第1676章：贵族之家（Ⅳ）
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“好了帕拉丁娜，可别把小伙子吓坏了，我整理出的经验公式无非纸上谈兵，只是一种纯粹的理论研究，给他看看也无妨。”西格蒙特笑着将手稿递给罗兰。
罗兰接过来翻了翻，抬头时眼中露出诧异：“这是……微分方程？”
西格蒙特轻轻点头，“为了研究这些数据资料，我特地聘请了一位数学教授，抽出空来就请他给我补课，现在看来为此花费的精力是值得的。”
罗兰穿越前在大学读书时主修经济史专业，虽说可以归为文科院系，基本的微积分课程还是必修的，只是多年不用这些知识难免有些生疏，连蒙带猜的勉强看懂西格蒙特元帅的论文。
这部手稿分为两个篇章，第一篇概述了战场上两军对垒的兵力配置。出于方便分析起见，西格蒙特将现实中那些非常复杂的兵种加以简化，统统归纳为两种基本类型：近战兵种与远程兵种。近战包括步兵与骑兵，远程则包括弓弩与大炮，因此其研究无论对单纯的冷兵器时代抑或大量运用枪炮与魔法的当代战争都适用。
论文的第二个篇章，西格蒙特元帅对其多年来搜集的数据进行了分类整理。这些数据全部来自历史上真实发生过的战争，其中也包括他亲身参与和指挥过的大小战役。
运用计量统计工具处理上述数据，西格蒙特元帅总结出两个经验公式，统称为“战斗方程”。
根据第一篇提出的兵种分类，西格蒙特进一步将战场上双方冲突简化为两种基本情况：远距离交火和近距离厮杀，两种情况适用于不同的战斗方程式。
当战场双方远距离隔空对射时，一方的损失率既和对方兵力成正比，也和己方兵力成正比，通过数学运算——解一个常微分方程组——可知，一方的实力和本身战斗单位的数量成线性关系，西格蒙特在手稿中将之命名为“线性律”；反之，当战场上的双方在近距离集中火力杀伤对手时，战场上一方的损失率仅和对方战斗单位数量成正比，而与己方战斗单位数量无关，同样通过解微分方程运算可知，任一方实力和本身战斗单位数量的平方成正比，亦即西格蒙特在手稿中命名的“平方律”。
为了方便罗兰和帕拉丁娜理解，西格蒙特在黑板上画出两军交战的简图。
“假设交战双方分别是蓝军和红军，考虑到武器装备和训练等因素的差异，设定蓝军平均单兵战斗力是红军四倍，那么00名蓝军和400名红军的战斗力相同，现在00名蓝军和400名红军远程对射，战斗持续到至死方休，那么交战的结果将是双方耗尽最后一兵一卒，同归于尽。”
西格蒙特拿抹布擦净黑板，又画出红蓝双方的近战图解。
“现在还是假定蓝军平均单兵战斗力是红军的四倍，00名蓝军和400名红军进行肉搏战，通过简单的计算可知，当蓝军00人全军覆没时红军仍有346人存活，即损失54人，由此可见近战中优势兵力一方的实际损失比劣势兵力一方的损失小得多，而单兵实力的优势则被大大削弱。”
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