Resistance to Motion of SMps. 389

quired on the plan of making the Lake of Nicaragua the summit level of the canal.

Having, from personal examinations~ formed the opinion that the general features of the country, aiIbcting the feasibility of con- structing the canal between the lakes of Nicaragua and Managua, were no more favorable than had been represented, there appeared to be no good reasons for regarding existing facilities for the con- struction of that beyond the Lake of Managua, not examined by the undersigned, with more favor than representations from the same sources seemed to justify.

(To be continued.)

RESISTANCE TO MOTION OF SHIPS, BY JOH~I Iaowl~ Second Assistant Engineer~ U. S. N.

Do~s the force propelling a vessel vary with the 1st, 2nd, 3rd or nth power of the speed ?

There is much difference of opinion upon this subject; some holding, that the force varies with the square, others, with the cube of the speed, while some hold that the resistance of the water to the vessel varies with the square of the speed, while the power necessary to overcome that resistance varies with the cube of the speed.

It is hardly worth while to investigate the subject of power and speed until this first condition is firmly fixed.

Without entering into argument as to which of these is true, it is proposed in the following to show how by the simple experiment of running a vessel againsg a stream, this subject may be placed beyond controversy.

W e will first assume the power to vary with the square, and ask~ What is the most economic speed against a current under this con- dition ? Let c = a co-efficient suitable to a particular vessel:

" u = power required to propel the vessel x knots per hour : " x = s p e e d of the ship through the water: " v = speed of the current:

Then ( x - - v ) = net speed of the ship:

cx 2 ur __ (z~wv) -" Power expended in advancing the vessel

1 knot net against the current~ which we require to be minimum,

390 G i v i l a n d M e c h a n i c a l E n g i n e e r i n g .

d u 2 cx ( x - - v ) ~ c x 2 ~ 2 x - - x~ Differentiating; d~-x= (2--v) 2 (x~v) - ~ 0

Whence 2 x - - 2v = x, or x ~ 2v That is, if the power varies with the square of the speed, then the most economic speed against a current is, twice the speed of the current.

Similarly it may be proved, if the power varies with the cube of the speed, then 1½ times the current is the economic speed. If u ---- c x 4 then x --=- 1½ v, etc. etc.

This much proved. The experiment is simply in running a ves- sel twice as fast, 1½ times as fast, 1½ times as fast, etc., as the cur- rent. Then the most economic power, that is, the power and speed producing the best results per knot advanced against the current, will indicate, in an unmistakeable manner, which is the correct function.

The vessel chosen should be small, and therefore inexpensive to operate, easily and quickly handled, and the revolutions of the engines should be under complete control.

Magic-Lantern Pictures on Gelatine by a New Method. ~ A t the last meeting of the Franklin Institute, the Resident Sec- retary, Prof. Morton, exhibited in the lantern some pictures on gelatine, prepared in a manner devised by Mr. Sheperd ttolman, a member of the Institute.

For this purpose a sheet of gelatine such as is used for tracing by engravers, was securely fixed over an engraving, and with a sharp steel point, (made by grinding down the end of a small round file,) the lines of the original traced pretty deeply on the transparent substance. Lead-pencil or crayon dust was then lightly rubbed in with the finger, and the picture was at once ready for use.

A number of such drawings could be easily carried between the leaves of a book, could each in succession be in a frame or cell made of two plates of glass separated by a frame of thin card or three edges and united by paper or muslin pasted around the same edges. The effect of these drawings in the lantern was excellent, and their ease of production very great,