For a pendent drop whose contact line is a circle of radius $r_0$, we derive the Furmidge-like relation $mgsin\alpha =\frac{\pi }{2}\gamma r_0(cos{\theta }^{min}-cos{\theta }^{max})$ at first order in the Bond number, where ${\theta }^{min}$ and ${\theta }^{max}$ are the contact angles at the back (uphill) and at the front (downhill), $m$ is the mass of the drop and $\gamma$ the surface tension of the liquid. The Bond (or Eötvös) number is taken as $Bo=mg∕\left(2r_0\gamma \right)$. The tilt angle $\alpha$ may increase from $\alpha =0$ (sessile drop) to $\alpha =\pi ∕2$ (drop pinned on vertical wall) to $\alpha =\pi$ (drop pendent from ceiling). The focus will be on pendent drops with $\alpha =\pi ∕2$ and $\alpha =3\pi ∕4$, while $\alpha =\pi ∕4$ is also included for comparison. The drop profile is computed exactly, in the same approximation. Results are compared with Surface Evolver simulations, showing good agreement up to about $Bo=1.2$, corresponding for example to hemispherical water droplets of volume up to about $50\mu$L. An explicit formula for each contact angle ${\theta }^{min}$ and ${\theta }^{max}$ is also given and compared with the almost exact Surface Evolver values.

对于垂线，其接触线是半径的圆 ${\mathrm{[R}}_0$，我们得出类似Furmidge的关系 $米G罪\alpha =\frac{\pi }{2}\gamma {\mathrm{[R}}_0（cos{\theta }^{分}-cos{\theta }^{最高}）$ 以债券编号的第一顺序，其中 ${\theta }^{分}$ 和 ${\theta }^{最高}$ 是后面（上坡）和前面（下坡）的接触角， $米$ 是下降的质量， $\gamma$液体的表面张力。债券号（或Eötvös）取为$乙Ø=米G∕（2{\mathrm{[R}}_0\gamma ）$。倾斜角度$\alpha$ 可能从 $\alpha =0$ （无滴）到 $\alpha =\pi ∕2$ （将水滴固定在垂直墙上） $\alpha =\pi$（从天花板垂下）。重点将放在$\alpha =\pi ∕2$ 和 $\alpha =3\pi ∕4$，而 $\alpha =\pi ∕4$还包括用于比较。下降轮廓以相同的近似值精确计算。将结果与Surface Evolver模拟进行了比较，显示出良好的一致性，直到大约$乙Ø=\mathrm{1个}。2$，例如对应于体积最大约为 $50\mu$L.每个接触角的明确公式 ${\theta }^{分}$ 和 ${\theta }^{最高}$还给出并与几乎精确的Surface Evolver值进行比较。