ON THE COHESrOK OF FLUIDS. 



667 



care, and by difteient methods. I had before 

 formed a table, by means of diagrams, which 

 I had actually constructed for each case, 

 upon a sufficiently accurate approximation : 

 1 have now followed nearly the same steps 

 in calculatint;, bv means of tables of sines 

 and cosines, the precise form of the surface 

 in a variet}' of cases. Beginning from the 

 vertex of the curve, I have determined the 

 mean curvature for every small arc, from the 

 approximate height of its middle point; calcu- 

 lating, with the assistance of a series of diffe- 

 rences, the normal of the curve at each step 

 for the same point, in order to find the trans- 

 verse curvature. I have also pursued, in 

 some cases, in order to confirm these calcu- 

 lations, a method totally different, finding 

 the mass of the quantity of fluid to be sup- 

 ported by the tension of the surface at each 

 concentric circle, and inferring from its mag- 

 nitude the inclination of the curve to the ho- 

 rizon : taking the height of the external cir- 

 cumference of each portion, thus calculated, 

 for the mean height; a supposition which 

 nearly compensates for the omission of the 

 curvature of its surface. But the accumu- 

 lated effect of this curvature becomes very 

 sensible in the vertical height of the surface, 

 and I have' therefore allowed for it, upon tiie 

 supposition of a simple curvature varying 

 with the height; but this correction, for 

 want of including the effect of the variation 

 of the transverse curvature, is still a Ifttle too 

 small; the horizontal diameter of the sur- 

 face, however, agrees extremely well with 

 the former mode of calculation. In order 

 that the results of these investigations may 

 be the more easily compared with each other, 

 and with experiment, I shall insert some spe- 

 cimens, by means of which, if it be required, 

 the curves may be very correctly delineated. 



1. Central depression .007. 



FIRST METHOD, BY THE CURVATUBI» 



Arc. Horizontal Depression. 



0'' 

 1 



2 

 , 3 



4 



S 



6 



7 



8 



9 

 10 

 12 

 14 

 10 

 18 

 20 

 3S 

 30 

 35 

 40 

 45 

 50 



ordinate. 



.00000 

 .02444 

 .04758 

 .06651 

 .0S338 

 .09?91 

 .11049 

 .12153 

 .13146 

 .14033 

 .14814 

 .16177 

 .17338 

 .18344 

 .ly220 

 .20012 

 .21603 

 .22869 

 ' .23891 

 .2473! 

 .25420 

 .25986 



.00700 

 .00721 

 .00782 

 .00865 

 .00968 

 .01082 

 .01203 

 .0)329 

 .01458 

 .01589 

 .01721 

 .01986 

 .02354 

 .02524 

 .02793 

 .03063 

 .03722 

 .04381 

 .05033 

 .05676 

 .06307 

 .06911 



SECOND M«TH0D, HT THE TENSION. 



Arc. 



Horizontal Depression, 

 ordinate. 



.00 

 .02 

 .04 

 .OS 

 .08 

 .10 

 .13 

 .14 

 .10 

 .18 

 .20 

 .22 

 .34 

 .26 

 .270s 



.00000 

 .02000 

 .04000 

 .05999 

 .07997 

 .09993 

 .11985 

 .13971 

 .15948 

 .17908 

 .19842 

 .21732 

 .23550 

 .25039 

 .25740 



.00709 

 .00714 

 .00757 

 .00830 

 .00939 

 .01101 

 .01303 

 .0156S 

 .01909 

 .02353 

 .02923 

 .03653 

 .04530 

 .05707 

 .06459 



2. Central depression .05. 



Arc. 



00 



1 



2 



3 



4 



5 



6 



7 



FIRST METHOD. 



Depression. 



Horizontal 

 ordinate. 



.00000 

 .00349 

 .00697 

 .01044 

 .01388 

 .01729 

 .02063 

 .02402 

 .02731 

 .0305S 



.05000 

 .05003 

 .05012 

 .05027 

 .05048 

 .0507 » 

 •05107 

 .05145 

 .0518* 

 .05237 



