated for every 10 feet of velocity. 

 The question, then, is to solve the problem of the motion of a shot in 

 conjunction and agreement with the Tables for K. The problem is a 

 very important one, not only to the gunner but the gun-maker, there 

 being many practical questions, for example, connected with the dimen- 



