Which the area represents from the following formula, which is expressed in terms of the absolute temperature T, of the steam at the steam-pipe, and the temperature T2= 461°H-212° =673° absolute corresponding to the back pressure: - Maximu per pound oflsteaelwork =U=(T - T) (i -f -**Lr**--.1) - T2loge.Tr--2.

(n+--r-1)**lr**!=n[r]**lr**!; this may, by analogy with the notation of ï¿½41, be denoted by n [r 7.

Now if k denotes the component of absolute velocity in a direction fixed in space whose direction cosines are 1, m, n, k=lu+mv+nw; (2) and in the infinitesimal element of time dt, the coordinates of the fluid particle at (x, y, z) will have changed by (u', v', w')dt; so that Dk dl, do dt dt dt dt + dtw +1 (?t +u, dx +v, dy +w, dz) +m (d +u dx + v dy +w' dz) dw, dw +n (dt ?dx+v?dy +w dz) But as 1, m, n are the direction cosines of a line fixed in space, dl= m R-n Q, d m = nP-**lR** an =1Q-mP dt dt ' dt ' so that Dk __ du, du, du, du dt l (dt -vR+ wQ+u + v dy + w dz) +m(..

Also P. Paulitschke, Harar: Forschungsreise nach den Smalland Galla-**Lr** ndern Ost-Afrikas (Leipzig, 1888).

In the case of the sphere, for instance, whose radius is R, the area of the section at distance x from the centre is **lr**(R 2 -x 2), which is a quadratic function of x; the values of So, Si, and S2 are respectively o, 7rR 2, and o, and the volume is therefore s.

Then w 3 = (w l +w 2)1 2 /(Cds-1 2) = (w i -Fw 2)**lr**/ (Cs -**lr**), where C is a constant for any type of girder.

Hence the formula is more useful in the form w = (w i +w2)1 2 / (Kd -1 2) = (wl +w 2)**lr**/ (K -**lr**) where k= (wl+w2-1-w3)**lr**/w3 is to be deduced from the data of some bridge previously designed with the same working stresses.

Run in tons, is wa = (wl+w2)1r/(K-**lr**) according to a formula already given, then w 3 becomes infinite if k-**lr** =o, or if 1 = K/r, F I --xJ- ----- ---- -?

,. ??, iP **lr** kkltt 9 Vlieland R% ?

The number of the Beast, 666, points certainly to Nero (**lr** -op =666, or

The orbit has therefore two asymptotes, inclined at an angle **lr**/m.

Hf?**lr**,dhead toekbrid ge 'a' 1 o olbor ne y?r ?

Here we have u„+1 =2un+(2nI)2un-**lr** whence uh+1 -(2n +I)ac„= -(2n-I)(un-(2n-I)un_1}, and we readily find that p n I I I I 2 n I whence the value of the fraction taken to infinity is t r.

For a crossed belt: L = 2-.lCf (ri +r2)2+ (Ti +ri) (lr_2 sin4~-~!i); (32A)