北京天安联合科技有限公司
【简单介绍】
0.5麦氏比浊管 【使用方法】：1、
轻摇标准试管。2、
无菌操作将被测定的肉汤培养物加到与标准管相同直径（大小）的无菌试管中。3、
以无菌操作向被测定试管加入无菌蒸馏水，直到浓度与所要求的标准管的浓度相同。【计算被测培养物试管的浓度
【详细说明】
0.5麦氏比浊管麦氏比浊管&管&号（McFarland）0.5123450.25%BaCl2（ml）0.20.40.81.21.62.01%H2SO4（ml）9.89.69.28.88.48.0细菌的近似浓度（&108/ml）1.53691215细菌的近似浓度（百万/ml）15030060090012001500&【使用方法】：1、&&轻摇标准试管。2、&&无菌操作将被测定的肉汤培养物加到与标准管相同直径（大小）的无菌试管中。3、&&以无菌操作向被测定试管加入无菌蒸馏水，直到浓度与所要求的标准管的浓度相同。【计算被测培养物试管的浓度】：1、&&第2个标准管为3&108细菌/ml的倍数。2、&&细菌浓度标准管号&3&108=该管号的细菌/ml。3、&&例如：3号管（#3）为9&108细菌/ml。【制备所要求的浓度，如需要105细菌的浓度】：1、&&相当1号管（3&108）的细菌作1：3稀释到108。2、&&再作1：1000稀释。3、&&108-103=105【注意事项】：1、&&如果测定的肉汤培养物不澄清。A、由培养物的值减去未接种培养基的值来校正细菌浓度。B、列: 4号管（肉汤培养物）-1号管（孵育过的未接种的肉汤管）=3号管（校正读数）&2、如果肉汤颜色很深,把未接种试管放在标准管的后面读数即可。联系人：李小姐
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扫一扫访问手机站Glutamate and Hypoxia as a Stress Model for the Isolated Perfused Vertebrate Retina | Protocol (Translated to Chinese)
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有了这个研究中，我们实行规范的应力模型的隔离灌流牛视网膜对未来临床治疗试验。要么缺氧（纯的N 2）或谷氨酸应力（250μM谷氨酸）对由a-和b-波振幅为代表视网膜功能的效果进行了评价。
Cite this Article
Januschowski, K., Müller, S., Krupp, C., Spitzer, M. S., Hurst, J., Schultheiss, M., Bartz-Schmidt, K. U., Szurman, P., Schnichels, S. Glutamate and Hypoxia as a Stress Model for the Isolated Perfused Vertebrate Retina. J. Vis. Exp. (97), e52270, doi:10. (2015).
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神经保护已调查的一个强电场在眼科研究在过去的几十年，并影响疾病如青光眼，视网膜血管阻塞症，视网膜脱落，以及糖尿病视网膜病变。它是本研究引入一个标准化应力模型为未来的临床前治疗试验的对象。 制备牛视网膜和灌注的饱和氧标准溶液中，ERG记录。记录稳定的B-波，缺氧（纯的N 2）或谷氨酸应力（250微米谷氨酸）后施加45分钟。调查于光感受器功能单独的影响，1毫天冬氨酸加到得到波。 ERG恢复75分钟进行监测。 对于缺氧，在为87.0％，波幅下降注意到（P &0.01），后45分钟（减少36.5％的冲刷P = 0.03结束后）博览会时间。此外，初始DECR缓解的记录87.23％b波振幅，即达到统计学意义（p &0.01，减少了25.5％，在冲洗结束时，p值= 0.03）。 为250微米的谷氨酸，初始还原，随后还原了1.9％（P& 0.05）a-波振幅（P& 0.05）7.8％。减少b波振幅（P &0.01），指出了83.7％;减少了75分钟的冲洗后为2.3％（P = 0.62）。在这项研究中，一个标准化的应力模型被呈现，可能是有用的，以确定在未来可能的神经保护作用。
Introduction
神经保护一直在调查研究的眼科在过去几十年的强场。视网膜是氧合显著取决于并强烈地受到其周围细胞的代谢的影响高度敏感的神经元网络。涉及神经细胞的损伤大眼病症是视网膜血管闭塞，青光眼和视网膜脱离。 视网膜动脉闭塞，作为网膜血管闭塞症，例如，导致视力突然损失，由于视网膜内层1缺氧。它通常与一般的血管病理学2和导线的持久视觉损失相关联，只有8％的患者恢复视力显著1。虽然动脉纤溶 已建议作为一种治疗选择，好处不能显示在一个随机临床试验3。 青光眼和视网膜脱离都有增加谷氨酸浓度4-6。生理条件下，谷氨酸遇到作为兴奋性发射机在整个中枢神经系统和视网膜内层7,8。提高谷氨酸含量已经发现不仅在青光眼和视网膜脱离5,6而且在增殖性糖尿病视网膜病变9。谷氨酸的增加可能会导致兴奋性毒性，因此，神经细胞的损伤10。在视网膜脱离和在某些情况下在视网膜上（玻璃体）增生性糖尿病性视网膜病的手术大多数情况下是必要的。在玻璃体机械操纵，明亮的光线光纤或在长期的经营中灌溉解决方案的高流速产生的剪切应力对视网膜11,12施加了额外的压力。 所有的提到的疾病的共同之处在于所述病理定位于雷廷一个单独构成的眼科界的挑战，想方设法保护视网膜神经上一个系统。 电图（ERG）是用于在体内光感受器功能（一个波）和内视网膜（b波）的功能的评价的标准方法。 ERG的被引入到角膜银电极来测量和眼睛正在刺激光的增加的水平，以检测在杆或视锥细胞或视网膜内层缺陷。在视网膜的不同的缺陷可以通过改变幅度（响应的强度）或ERG的延迟（时间到响应的时间间隔）来检测。不同的ERG协议和测量方法（模式-ERG，多焦-ERG或明场ERG）允许缺陷进一步分化。分离的视网膜的技术最近已经引入，使得可以评估，而不脱离如一个研究动物的干扰在视网膜上的影响一般反应13,14。 正是这种研究，评估和引进定义和标准化应力模型的缺氧和谷氨酸应力的隔离灌流视网膜的目的。因此，我们希望能为今后的某些代理商或眼内冲洗液的保护作用的研究奠定了基础。 Subscription Required. Please recommend JoVE to your librarian.
1.准备牛眼睛获得牛眼中的动物屠宰后直接。 输送保护眼睛“Sickel溶液”含有120mM氯化钠，2mM的氯化钾，0.1mM的MgCl 2的，0.15毫氯化钙 ，1.5mM的的NaH 2 PO 4，13.5毫的Na 2 HPO 4和5mM葡萄糖在一个特殊的介质RT。 用昏暗红光暗适应的条件下进行视网膜的制备。 取出眼睛的前部。执行赤道切口长约4毫米后的角膜缘。此后在一块除去角膜，虹膜，睫状体和透镜。请Sickel-解决方案的视网膜。 机械地松开玻璃体附着物视网膜表面，并从打开的眼杯除去玻璃体。 随后划分眼睛成四个象限和切出圆约领域直径7mm使用环钻。 轻轻分开视网膜从色素上皮，并将其放置在记录设备上的内避光的盒子。该记录装置由一个塑料维护者在中间的网格的;放置在网格的视网膜，然后用一个塑料环，直接在电极上固定。 注：塑料维护者有两个通道，以允许介质的恒定流速。
2.录音电图（ERG） 为了记录的电图，使用两个银/氯化银电极在视网膜上的任一侧和灌注的视网膜在大约恒定的灌注速度1毫升/分钟和37℃的恒温。使用与氧饱和“Sickel-的解决方案”。 开始测量之前，暗适应视网膜（在所有测量保护其不受光），并使用了5分钟的刺激间隔。使用1赫兹单一白色氙气闪光灯的刺激强度设定为6.3 MLX在视网膜表面。 </LI& 使用校准的中性密度滤光片和10微秒的光刺激由计时器为了具有最佳的反应进行控制。 测量和处理数据，过滤的ERG，并用草RPS312RM放大器放大它（100赫兹的高通滤波器，50赫兹的陷波滤波器，100,000×放大）。试图筛选出可能的干扰频率，可能会干扰信号。为了处理数据，使用模拟 - 数字数据采集板的台式计算机（PC兼容）上。 在恒定灌注的暗适应期后，测量的电信号的幅度，直到稳定b波振幅被记录。 注：振幅被认为是稳定的，如果五个单测量达到一个平均值和偏差小于10％。单次测量的一个很好的例子是在图1。 开始测试，无论是纯氮气代替纯氧（单实验数n = 5）来测试缺氧或250微米谷氨酸（N = 5）。 记录电反应，每5分钟45分钟。 在测试期结束后，灌注的视网膜与氧饱和75分钟的标准培养基，并期待在b-波振幅的变化。这是洗出阶段。测量从一个波到b-波的峰值的波谷的b-波幅度。 调查低氧或谷氨酸上暗的条件下的感光体电位的效果，抑制b-波通过加入1mM至所述营养液。 记录一个稳定的光感受器电位30分钟后，执行程序和以前一样，露出了视网膜45分钟，以不同的冲洗液以1 mM的天门冬氨酸。使用相同的洗脱期（步骤2.8）正如前面提到的。
3.数据分析为了统计评估数据，确保正常的分布所有的数据， 如使用柯尔莫哥洛夫-斯米尔诺夫测试15。 计算的a-和b-波振幅的百分比在曝光阶段之后的减少相比，最后一次测量的论述之前。 45分钟后，比较ERG-振幅的减小 - 在暴露时段的结束 - 到ERG应用之前测量。 比较在冲洗阶段相应幅度的论述之前结束的A股和B超波，研究可能的复苏。 进行统计分析，使用该软件JMP统计软件SPSS或软件。整个计算的平均值±标准差的数据。估计由相应的统计检验的意义。 注：这些测试可能会根据不同的实验范围。在这种背景下，使用学生的配对t检验。 Subscription Required. Please recommend JoVE to your librarian.
Representative Results
1小时视网膜制剂与氧饱和标准溶液（ 图1A和B）的灌注后ERG-振幅表现出稳定和单次测量之间的振幅的变化较小。 pH值，渗透压，温度和PO 2（除了低氧测试）保持恒定为所有测试。 为了隔离从内视网膜的信号的感光信号，1mM的天冬氨酸加入到标准溶液来抑制b-波（ 图1A）。在缺氧的效果测试，为87.0％，波幅下降注意到（P &0.01），后45分钟的曝光时间。在冲洗结束后，下降了36.5％，有人指出，有统计学显著（P = 0.03， 图2A）。此外，在87.23％，b波振幅初步录得跌幅，这同样达到统计学意义（P &0.01）。在这种设置减少了25.5％有人指出，这是统计上显著（p值= 0.03， 图2B）。 论述与250微米谷氨酸，7.8％的非显著减少（P& 0.05）所定义的时间间隔后检测幅度的波数据。其次是非显著减少1.9％（P& 0.05， 图3A）。单次测量示于表1和2。 关于b波，降低ERG的幅度由83.7％录得的统计学显著（P &0.01， 图3B）。在冲洗结束时，一个b波恢复指出导致75分钟灌注用标准溶液（p值= 0.62）后的非显著减少为2.3％。
图1：从离体牛视 网膜的ERG测量实例 （A）的一个波如图4所示。离体灌注牛视网膜的ERG。 b-波通过加入1mM的天冬氨酸到营养液抑制。（B）中的b波是暗光条件下占主导地位。 10毫秒的光刺激在6.3毫升×光强度使用。
图2：效果缺氧的45分钟中的（A）中的曝光时间之后的波和在ERG的（B）的 b波的振幅。代表药物系列平均值（N = 5）。曲线上方单杠标志着缺氧时间。虚线（A）标志着天门冬氨酸1毫米的应用揭露感光潜力。标准偏差为每个系列实验直接之前和之后，以及在试验结束时给出。在使用标准偏差的时间点进行统计分析（直接之前和之后应用索引离子以及在试验结束时）：（A）在波的87.0％，幅度注意到后相比，试验初期45分钟博览会时间的减少。在试验结束时，显著下降36.5％，有人指出，（B）的87.23％，b波幅度的显著录得跌幅在博览会结束时间。在试验结束时，显著减少25.5％，有人指出。
图3：影响施加45分钟的（A）的 250μM谷氨酸一波振幅与离体灌注牛视网膜平均的代表性药物系列的ERG的（B）的 b波振幅（N = 5） 。曲线上方的水平杆马克谷氨酸的应用。虚线（A）标志着天门冬氨酸1毫米的应用揭露感光潜力。站ndard偏差每个系列实验直接之前和之后，以及在试验结束时给出。 （A）的250微米谷氨酸非显著减少一个波的曝光时间后：在时间点与标准偏差（直接前和使用后在试验结束以及）进行统计分析幅度（7.8％）进行检测。在试验结束时，发现非显著减少1.9％。（B）关于b波，显著降低ERG的幅度由83.7％的记录。在试验结束时，非显著减少2.3％，有人指出。
时间[分钟]
b波振幅[μV]
一个波振幅[μV]
&TD ALIGN =“右”& 0.
0. <td a河旁=“右”& 30
-3.4 </TD&
85 <td aligN =“右”& 6.2
&TD ALIGN =“右”& 2.
表1：柯尔莫哥洛夫-斯米尔诺夫的结果。 时间[分钟]
b波振幅[μV]
SD 一个波振幅[μV] </td&
0.5 <td对齐=“正确”&
55 <tdALIGN =“右”& 2.5
11.75 <td aligN =“右”& 2.5
表2：对缺氧b波振幅和波振幅代表测量。 <tR& 谷氨酸一个波数据谷氨酸b波数据缺氧波数据缺氧b波数据 ?
0.781 阿尔法 0.05
表3：250μM谷氨酸b波振幅代表测量和波振幅。 Subscription Required. Please recommend JoVE to your librarian.
Discussion
在这项研究中，在缺氧的45分钟后的b波振幅的显著影响被发现。本次减持仍是冲洗阶段后显著。可以观察到在感光体电位类似的效果。 结果被其他公布的数据16，给我们研究缺氧后可能神经保护作用的机会的支持。 后45分钟的论述250μM谷氨酸，我们没有发现只在b-波振幅为完全可逆的清除期的结束在统计学显著影响。感光体电位不是由250μM谷氨酸的影响。只有内视网膜受缺氧的事实表明该变化是非常微妙的，我们，因此，有可能的神经保护一个非常敏感的和标准化的指示器。天冬氨酸特异性抑制传输从感光体向地平线人或双极细胞，从而抑制b-波。 这一发现是违背绿色DG和Kapousta -布诺NV，谁发现，250和500毫米谷氨酸浓度比单独17家媒体的B波记录是随着时间的推移更加稳定的结果。为了解释这个矛盾，在设置几个不同需要加以考虑：Sickel-溶液用于在该模型中使用的其它出版物林格溶液。 测量进行与数组中的其他出版物有一个电极。而其他出版物所描述的新鲜大鼠的眼睛牛眼从屠宰场被使用。其效果是可逆的，在高浓度的谷氨酸一个时间的抑制。众所周知，一个特定的谷氨酸的量非常低的是必要的良好的维护眼睛和更高的量是有毒的。我们可以假设，在牛的眼睛从SLaughterhouse更多相比，导致谷氨酸含量是不同的实验添加谷氨酸比预期新鲜烹制的眼睛谷氨酸被释放。 测量使用阵列在整个视网膜而不是一个电极，其主要受最接近细胞的反应，也可能导致更长的存活时间，由于较低的机械损伤。最后，该媒体的组合物是至关重要的。在20世纪60年代，Sickel教授投入巨资开发这个 专业媒体对这些测量，他能够找到一个优化的媒体，而无需为谷氨酸稳定的视网膜反应13,14。 所描述的模型依赖于一个孤立的视网膜上，而不是整个动物。 在体内系统中，眼睛是由从该动物的其他器官的血液-视网膜屏障隔离。该模型的优点是，在干扰研究动物的参数，如麻醉或电极的位置不发生，其允许更高程度的标准化。标准化是在动物实验中的关键点上，特别是关于眼18。 该方法的局限性是短期测试期间和事实，即它不是一个动物模型。我们从经验中知道，ERG幅度保持稳定，约8小时，因此在介绍中提到的测试期可以延长到更长的论述和随访期，但每个人都应该考虑的不再是单一的实验延长，更可能会出现更高的标准偏差。 该模型的一个缺点是，因此，没有长期的研究可以进行和操作，以在视网膜只有有限数量是可能的。为广泛的操作和特殊尔格等作为在Dutescu 等人所述通过SLO引导多焦点ERG。例如， 在体内实验s为必要的19。 这种模式可以很容易地用于例如从摘除眼睛人类视网膜外植。由于这个敏感材料复杂获得，对牛视网膜实验是比较可行的，但应理解牢记这一点。 在协议中的关键步骤是运输和暗适应条件下准备视网膜。这是很重要的，以获得最大可能的响应。它有时可能需要几分钟从底层色素上皮轻轻分开视网膜。的冲压出视网膜轻轻摇动有时有助于这一过程。同时将在视网膜上的网，它放置在视网膜上的净的外视网膜是重要的。 trephanization后，在视网膜的边缘将稍微弯曲向上指示的内视网膜层的位置。 牛视网膜更类似于人的视网膜比较d，来啮齿动物眼睛的，因为类似的玻璃体透镜比和血管结构类似于人眼20的1视网膜;因此，虽然小型实验室动物如大鼠或小鼠被广泛用于测试视网膜的生物相容性，对这样的动物进行的毒性研究往往不太适用于人类20。所述myocilin基因的系统发育分析-一种基因在其突变形式引起的常染色体显性少年开角型青光眼-表明牛基因更密切相关的人基因比大鼠或小鼠21。 Myocilin可以发现在小梁细胞，以及在视网膜上。最后我们发现牛和人的孤立和尔格ERG效果12之间的良好关系。 在我们的模型天冬氨酸受雇于废除b波揭露感光潜在的P III。这给研究者的机会，以区分之间的内视网膜网络和光感受器功能22上的影响。而b波是一个关于集成功能更加敏感参数，所述一个波振幅更稳定，应力更耐，由于这样的事实，该一个波仅反映了光感受器的光反应它。与此相反，b波取决于不同的视网膜细胞的细胞 - 细胞相互作用和光感受器的活性。通过使用天冬氨酸以分离一个波是可能的检查操作的独自23的感光体的作用。 在这项研究中，可以用来测试神经保护剂的标准化的神经毒性模型中评估。作为一个前景将是有趣的，相关电生理功能与蛋白的生化分析或关联与细胞代谢，甚至表达的功能。 Subscription Required. Please recommend JoVE to your librarian.
Catalog Number
120 mM NaCl&
Merck Pharma, Germany
1,064,041,000
2 mM KCl,&&
Merck Pharma, Germany
1,050,010,250
0.1 mM MgCl2,&
Merck Pharma, Germany
58,330,250
0.15 mM CaCl2
Merck Pharma, Germany
111 TA106282
1.5 mM NaH2PO4/13.5 mM Na2HPO4&&
Merck Pharma, Germany
1,065,860,500
5 mM glucose
Merck Pharma, Germany
40,741,000
References
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24÷1.5-8.4×0.25 1+0.45÷0.9-8分之7 （5分之4-3分之2）X=12 0.4X+4×1.7=16.824÷1.5-8.4×0.25 1+0.45÷0.9-8分之7 （5分之4-3分之2）X=12 0.4X+4×1.7=16.8
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24÷1.5-8.4×0.25=16-2.1*（4*0.25）= 16-2.1=13.9 1+0.45÷0.9-7/8=1+0.5-0.875=0.625 （4/5-2/3）X=12（12/15-10/15）x=12 2/15x=12 x=90 0.4X+4×1.7=16.8 0.4x+6.8=16.8 0.4x=10 x=25
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扫描下载二维码MACHINERY''''S HANDBOOK 27th ED Part 5 pot - Tài li?u text
MACHINERY''''S HANDBOOK 27th ED Part 5 pot
FORCE AND SHRINK FITS 663Table 11. ANSI Standard Force and Shrink Fits ANSI B4.1-1967 (R1999)NominalSize Range,InchesClass FN 1 Class FN 2 Class FN 3 Class FN 4 Class FN 5Inter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsHoleH6 ShaftHoleH7Shafts6HoleH7Shaftt6HoleH7Shaftu6HoleH8Shaftx7Over To Values shown below are in thousandths of an inch0– 0.120.05 +0.25 +0.5 0.2 +0.4 +0.85 0.3 +0.4 +0.95 0.3 +0.6 +1.30.5 0 +0.3 0.85 0 +0.6 0.95 0 +0.7 1.3 0 +0.90.12– 0.240.1 +0.3 +0.6 0.2 +0.5 +1.0 0.4 +0.5 +1.2 0.5 +0.7 +1.70.6 0 +0.4 1.0 0 +0.7 1.2 0 +0.9 1.7 0 +1.20.24– 0.400.1 +0.4 +0.75 0.4 +0.6 +1.4 0.6 +0.6 +1.6 0.5 +0.9 +2.00.75 0 +0.5 1.4 0 +1.0 1.6 0 +1.2 2.0 0 +1.40.40– 0.560.1 +0.4 +0.80.5 +0.7 +1.6 0.7 +0.7 +1.8 0.6 +1.0 +2.30.8 0 +0.5 1.6 0 +1.2 1.8 0 +1.4 2.3 0 +1.60.56– 0.710.2 +0.4 +0.9 0.5 +0.7 +1.6 0.7 +0.7 +1.8 0.8 +1.0 +2.50.9 0 +0.6 1.6 0 +1.2 1.8 0 +1.4 2.5 0 +1.80.71– 0.950.2 +0.5 +1.1 0.6 +0.8 +1.9 0.8 +0.8 +2.1 1.0 +1.2 +3.01.1 0 +0.7 1.9 0 +1.4 2.1 0 +1.6 3.0 0 +2.20.95– 1.190.3 +0.5 +1.2 0.6 +0.8 +1.9 0.8 +0.8 +2.1 +1.0 +0.8 +2.3 1.3 +1.2 +3.31.2 0 +0.8 1.9 0 +1.4 2.1 0 +1.6 2.3 0 +1.8 3.3 0 +2.51.19– 1.580.3 +0.6 +1.3 0.8 +1.0 +2.4 1.0 +1.0 +2.6 1.5 +1.0 +3.1 1.4 +1.6 +4.01.3 0 +0.9 2.4 0 +1.8 2.6 0 +2.0 3.1 0 +2.5 4.0 0 +3.01.58– 1.970.4 +0.6 +1.4 0.8 +1.0 +2.4 1.2 +1.0 +2.8 1.8 +1.0 +3.4 2.4 +1.6 +5.01.4 0 +1.0 2.4 0 +1.8 2.8 0 +2.2 3.4 0 +2.8 5.0 0 +4.01.97– 2.560.6 +0.7 +1.8 0.8 +1.2 +2.7 1.3 +1.2 +3.2 2.3 +1.2 +4.2 3.2 +1.8 +6.21.8 0 +1.3 2.7 0 +2.0 3.2 0 +2.5 4.2 0 +3.5 6.2 0 +5.02.56– 3.150.7 +0.7 +1.9 1.0 +1.2 +2.9 1.8 +1.2 +3.7 2.8 +1.2 +4.7 4.2 +1.8 +7.21.9 0 +1.4 2.9 0 +2.2 3.7 0 +3.0 4.7 0 +4.0 7.2 0 +6.03.15– 3.940.9 +0.9 +2.4 1.4 +1.4 +3.7 2.1 +1.4 +4.4 3.6 +1.4 +5.9 4.8 +2.2 +8.42.4 0 +1.8 3.7 0 +2.8 4.4 0 +3.5 5.9 0 +5.0 8.4 0 +7.03.94– 4.731.1 +0.9 +2.6 1.6 +1.4 +3.9 2.6 +1.4 +4.9 4.6 +1.4 +6.9 5.8 +2.2 +9.42.6 0 +2.03.9 0 +3.0 4.9 0 +4.0 6.9 0 +6.0 9.4 0 +8.0Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYFORCE AND SHRINK FITS664All data above heavy lines are in accordance with American-British-Canadian (ABC) agreements. Symbols H6, H7, s6, etc., are hole and shaft designations in theABC system. Limits for sizes above 19.69 inches are not covered by ABC agreements but are given in the ANSI standard.4.73– 5.521.2 +1.0 +2.9 1.9 +1.6 +4.5 3.4 +1.6 +6.0 5.4 +1.6 +8.0 7.5 +2.5 +11.62.9 0 +2.2 4.5 0 +3.5 6.0 0 +5.0 8.0 0 +7.0 11.6 0 +10.05.52– 6.301.5 +1.0 +3.2 2.4 +1.6 +5.0 3.4 +1.6 +6.0 5.4 +1.6 +8.0 9.5 +2.5 +13.63.2 0 +2.5 5.0 0 +4.0 6.0 0 +5.0 8.0 0 +7.0 13.6 0 +12.06.30– 7.091.8 +1.0 +3.5 2.9 +1.6 +5.5 4.4 +1.6 +7.0 6.4 +1.6 +9.0 9.5 +2.5 +13.63.5 0 +2.8 5.5 0 +4.5 7.0 0 +6.0 9.0 0 +8.0 13.6 0 +12.07.09– 7.881.8 +1.2 +3.83.2 +1.8 +6.2 5.2 +1.8 +8.2 7.2 +1.8 +10.2 11.2 +2.8 +15.83.8 0 +3.0 6.2 0 +5.0 8.2 0 +7.0 10.2 0 +9.0 15.8 0 +14.07.88– 8.862.3 +1.2 +4.3 3.2 +1.8 +6.2 5.2 +1.8 +8.2 8.2 +1.8 +11.2 13.2 +2.8 +17.84.3 0 +3.5 6.2 0 +5.0 8.2 0 +7.0 11.2 0 +10.0 17.8 0 +16.08.86– 9.852.3 +1.2 +4.3 4.2 +1.8 +7.2 6.2 +1.8 +9.2 10.2 +1.8 +13.2 13.2 +2.8 +17.84.3 0 +3.5 7.2 0 +6.0 9.2 0 +8.0 13.2 0 +12.0 17.8 0 +16.09.85– 11.032.8 +1.2 +4.94.0 +2.0 +7.2 7.0 +2.0 +10.2 10.0 +2.0 +13.2 15.0 +3.0 +20.04.9 0 +4.0 7.2 0 +6.0 10.2 0 +9.0 13.2 0 +12.0 20.0 0 +18.011.03– 12.412.8 +1.2 +4.9 5.0 +2.0 +8.2 7.0 +2.0 +10.2 12.0 +2.0 +15.2 17.0 +3.0 +22.04.9 0 +4.0 8.2 0 +7.0 10.2 0 +9.0 15.2 0 +14.0 22.0 0 +20.012.41– 13.983.1 +1.4 +5.5 5.8 +2.2 +9.4 7.8 +2.2 +11.4 13.8 +2.2 +17.4 18.5 +3.5 +24.25.5 0 +4.5 9.4 0 +8.0 11.4 0 +10.0 17.4 0 +16.0 24.2 0 +22.013.98– 15.753.6 +1.4 +6.1 5.8 +2.2 +9.49.8 +2.2 +13.4 15.8 +2.2 +19.4 21.5 +3.5 +27.26.1 0 +5.0 9.4 0 +8.0 13.4 0 +12.0 19.4 0 +18.0 27.2 0 +25.015.75– 17.724.4 +1.6 +7.0 6.5 +2.5 +10.6 +9.5 +2.5 +13.6 17.5 +2.5 +21.6 24.0 +4.0 +30.57.0 0 +6.0 10.6 0 +9.0 13.6 0 +12.0 21.6 0 +20.0 30.5 0 +28.017.72– 19.694.4 +1.6 +7.0 7.5 +2.5 +11.6 11.5 +2.5 +15.6 19.5 +2.5 +23.6 26.0 +4.0 +32.57.0 0 +6.0 11.6 0 +10.0 15.6 0 +14.0 23.6 0 +22.0 32.5 0 +30.0a Pairs of values shown represent minimum and maximum amounts of interference resulting from application of standard tolerance limits. Table 11. (Continued) ANSI Standard Force and Shrink Fits ANSI B4.1-1967 (R1999)NominalSize Range,InchesClass FN 1 Class FN 2 Class FN 3 Class FN 4 Class FN 5Inter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsInter-ferenceaStandard Tolerance LimitsHoleH6 ShaftHoleH7Shafts6HoleH7Shaftt6HoleH7Shaftu6HoleH8Shaftx7Over To Values shown below are in thousandths of an inchMachinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYINTERFERENCE LOCATIONAL FITS 665Table 12. ANSI Standard Interference Location Fits ANSI B4.1-1967 (R1999)All data in this table are in accordance with American-British-Canadian (ABC) agreements.Limits for sizes above 19.69 inches are not covered by ABC agreements but are given in the ANSIStandard.Symbols H7, p6, etc., are hole and shaft designations in the ABC system.Tolerance limits given in body of table are added or subtracted to basic size (as indicated by + or -sign) to obtain maximum and minimum sizes of mating parts.American National Standard Preferred Metric Limits and FitsThis standard ANSI B4.2-1978 (R1999) describes the ISO system of metric limits andfits for mating parts as approved for general engineering usage in the United States. It establishes: 1) the designation symbols used to define dimensional limits on drawings,material stock, related tools, gages, etc.; 2) the preferred basic sizes (first and secondchoices); 3) the preferred tolerance zones (first, second, and third choices); 4) the pre-ferred limits and fits for sizes (first choice only) up to and including 500 and5) the definitions of related terms.The general terms “hole” and “shaft” can also be taken to refer to the space containing orcontained by two parallel faces of any part, such as the width of a slot, or the thickness of akey.Definitions.—The most important terms relating to limits and fits are shown in Fig. 1 andare defined as follows: Basic Size: The size to which limits of deviation are assigned. The basic size is the samefor both members of a fit. For example, it is designated by the numbers 40 in 40H7. Deviation: The algebraic difference between a size and the corresponding basic size.NominalSize Range,InchesClass LN 1 Class LN 2 Class LN 3Limitsof Inter-ferenceStandard LimitsLimitsof Inter-ferenceStandard LimitsLimitsof Inter-ferenceStandard LimitsHoleH6Shaftn5HoleH7Shaftp6HoleH7Shaftr6Over To Values shown below are given in thousandths of an inch0– 0.120 +0.25 +0.45 0 +0.4 +0.65 0.1 +0.4 +0.750.45 0 +0.25 0.65 0 +0.4 0.75 0 +0.50.12– 0.240 +0.3 +0.5 0 +0.5 +0.8 0.1 +0.5 +0.90.5 0 +0.3 0.8 0 +0.5 0.9 0 +0.60.24– 0.400 +0.4 +0.65 0 +0.6 +1.0 0.2 +0.6 +1.20.65 0 +0.4 1.0 0 +0.6 1.2 0 +0.80.40– 0.710 +0.4 +0.8 0 +0.7 +1.1 0.3 +0.7 +1.40.80 +0.4 1.1 0 +0.7 1.4 0 +1.00.71– 1.190 +0.5 +1.0 0 +0.8 +1.3 0.4 +0.8 +1.71.0 0 +0.5 1.3 0 +0.8 1.7 0 +1.21.19– 1.970 +0.6 +1.1 0 +1.0 +1.6 0.4 +1.0 +2.01.1 0 +0.6 1.6 0 +1.0 2.0 0 +1.41.97– 3.150.1 +0.7 +1.3 0.2 +1.2 +2.1 0.4 +1.2 +2.31.3 0 +0.8 2.1 0 +1.4 2.3 0 +1.63.15– 4.730.1 +0.9 +1.6 0.2 +1.4 +2.5 0.6 +1.4 +2.91.6 0 +1.0 2.5 0 +1.6 2.9 0 +2.04.73– 7.090.2 +1.0 +1.9 0.2 +1.6 +2.80.9 +1.6 +3.51.9 0 +1.2 2.8 0 +1.8 3.5 0 +2.57.09– 9.850.2 +1.2 +2.2 0.2 +1.8 +3.2 1.2 +1.8 +4.22.2 0 +1.4 3.2 0 +2.0 4.2 0 +3.09.85– 12.410.2 +1.2 +2.3 0.2 +2.0 +3.4 1.5 +2.0 +4.72.3 0 +1.4 3.4 0 +2.2 4.7 0 +3.512.41– 15.750.2 +1.4 +2.6 0.3 +2.2 +3.9 2.3 +2.2 +5.92.6 0 +1.6 3.9 0 +2.5 5.9 0 +4.515.75– 19.690.2 +1.6 +2.8 0.3 +2.5 +4.4 2.5 +2.5 +6.62.8 0 +1.8 4.4 0 +2.8 6.6 0 +5.0Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYPREFERRED METRIC FITS 667A fundamental deviation establishes the position of the tolerance zone with respect to thebasic size (see Fig. 1). Fundamental deviations are expressed by tolerance position letters.Capital letters are used for internal dimensions and lowercase or small letters for externaldimensions.Symbols.—By combining the IT grade number and the tolerance position letter, the toler-ance symbol is established that identifies the actual maximum and minimum limits of thepart. The toleranced size is thus defined by the basic size of the part followed by a symbolcomposed of a letter and a number, such as 40H7, 40f7, etc.A fit is indicated by the basic size common to both components, followed by a symbolcorresponding to each component, the internal part symbol preceding the external partsymbol, such as 40H8/f7.Some methods of designating tolerances on drawings are:The values in parentheses indicate reference only.Preferred Metric Fits.—First-choice tolerance zones are used to establish preferred fitsin ANSI B4.2, Preferred Metric Limits and Fits, as shown in Figs. 2 and 3. A completelisting of first-, second-, and third- choice tolerance zones is given in the Standard.Hole basis fits have a fundamental deviation of H on the hole, and shaft basis fits have afundamental deviation of h on the shaft and are shown in Fig. 2 for hole basis and Fig. 3 forshaft basis fits. A description of both types of fits, that have the same relative fit condition,is given in Table 1. Normally, the hole basis however, when a commonshaft mates with several holes, the shaft basis system should be used.The hole basis and shaft basis fits shown in the table Description of Preferred Fits onpage 669 are combined with the first-choice preferred metric sizes from Table 1 onpage 690, to form Tables 2, 3, 4, and 5, in which specific limits as well as the resultant fitsare tabulated.If the required size is not found tabulated in Tables 2 through 5 then the preferred fit canbe calculated from numerical values given in an appendix of ANSI B4.2-1978 (R1999). Itis anticipated that other fit conditions may be necessary to meet special requirements, anda preferred fit can be loosened or tightened simply by selecting a standard tolerance zone asgiven in the Standard. Information on how to calculate limit dimensions, clearances, andinterferences, for nonpreferred fits and sizes can be found in an appendix of this Standard.Conversion of Fits: It may sometimes be neccessary or desirable to modify the tolere-ance zone on one or both of two mating parts, yet still keep the total tolerance and fit condi-tion the same. Examples of this appear in Table 1 on page 669 when converting from a holebasis fit to a shaft basis fit. The corresponding fits are identical yet the individual tolerancezones are different.To convert from one type of fit to another, reverse the fundamental devations between theshaft and hole keeping the IT grade the same on each individual part. The examples belowrepresent preferred fits from Table 1 for a 60-mm basic size. These fits have the same max-imum clearance (0.520) and the same minimum clearance (0.140).40H840H8 40H8Hole basis, loose running fit, values from Table 2Hole 60H11 Shaft 60c11 Fit 60H11/c11Hole basis, loose running fit, values from Table 4Hole 60C11 Shaft 60h11 Fit 60C11/h1140.03940.000????40.03940.000????60.19060.000????59.86059.670????0.5200.140????60.33060.140????60.00059.810????0.5200.140????Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYHOLE BASIS METRIC CLEARANCE FITS 671All dimensions are in millimeters.30Max 30.130 29.890 0.370 30.052 29.935 0.169 30.033 29.980 0.074 30.021 29.993 0.041 30.021 30.000 0.034Min 30.000 29.760 0.110 30.000 29.883 0.065 30.000 29.959 0.020 30.000 29.980 0.007 30.000 29.987 0.00040Max 40.160 39.880 0.440 40.062 39.920 0.204 40.039 39.975 0.089 40.025 39.991 0.050 40.025 40.000 0.041Min 40.000 39.720 0.120 40.000 39.858 0.080 40.000 39.950 0.025 40.000 39.975 0.009 40.000 39.984 0.00050Max 50.160 49.870 0.450 50.062 49.920 0.204 50.039 49.975 0.089 50.025 49.991 0.050 50.025 50.000 0.041Min 50.000 49.710 0.130 50.000 49.858 0.080 50.000 49.950 0.025 50.000 49.975 0.009 50.000 49.984 0.00060Max 60.190 59.860 0.520 60.074 59.900 0.248 60.046 59.970 0.106 60.030 59.990 0.059 60.030 60.000 0.049Min 60.000 59.670 0.140 60.000 59.826 0.100 60.000 59.940 0.030 60.000 59.971 0.010 60.000 59.981 0.00080Max 80.190 79.850 0.530 80.074 79.900 0.248 80.046 79.970 0.106 80.030 79.990 0.059 80.030 80.000 0.049Min 80.000 79.660 0.150 80.000 79.826 0.100 80.000 79.940 0.030 80.000 79.971 0.010 80.000 79.981 0.000100Max 100.220 99.830 0.610 100.087 99.880 0.294 100.054 99.964 0.125 100.035 99.988 0.069 100.035 100.000 0.057Min 100.000 99.610 0.170 100.000 99.793 0.120 100.000 99.929 0.036 100.000 99.966 0.012 100.000 99.978 0.000120Max 120.220 119.820 0.620 120.087 119.880 0.294 120.054 119.964 0.125 120.035 119.988 0.069 120.035 120.000 0.057Min 120.000 119.600 0.180 120.000 119.793 0.120 120.000 119.929 0.036 120.000 119.966 0.012 120.000 119.978 0.000160Max 160.250 159.790 0.710 160.100 159.855 0.345 160.063 159.957 0.146 160.040 159.986 0.079 160.040 160.000 0.065Min 160.000 159.540 0.210 160.000 159.755 0.145 160.000 159.917 0.043 160.000 159.961 0.014 160.000 159.975 0.000200Max 200.290 199.760 0.820 200.115 199.830 0.400 200.072 199.950 0.168 200.046 199.985 0.090 200.046 200.000 0.075Min 200.000 199.470 0.240 200.000 199.715 0.170 200.000 199.904 0.050 200.000 199.956 0.015 200.000 199.971 0.000250Max 250.290 249.720 0.860 250.115 249.830 0.400 250.072 249.950 0.168 250.046 249.985 0.090 250.046 250.000 0.075Min 250.000 249.430 0.280 250.000 249.715 0.170 250.000 249.904 0.050 250.000 249.956 0.015 250.000 249.971 0.000300Max 300.320 299.670 0.970 300.130 299.810 0.450 300.081 299.944 0.189 300.052 299.983 0.101 300.052 300.000 0.084Min 300.000 299.350 0.330 300.000 299.680 0.190 300.000 299.892 0.056 300.000 299.951 0.017 300.000 299.968 0.000400Max 400.360 399.600 1.120 400.140 399.790 0.490 400.089 399.938 0.208 400.057 399.982 0.111 400.057 400.000 0.093Min 400.000 399.240 0.400 400.000 399.650 0.210 400.000 399.881 0.062 400.000 399.946 0.018 400.000 399.964 0.000500Max 500.400 499.520 1.280 500.155 499.770 0.540 500.097 499.932 0.228 500.063 499.980 0.123 500.063 500.000 0.103Min 500.000 499.120 0.480 500.000 499.615 0.230 500.000 499.869 0.068 500.000 499.940 0.020 500.000 499.960 0.000a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b All fits shown in this table have clearance. Table 2. (Continued) American National Standard Preferred Hole Basis Metric Clearance Fits ANSI B4.2-1978 (R1999)BasicSizeaLoose Running Free Running Close Running Sliding Locational ClearanceHoleH11ShaftC11 FitbHoleH9Shaftd9 FitbHoleH8Shaftf7 FitbHoleH7Shaftg6 FitbHoleH7Shafth6 FitbMachinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYHOLE BASIS METRIC TRANSITION FITS 673All dimensions are in millimeters.30 Max 30.021 30.015 +0.019 30.021 30.028 +0.006 30.021 30.035 -0.001 30.021 30.048 -0.014 30.021 30.061 -0.027Min 30.000 30.002 -0.015 30.000 30.015 -0.028 30.000 30.022 -0.035 30.000 30.035 -0.048 30.000 30.048 -0.06140 Max 40.025 40.018 +0.023 40.025 40.033 +0.008 40.025 40.042 -0.001 40.025 40.059 -0.018 40.025 40.076 -0.035Min 40.000 40.002 -0.018 40.000 40.017 -0.033 40.000 40.026 -0.042 40.000 40.043 -0.059 40.000 40.060 -0.07650 Max 50.025 50.018 +0.023 50.025 50.033 +0.008 50.025 50.042 -0.001 50.025 50.059 -0.018 50.025 50.086 -0.045Min 50.000 50.002 -0.018 50.000 50.017 -0.033 50.000 50.026 -0.042 50.000 50.043 -0.059 50.000 50.070 -0.08660 Max 60.030 60.021 +0.028 60.030 60.039 +0.010 60.030 60.051 -0.002 60.030 60.072 -0.023 60.030 60.106 -0.057Min 60.000 60.002 -0.021 60.000 60.020 -0.039 60.000 60.032 -0.051 60.000 60.053 -0.072 60.000 60.087 -0.10680 Max 80.030 80.021 +0.028 80.030 80.039 +0.010 80.030 80.051 -0.002 80.030 80.078 -0.029 80.030 80.121 -0.072Min 80.000 80.002 -0.021 80.000 80.020 -0.03980.000 80.032 -0.051 80.000 80.059 -0.078 80.000 80.102 -0.121100 Max 100.035 100.025 +0.032 100.035 100.045 +0.012 100.035 100.059 -0.002 100.035 100.093 -0.036 100.035 100.146 -0.089Min 100.000 100.003 -0.025 100.000 100.023 -0.045 100.000 100.037 -0.059 100.000 100.071 -0.093 100.000 100.124 -0.146120 Max 120.035 120.025 +0.032 120.035 120.045 +0.012 120.035 120.059 -0.002 120.035 120.101 -0.044 120.035 120.166 -0.109Min 120.000 120.003 -0.025 120.000 120.023 -0.045 120.000 120.037 -0.059 120.000 120.079 -0.101 120.000 120.144 -0.166160 Max 160.040 160.028 +0.037 160.040 160.052 +0.013 160.040 160.068 -0.003 160.040 160.125 -0.060 160.040 160.215 -0.150Min 160.000 160.003 -0.028 160.000 160.027 -0.052 160.000 160.043 -0.068 160.000 160.100 -0.125 160.000 160.190 -0.215200 Max 200.046 200.033 +0.042 200.046 200.060 +0.015 200.046 200.079 -0.004 200.046 200.151 -0.076 200.046 200.265 -0.190Min 200.000 200.004 -0.033 200.000 200.031 -0.060 200.000 200.050 -0.079 200.000 200.122 -0.151 200.000 200.236 -0.265250 Max 250.046 250.033 +0.042 250.046 250.060 +0.015 250.046 250.079 -0.004250.046 250.169 -0.094 250.046 250.313 -0.238Min 250.000 250.004 -0.033 250.000 250.031 -0.060 250.000 250.050 -0.079 250.000 250.140 -0.169 250.000 250.284 -0.313300 Max 300.052 300.036 +0.048 300.052 300.066 +0.018 300.052 300.088 -0.004 300.052 300.202 -0.118 300.052 300.382 -0.298Min 300.000 300.004 -0.036 300.000 300.034 -0.066 300.000 300.056 -0.088 300.000 300.170 -0.202 300.000 300.350 -0.382400 Max 400.057 400.040 +0.053 400.057 400.073 +0.020 400.057 400.098 -0.005 400.057 400.244 -0.151 400.057 400.471 -0.378Min 400.000 400.004 -0.040 400.000 400.037 -0.073 400.000 400.062 -0.098 400.000 400.208 -0.244 400.000 400.435 -0.471500 Max 500.063 500.045 +0.058 500.063 500.080 +0.023 500.063 500.108 -0.005 500.063 500.292 -0.189 500.063 500.580 -0.477Min 500.000 500.005 -0.045 500.000 500.040 -0.080 500.000 500.068 -0.108 500.000 500.252 -0.292 500.000 500.540 -0.580a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b A plus sign a minus sign indicates interference. Table 3. (Continued) American National Standard Preferred Hole Basis Metric Transition and Interference Fits ANSI B4.2-1978 (R1999)BasicSizeaLocational Transition Locational Transition Locational Interference Medium Drive ForceHoleH7Shaftk6 FitbHoleH7Shaftn6 FitbHoleH7Shaftp6 FitbHoleH7Shafts6 FitbHoleH7Shaftu6 FitbMachinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYSHAFT BASIS METRIC CLEARANCE FITS 675All dimensions are in millimeters.30 Max 30.240 30.000 0.370 30.117 30.000 0.169 30.053 30.000 0.074 30.028 30.000 0.041 30.021 30.000 0.034Min 30.110 29.870 0.110 30.065 29.948 0.065 30.020 29.979 0.020 30.007 29.987 0.007 30.000 29.987 0.00040 Max 40.280 40.000 0.440 40.142 40.000 0.204 40.064 40.000 0.089 40.034 40.000 0.050 40.025 40.000 0.041Min 40.120 39.840 0.120 40.080 39.938 0.080 40.025 39.975 0.025 40.009 39.984 0.009 40.000 39.984 0.00050 Max 50.290 50.000 0.450 50.142 50.000 0.204 50.064 50.000 0.089 50.034 50.000 0.050 50.025 50.000 0.041Min 50.130 49.840 0.130 50.080 49.938 0.080 50.025 49.975 0.025 50.009 49.984 0.009 50.000 49.984 0.00060 Max 60.330 60.000 0.520 60.174 60.000 0.248 60.076 60.000 0.106 60.040 60.000 0.059 60.030 60.000 0.049Min 60.140 59.810 0.140 60.100 59.926 0.100 60.030 59.970 0.030 60.010 59.981 0.010 60.000 59.981 0.00080 Max 80.340 80.000 0.530 80.174 80.000 0.248 80.076 80.000 0.106 80.040 80.000 0.059 80.030 80.000 0.049Min 80.150 79.810 0.150 80.100 79.926 0.100 80.030 79.970 0.030 80.010 79.981 0.010 80.000 79.981 0.000100 Max 100.390 100.000 0.610 100.207 100.000 0.294 100.090 100.000 0.125 100.047 100.000 0.069 100.035 100.000 0.057Min 100.170 99.780 0.170 100.120 99.913 0.120 100.036 99.965 0.036 100.012 99.978 0.012 100.000 99.978 0.000120 Max 120.400 120.000 0.620 120.207 120.000 0.294 120.090 120.000 0.125 120.047 120.000 0.069 120.035 120.000 0.057Min 120.180 119.780 0.180 120.120 119.913 0.120 120.036 119.965 0.036 120.012 119.978 0.012 120.000 119.978 0.000160 Max 160.460 160.000 0.710 160.245 160.000 0.345 160.106 160.000 0.146 160.054 160.000 0.079 160.040 160.000 0.065Min 160.210 159.750 0.210 160.145 159.900 0.145 160.043 159.960 0.043 160.014 159.975 0.014 160.000 159.975 0.000200 Max 200.530 200.000 0.820 200.285 200.000 0.400 200.122 200.000 0.168 200.061 200.000 0.090 200.046 200.000 0.075Min 200.240 199.710 0.240 200.170 199.885 0.170 200.050 199.954 0.050 200.015 199.971 0.015 200.000 199.971 0.000250 Max 250.570 250.000 0.860 250.285 250.000 0.400 250.122 250.000 0.168 250.061 250.000 0.090 250.046 250.000 0.075Min 250.280 249.710 0.280 250.170 249.885 0.170 250.050 249.954 0.050 250.015 249.971 0.015 250.000 249.971 0.000300 Max 300.650 300.000 0.970 300.320 300.000 0.450 300.137 300.000 0.189 300.069 300.000 0.101 300.052 300.000 0.084Min 300.330 299.680 0.330 300.190 299.870 0.190 300.056 299.948 0.056 300.017 299.968 0.017 300.000 299.968 0.000400 Max 400.760 400.000 1.120 400.350 400.000 0.490 400.151 400.000 0.208 400.075 400.000 0.111 400.057 400.000 0.093Min 400.400 399.640 0.400 400.210 399.860 0.210 400.062 399.943 0.062 400.018 399.964 0.018 400.000 399.964 0.000500 Max 500.880 500.000 1.280 500.385 500.000 0.540 500.165 500.000 0.228 500.083 500.000 0.123 500.063 500.000 0.103Min 500.480 499.600 0.480 500.230 499.845 0.230 500.068 499.937 0.068 500.020 499.960 0.020 500.000 499.960 0.000a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b All fits shown in this table have clearance. Table 4. (Continued) American National Standard Preferred Shaft Basis Metric Clearance Fits ANSI B4.2-1978 (R1999)BasicSizeaLoose Running Free Running Close Running Sliding Locational ClearanceHoleC11Shafth11 FitbHoleD9Shafth9 FitbHoleF8Shafth7 FitbHoleG7Shafth6 FitbHoleH7Shafth6 FitbMachinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYSHAFT BASIS METRIC TRANSITION FITS 677All dimensions are in millimeters.30 Max 30.006 30.000 +0.019 29.993 30.000 +0.006 29.986 30.000 -0.001 29.973 30.000 -0.014 29.960 30.000 -0.027Min 29.985 29.987 -0.015 29.972 29.987 -0.028 29.965 29.987 -0.035 29.952 29.987 -0.048 29.939 29.987 -0.06140 Max 40.007 40.000 +0.023 39.992 40.000 +0.008 39.983 40.000 -0.001 39.966 40.000 -0.018 39.949 40.000 -0.035Min 39.982 39.984 -0.018 39.967 39.984 -0.033 39.958 39.984 -0.042 39.941 39.984 -0.059 39.924 39.984 -0.07650 Max 50.007 50.000 +0.023 49.992 50.000 +0.008 49.983 50.000 -0.001 49.966 50.000 -0.018 49.939 50.000 -0.045Min 49.982 49.984 -0.018 49.967 49.984 -0.033 49.958 49.984 -0.042 49.941 49.984 -0.059 49.914 49.984 -0.08660 Max 60.009 60.000 +0.028 59.991 60.000 +0.010 59.979 60.000 -0.002 59.958 60.000 -0.023 59.924 60.000 -0.087Min 59.979 59.981 -0.021 59.961 59.981 -0.039 59.949 59.981 -0.051 59.928 59.981 -0.072 59.894 59.981 -0.10680 Max 80.009 80.000 +0.028 79.991 80.000 +0.010 79.979 80.000 -0.002 79.952 80.000 -0.029 79.909 80.000 -0.072Min 79.979 79.981 -0.021 79.961 79.981 -0.039 79.949 79.981 -0.051 79.922 79.981 -0.078 79.879 79.981 -0.121100 Max 100.010 100.000 +0.032 99.990 100.000 +0.012 99.976 100.000 -0.002 99.942 100.000 -0.036 99.889 100.000 -0.089Min 99.975 99.978 -0.025 99.955 99.978 -0.045 99.941 99.978 -0.059 99.907 99.978 -0.093 99.854 99.978 -0.146120 Max 120.010 120.000 +0.032 119.990 120.000 +0.012 119.976 120.000 -0.002 119.934 120.000 -0.044 119.869 120.000 -0.109Min 119.975 119.978 -0.025 119.955 119.978 -0.045 119.941 119.978 -0.059 119.899 119.978 -0.101 119.834 119.978 -0.166160 Max 160.012 160.000 +0.037 159.988 160.000 +0.013 159.972 160.000 -0.003 159.915 160.000 -0.060 159.825 160.000 -0.150Min 159.972 159.975 -0.028 159.948 159.975 -0.052 159.932 159.975 -0.068 159.875 159.975 -0.125 159.785 159.975 -0.215200 Max 200.013 200.00 +0.042 199.986 200.000 +0.015 199.967 200.000 -0.004 199.895 200.000 -0.076 199.781 200.000 -0.190Min 199.967 199.971 -0.033 199.940 199.971 -0.060 199.921 199.971 -0.079 199.849 199.971 -0.151 199.735 199.971 -0.265250 Max 250.013 250.000 +0.042 249.986 250.000 +0.015 249.967 250.000 -0.004249.877 250.000 -0.094 249.733 250.000 -0.238Min 249.967 249.971 -0.033 249.940 249.971 -0.060 249.921 249.971 -0.079 249.831 249.971 -0.169 249.687 249.971 -0.313300 Max 300.016 300.000 +0.048 299.986 300.000 +0.018 299.964 300.000 -0.004 299.850 300.000 -0.118 299.670 300.000 -0.298Min 299.964 299.968 -0.036 299.934 299.968 -0.066 299.912 299.968 -0.088 299.798 299.968 -0.202 299.618 299.968 -0.382400 Max 400.017 400.000 +0.053 399.984 400.000 +0.020 399.959 400.000 -0.005 399.813 400.000 -0.151 399.586 400.000 -0.378Min 399.960 399.964 -0.040 399.927 399.964 -0.073 399.902 399.964 -0.098 399.756 399.964 -0.244 399.529 399.964 -0.471500 Max 500.018 500.000 +0.058 499.983 500.000 +0.023 499.955 500.000 -0.005 499.771 500.000 -0.189 499.483 500.000 -0.477Min 499.955 499.960 -0.045 499.920 499.960 -0.080 499.892 499.960 -0.108 499.708 499.960 -0.292 499.420 499.960 -0.580a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b A plus sign a minus sign indicates interference. Table 5. (Continued) American National Standard Preferred Shaft Basis Metric Transition and Interference Fits ANSI B4.2-1978 (R1999)BasicSizeaLocational Transition Locational Transition Locational Interference Medium Drive ForceHoleK7Shafth6 FitbHoleN7Shafth6 FitbHoleP7Shafth6 FitbHoleS7Shafth6 FitbHoleU7Shafth6 FitbMachinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NY678 GAGEMAKERS TOLERANCESTable 6. American National Standard Gagemakers Tolerances
ANSI B4.4M-1981 (R1987)For workpiece tolerance class values, see previous Tables 2 through 5, incl.Table 7. American National Standard Gagemakers Tolerances
ANSI B4.4M-1981 (R1987)All dimensions are in millimeters. For closer gagemakers tolerance classes than Class XXXM,specify 5 per cent of IT5, IT4, or IT3 and use the designation 0.05 IT5, 0.05 IT4, etc.Fig. 4. Relationship between Gagemakers Tolerance, Wear Allowance and Workpiece ToleranceGagemakers Tolerance Workpiece ToleranceClassISO Sym-bolaa Gagemakers tolerance is equal to 5 per cent of workpiece tolerance or 5 per cent of applicable ITgrade value. See Table 7. IT Grade Recommended Gage UsageZM 0.05 IT11 IT11 Low-precision gages recommended to be used to inspect workpieces held to internal (hole) tolerances C11 and H11 and to external (shaft) tolerances c11 and h11.YM 0.05 IT9 IT9 Gages recommended to be used to inspect workpieces held to internal (hole) tolerances D9 and H9 and to external (shaft) tolerances d9 and h9.XM 0.05 IT8 IT8 Precision gages recommended to be used to inspect work-pieces held to internal (hole) tolerances F8 and H8.XXM 0.05 IT7 IT7 Recommended to be used for gages to inspect workpieces held to internal (hole) tolerances G7, H7, K7, N7, P7, S7, and U7, and to external (shaft) tolerances f7 and h7.XXXM0.05 IT6 IT6 High-precision gages recommended to be used to inspect workpieces held to external (shaft) tolerances g6, h6, k6, n6, p6, s6, and u6.Basic Size Class ZM Class YM Class XM Class XXM Clas XXXMOver To (0.05 IT11) (0.05 IT9) (0.05 IT8) (0.05 IT7) (0.05 IT6)0 3 0.2 0.5 0.00033 6 0.5 0.6 0.00046 10 0.8 0.7 0.000510 18 0.1 0.9 0.000618 30 0.6 0.0 0.000730 50 0.1 0.2 0.000850 80 0.7 0.5 0.001080 120 0.3 0.7 0.0011120 180 0.0 0.0 0.0013180 250 0.7 0.3 0.0015250 315 0.5 0.6 0.0016315 400 0.0 0.8 0.0018400 500 0.7 0.1 0.0020Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYTOLERANCE APPLICATION 679Applications.—Many factors such as length of engagement, bearing load, speed, lubrica-tion, operating temperatures, humidity, surface texture, and materials must be taken intoaccount in fit selections for a particular application.Choice of other than the preferred fits might be considered necessary to satisfy extremeconditions. Subsequent adjustments might also be desired as the result of experience in aparticular application to suit critical functional requirements or to permit optimum manu-facturing economy. Selection of a departure from these recommendations will dependupon consideration of the engineering and economic factors th how-ever, the benefits to be derived from the use of preferred fits should not be overlooked.A general guide to machining processes that may normally be expected to produce workwithin the tolerances indicated by the IT grades given in ANSI B4.2-1978 (R1999) isshown in Table 8. Practical usage of the various IT tolerance grades is shown in Table 9.Table 8. Relation of Machining Processes to IT Tolerance GradesTable 9. Practical Use of International Tolerance GradesBritish Standard for Metric ISO Limits and FitsBased on ISO Recommendation R286, this British Standard BS
is intended toprovide a comprehensive range of metric limits and fits for engineering purposes, andmeets the requirements of metrication in the United Kingdom. Sizes up to 3,150 mm arecovered by the Standard, but the condensed information presented here embraces dimen-sions up to 500 mm only. The system is based on a series of tolerances graded to suit allclasses of work from the finest to the most coarse, and the different types of fits that can beobtained range from coarse clearance to heavy interference. In the Standard, only cylindri-cal parts, designated holes and shafts are referred to explicitly, but it is emphasized that therecommendations apply equally well to other sections, and the general term hole or shaftIT GradesLapping & HoningCylindrical GrindingSurface GrindingDiamond TurningDiamond BoringBroachingPowder Metal sizesReamingTurningPowder Metal sinteredBoringMillingPlaning & ShapingDrillingPunchingDie CastingFor Measurig Tools For MaterialIT Grades 14 15 16For Fits For Large Manufacturing TolerancesMachinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NY680 BRITISH STANDARD METRIC ISO LIMITS AND FITScan be taken to mean the space contained by or containing two parallel faces or tangentplanes of any part, such as the width of a slot, or the thickness of a key. It is also stronglyemphasized that the grades series of tolerances are intended for the most general applica-tion, and should be used wherever possible whether the features of the componentinvolved are members of a fit or not.Definitions.—The definitions given in the Standard include the following: Limits of Size: The maximum and minimum sizes permitted for a feature. Basic Size: The reference size to which the limits of size are fixed. The basic size is thesame for both members of a fit. Upper Deviation: The algebraical difference between the maximum limit of size and thecorresponding basic size. It is designated as ES for a hole, and as es for a shaft, whichstands for the French term écart supérieur. Lower Deviation: The algebraical difference between the minimum limit of size and thecorresponding basic size. It is designated as EI for a hole, and as ei for a shaft, which standsfor the French term écart inférieur. Zero Line: In a graphical representation of limits and fits, the straight line to which thedeviations are referred. The zero line is the line of zero deviation and represents the basicsize. Tolerance: The difference between the maximum limit of size and the minimum limit ofsize. It is an absolute value without sign. Tolerance Zone: In a graphical representation of tolerances, the zone comprisedbetween the two lines representing the limits of tolerance and defined by its magnitude(tolerance) and by its position in relation to the zero line. Fundamental Deviation: That one of the two deviations, being the one nearest to thezero line, which is conventionally chosen to define the position of the tolerance zone inrelation to the zero line. Shaft-Basis System of Fits: A system of fits in which the different clearances and inter-ferences are obtained by associating various holes with a single shaft. In the ISO system,the basic shaft is the shaft the upper deviation of which is zero. Hole-Basis System of Fits: A system of fits in which the different clearances and inter-ferences are obtained by associating various shafts with a single hole. In the ISO system,the basic hole is the hole the lower deviation of which is zero.Selected Limits of Tolerance, and Fits.—The number of fit combinations that can bebuilt up with the ISO system is very large. However, experience shows that the majority offits required for usual engineering products can be provided by a limited selection of toler-ances. Limits of tolerance for selected holes are shown in Table 1, and for shafts, in Table2. Selected fits, based on combinations of the selected hole and shaft tolerances, are givenin Table 3.Tolerances and Fundamental Deviations.—There are 18 tolerance grades intended tomeet the requirements of different classes of work, and they are designated IT01, IT0, andIT1 to IT16. (IT stands for ISO series of tolerances.) Table 4 shows the standardizednumerical values for the 18 tolerance grades, which are known as standard tolerances. Thesystem provides 27 fundamental deviations for sizes up to and including 500 mm, andTables 5a and 5b contain the values for shafts and Tables 6a and 6b for holes. Uppercase(capital) letters designate hole deviations, and the same letters in lower case designateshaft deviations. The deviation js (Js for holes) is provided to meet the need for symmetricalbilateral tolerances. In this instance, there is no fundamental deviation, and the tolerancezone, of whatever magnitude, is equally disposed about the zero line.Calculated Limits of Tolerance.—The deviations and fundamental tolerances providedby the ISO system can be combined in any way that appears necessary to give a required fit.Thus, for example, the deviations H (basic hole) and f (clearance shaft) could be associ-ated, and with each of these deviations any one of the tolerance grades IT01 to IT16 couldMachinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYBRITISH STANDARD METRIC ISO LIMITS AND FITS 681be used. All the limits of tolerance that the system is capable of providing for sizes up toand including 500 mm can be calculated from the standard tolerances given in Table 4, andthe fundamental deviations given in Tables 5a, 5b, 6a and 6b. The range includes limits oftolerance for shafts and holes used in small high-precision work and horology.The system provides for the use of either hole-basis or shaft-basis fits, and the Standardincludes details of procedures for converting from one type of fit to the other.The limits of tolerance for a shaft or hole are designated by the appropriate letter indicat-ing the fundamental deviation, followed by a suffix number denoting the tolerance grade.This suffix number is the numerical part of the tolerance grade designation. Thus, a holetolerance with deviation H and tolerance grade IT7 is designated H7. Likewise, a shaftwith deviation p and tolerance grade IT6 is designated p6. The limits of size of a compo-nent feature are defined by the basic size, say, 45 mm, followed by the appropriate toler-ance designation, for example, 45 H7 or 45 p6. A fit is indicated by combining the basicsize common to both features with the designation appropriate to each of them, for exam-ple, 45 H7-p6 or 45 H7/p6.When calculating the limits of size for a shaft, the upper deviation es, or the lower devia-tion ei, is first obtained from Tables 5a or 5b, depending on the particular letter designa-tion, and nominal dimension. If an upper deviation has been determined, the lowerdeviation ei = es - IT. The IT value is obtained from Table 4 for the particular tolerancegrade being applied. If a lower deviation has been obtained from Tables 5a or 5b, the upperdeviation es = ei + IT. When the upper deviation ES has been determined for a hole fromTables 6a or 6b, the lower deviation EI = ES - IT. If a lower deviation EI has been obtainedfrom Table 6a, then the upper deviation ES = EI + IT.The upper deviations for holes K, M, and N with tolerance grades up to and includingIT8, and for holes P to ZC with tolerance grades up to and including IT7 must be calculatedby adding the delta (?) values given in Table 6b as indicated.Example 1:The limits of size for a part of 133 mm basic size with a tolerance designationg9 are derived as follows:From Table 5a, the upper deviation (es) is - 0.014 mm. From Table 4, the tolerance grade(IT9) is 0.100 mm. The lower deviation (ei) = es - IT = 0.114 mm, and the limits of size arethus 132.986 and 132.886 mm.Example 2:The limits of size for a part 20 mm in size, with tolerance designation D3, arederived as follows: From Table 6a, the lower deviation (EI) is + 0.065 mm. From Table 4,the tolerance grade (IT3) is 0.004 mm. The upper deviation (ES) = EI + IT = 0.069 mm, andthus the limits of size for the part are 20.069 and 20.065 mm.Example 3:The limits of size for a part 32 mm in size, with tolerance designation M5,which involves a delta value, are obtained as follows: From Table 6a, the upper deviationES is - 0.009 mm + ? = -0.005 mm. (The delta value given at the end of Table 6b for thissize and grade IT5 is 0.004 mm.) From Table 4, the tolerance grade (IT5) is 0.011 mm. Thelower deviation (EI) = ES - IT = - 0.016 mm, and thus the limits of size for the part are31.995 and 31.984 mm.Where the designations h and H or js and Js are used, it is only necessary to refer to Table4. For h and H, the fundamental deviation is always zero, and the disposition of the toler-ance is always negative ( - ) for a shaft, and positive ( + ) for a hole. Example 4:The limits for a part 40 mm in size, designated h8 are derived as follows:From Table 4, the tolerance grade (IT8) is 0.039 mm, and the limits are therefore 40.000and 39.961 mm.Example 5:The limits for a part 60 mm in size, designated js7 or Js7 are derived as fol-lows: From Table 4, the tolerance grade (IT7) is 0.030 mm, and this value is dividedequally about the basic size to give limits of 60.015 and 59.985 mm.Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYPREFERRED NUMBERS 689Preferred NumbersPreferred numbers are series of numbers selected to be used for standardization purposesin preference to any other numbers. Their use will lead to simplified practice and theyshould be employed whenever possible for individual standard sizes and ratings, or for aseries, in applications similar to the following:1) Important or characteristic linear dimensions, such as diameters and lengths, areas,volume, weights, capacities.2) Ratings of machinery and apparatus in horsepower, kilowatts, kilovolt-amperes, volt-ages, currents, speeds, power-factors, pressures, heat units, temperatures, gas or liquid-flow units, weight-handling capacities, etc.3) Characteristic ratios of figures for all kinds of units.American National Standard for Preferred Numbers.—This ANSI Standard Z17.1-1973 covers basic series of preferred numbers which are independent of any measurementsystem and therefore can be used with metric or customary units.The numbers are rounded values of the following five geometric series of numbers:10N/5, 10N/10, 10N/20, 10N/40, and 10N/80, where N is an integer in the series 0, 1, 2, 3, etc. Thedesignations used for the five series are respectively R5, R10, R20, R40, and R80, where Rstands for Renard (Charles Renard, originator of the first preferred number system) and thenumber indicates the root of 10 on which the particular series is based.The R5 series gives 5 numbers approximately 60 per cent apart, the R10 series gives 10numbers approximately 25 per cent apart, the R20 series gives 20 numbers approximately12 per cent apart, the R40 series gives 40 numbers approximately 6 per cent apart, and theR80 series gives 80 numbers approximately 3 per cent apart. The number of sizes for agiven purpose can be minimized by using first the R5 series and adding sizes from the R10and R20 series as needed. The R40 and R80 series are used principally for expressing tol-erances in sizes based on preferred numbers. Preferred numbers below 1 are formed bydividing the given numbers by 10, 100, etc., and numbers above 10 are obtained by multi-plying the given numbers by 10, 100, etc. Sizes graded according to the system may not beexactly proportional to one another due to the fact that preferred numbers may differ fromcalculated values by +1.26 per cent to -1.01 per cent. Deviations from preferred numbersare used in some instances — for example, where whole numbers are needed, such as 32instead of 31.5 for the number of teeth in a gear.Basic Series of Preferred Numbers ANSI Z17.1-1973Series DesignationR5 R10 R20 R40 R40 R80 R80 R80 R80Preferred Numbers1.00 1.00 1.00 1.00 3.15 1.00 1.80 3.15 5.601.60 1.25 1.12 1.06 3.35 1.03 1.85 3.25 5.802.50 1.60 1.25 1.12 3.55 1.06 1.90 3.35 6.004.00 2.00 1.40 1.18 3.75 1.09 1.95 3.45 6.156.30 2.50 1.60 1.25 4.00 1.12 2.00 3.55 6.30… 3.15 1.80 1.32 4.25 1.15 2.06 3.65 6.50… 4.00 2.00 1.40 4.50 1.18 2.12 3.75 6.70… 5.00 2.24 1.50 4.75 1.22 2.18 3.87 6.90… 6.30 2.50 1.60 5.00 1.25 2.24 4.00 7.10… 8.00 2.80 1.70 5.30 1.28 2.30 4.12 7.30……3.15 1.80 5.60 1.32 2.36 4.25 7.50……3.55 1.90 6.00 1.36 2.43 4.37 7.75……4.00 2.00 6.30 1.40 2.50 4.50 8.00……4.50 2.12 6.70 1.45 2.58 4.62 8.25……5.00 2.24 7.10 1.50 2.65 4.75 8.50……5.60 2.36 7.50 1.55 2.72 4.87 8.75……6.30 2.50 8.00 1.60 2.80 5.00 9.00……7.10 2.65 8.50 1.65 2.90 5.15 9.25……8.00 2.80 9.00 1.70 3.00 5.20 9.50……9.00 3.00 9.50 1.75 3.07 5.45 9.75Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NYBRITISH STANDARD PREFERRED SIZES 691products, the preferred number series R5 to R40 (see page 689) should be used, and (b)whenever linear sizes are concerned, the preferred sizes as given in the following tableshould be used. The presentation of preferred sizes gives designers and users a logicalselection and the benefits of rational variety reduction.The second-choice size given should only be used when it is not possible to use the firstchoice, and the third choice should be applied only if a size from the second choice cannotbe selected. With this procedure, common usage will tend to be concentrated on a limitedrange of sizes, and a contribution is thus made to variety reduction. However, the decisionto use a particular size cannot be taken on the basis that one is first choice and the other not.Account must be taken of the effect on the design, the availability of tools, and other rele-vant factors.For dimensions above 300, each series continues in a similar manner, i.e., the intervals betweeneach series number are the same as between 200 and 300.Table 2. British Standard Preferred Sizes, PD
(1983)Choice Choice Choice Choice Choice Choice1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd1 5.2 23 65 122 1881.1 5.5 24 66 125 1901.2 5.8 25 68 128 1921.3 6 26 70 130 1951.4 6.2 28 72 132 1981.5 6.5 30 74 135 2001.6 6.8 32 75 138 2051.7 7 34 76 140 2101.8 7.5 35 78 142 2151.9 8 36 80 145 2202 8.5 38 82 148 2252.1 9 40 85 150 2302.2 9.5 42 88 152 2352.4 10 44 90 155 2402.5 11 45 92 158 2452.6 12 46 95 160 2502.8 13 48 98 162 2553 14 50 100 165 2603.2 15 52 102 168 2653.5 16 54 105 170 2703.8 17 55 108 172 2754 18 56 110 175 2804.2 19 58 112 178 2854.5 20 60 115 180 2904.8 21 62 118 182 2955 22 64 120 185 300Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NY692 MEASURING INSTRUMENTSMEASURING INSTRUMENTS AND INSPECTION METHODSVerniers and MicrometersReading a Vernier.—A general rule for taking readings with a vernier scale is as follows:Note the number of inches and sub-divisions of an inch that the zero mark of the vernierscale has moved along the true scale, and then add to this reading as many thousandths, orhundredths, or whatever fractional part of an inch the vernier reads to, as there are spacesbetween the vernier zero and that line on the vernier which coincides with one on the truescale. For example, if the zero line of a vernier which reads to thousandths is slightlybeyond the 0.5 inch division on the main or true scale, as shown in Fig. 1, and graduationline 10 on the vernier exactly coincides with one on the true scale, the reading is 0.5 +0.010 or 0.510 inch. In order to determine the reading or fractional part of an inch that canbe obtained by a vernier, multiply the denominator of the finest sub-division given on thetrue scale by the total number of divisions on the vernier. For example, if one inch on thetrue scale is divided into 40 parts or fortieths (as in Fig. 1), and the vernier into twenty-fiveparts, the vernier will read to thousandths of an inch, as 25 × 40 = 1000. Similarly, if thereare sixteen divisions to the inch on the true scale and a total of eight on the vernier, the latterwill enable readings to be taken within one-hundred-twenty-eighths of an inch, as 8 × 16 =128.If the vernier is on a protractor, note the whole number of degrees passed by the vernierzero mark and then count the spaces between the vernier zero and that line which coincideswith a graduation on the protractor scale. If the vernier indicates angles within five minutesor one-twelfth degree (as in Fig. 2), the number of spaces multiplied by 5 will, of course,give the number of minutes to be added to the whole number of degrees. The reading of theprotractor set as illustrated would be 14 whole degrees (the number passed by the zeromark on the vernier) plus 30 minutes, as the graduation 30 on the vernier is the only one toFig. 1. Fig. 2. Machinery&s Handbook 27th EditionCopyright 2004, Industrial Press, Inc., New York, NY694 MEASURING INSTRUMENTSequals one-fiftieth of 2.45 inches = 0.02 × 2.45 = 0.049 inch. Thus, the difference betweenthe length of a bar division and a vernier division is 0.050-0.049 = 0.001 inch. The vernierscale is graduated for direct reading to 0.001 inch. In the example, the vernier zero is pastthe 1.05 graduation on the bar, and the 0.029 graduation on the vernier coincides with a lineon the bar. Thus, the total reading is 1.079 inches.Fig. 2. Reading a Micrometer.—The spindle of an inch-system micrometer has 40 threads perinch, so that one turn moves the spindle axially 0.025 inch (1 ÷ 40 = 0.025), equal to thedistance between two graduations on the frame. The 25 graduations on the thimble allowthe 0.025 inch to be further divided, so that turning the thimble through one division movesthe spindle axially 0.001 inch (0.025 ÷ 25 = 0.001). To read a micrometer, count the num-ber of whole divisions that are visible on the sca