立木之樹幹材積，不論其製品或價值上皆佔極重要地位，故為測計之主要對象。在森林調查或欲編製森林經營計劃時，對於立木材積資料之獲取，皆必須使用立木材積表，而當材積表之編製距現時太久；或無某樹種材積表，又不能伐倒立木測其材積時，有必要發展測計立木材積之新方法。1947年奧國森林學家Bitterlich發表使用角度計數調查法後，陸續發展出多種測計儀器，Tele-relaskop除能以無邊樣區取樣法選取樣木外，並具有測計胸高斷面積、樹高及樹幹任意位置之直徑與高度的相對值，利用所測計之資料，進而由幾種求積法得到立木之材積。本論文將以不等機率取樣理論為基礎，採用無邊樣區取樣法中之水平樣點取樣法，使用Tele-relaskop選取樣木及測定林木，而能在沒有材積表的狀況下，推算材積。
　　本研究主要使用雙重取樣法，第一面取樣由無邊樣區取樣法，使用Tele-relaskop選取樣木推算林分斷面積，再以比率估計之Midzuno氏不等機率設計法抽取第二面樣區，採用Tele-relaskop測計第二面樣區之林木推算樹徑及樹高，進行幾種求積法之比較，結果發現由任意直徑之最小資料求積法（四點法）推算材積，進而推算每公頃林分平均材積與株數之結果最佳。使得森林調查從取樣、測計到材積推論，都能達到精簡且精密的目的。

The stem volume of a tree is the most important either in it's wood product or in it's value, therefore the volume estimated is the major subject of forest mensuration. In the forest survey or preparing the forest management plan, the data of tree volume must get from volume table. When the tree volume table was constructed for a long time, or shortage, and not able to cut standing tree to measure it's volume, it is necessary to develop a new method to measure standing volume. After Bitterlich, an forester of Austrian, developed the angle gauge sampling in 1974, several measured instrument are created continually. Tele-relaskop can be used to choice sample tree by plotless sampling, and it can measure the basal area at breast height, the tree height and the relative value of diameter and height at any point. Using the measured data we can get the volume by several estimated methods. This study will use unequal probability sampling as a basis, adopt the horizontal point sampling of plotless sampling, and final use Tele-relaskop to choice sample trees. Then we can estimate volume without volume table.
In this study, double sampling is a major method. It uses plotless sampling at first-phase sample, then chooses sample trees and estimates stand basal area by Tele-relaskop. After that, we use ratio estimator with Midzuno's design of unequal probability sampling to get the data of second-phase sample. Then, using Tele-relaskop to measure trees in second-phase sample and estimate the diameters and the tree heights. Proceeding to the last step, we will compare several methods of estimating volume. The result showed that when we use any visible diameters method for minimum data(four points) to estimate volume and to estimate stand average volume and number of tree per acre, we can get the best outcome. So, this study can reach the objectives of simplicity and precision, no matter with sampling, measuring or estimating volume.

中文摘要
英文摘要
一．緒論............................... 1
（一）前言...................................1
（二）研究動機...........................2
（三）研究目的...........................4
二．前人之研究成果............6
（一）PPF與PPS.......................6
（二）取樣方法比較之研究.............. 6
（三）水平樣點取樣法之取樣設計研究....... 9
（四）鄰界影響偏差.......................................10
三．不等機率取樣理論..........................12
（一）無邊樣區取樣法...................................13
（二）不等機率之取樣設計...........................15
　　１．不等機率之歸還取樣.......................15
　　２．不等機率之不歸還取樣...................19
　　３．順序樣本與非順序樣本...................23
　　４．Midzuno氏設計法............................24
　　５．比率估計法.......................................25
（三）不等機率之取樣程序............................28
　　１．列表取樣法........................................29
　　２．Lahiri法.............................................30
四．研究材料與方法...............................31
（一）供試材料...............................................31
１．樹種與立地概況...............................31
　　２．調查方法與步驟...............................32
（二）不等機率之取樣...................................34
１．無邊樣區取樣法...............................34
　　２．取樣設計...........................................34
　　３．決定樣本大小...................................39
（三）應用Tele-relaskop之研究....................40
１．樹幹任意位置直徑與高度之計算............40
　　２．Tele-relaskop之可信度..............................41
　　３．六種求積法.........................................43
　　４．建立迴歸模型.......................................47
　　５．計算材積...........................................48
　　６．比較六種方法.......................................49
　　７．估計族群平均每公頃材積.........................50
五．結果與分析.........................................51
（一）不等機率之取樣結果分析...........................51
　　１．無邊樣區取樣之結果分析.........................51
　　２．八種取樣方法之樣本分佈.........................53
　　３．八種取樣方法之MLE..............................56
　　４．樣本數大小.....................................58
（二）Tele-relaskop測計結果分析........................60
　　１．Tele-relaskop可信度分析........................60
　　２．迴歸模型之建立.................................63
　　３．計算材積結果...................................64
　　４．變異數分析法...................................66
　　５．平均每公頃材積.................................69
　　６．四點法之測點...................................70
六．結論與討論.........................................72
（一）不等機率取樣.....................................72
（二）Tele-relaskop之測計..............................73
七．引用文獻...........................................77
八．附錄...............................................83

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