DETAILS OF CURVE PRODUCTION. 61 



overlapping periods is applied to the mean of the 4, producing a prob- 

 able value of the fifth between the years 1720 and 1820. This probable 

 value is inserted in parenthesis in the table and all 5 values added up 

 for an average. As a rule, groups are carried back only far enough to 

 make assumed values of this kind a minimum in number. 



There is one other problem in this immediate connection, namely, 

 that of " gross rings." By gross rings I mean certain regions in a section 

 where the average size of the rings becomes 2 to 5 times as great as 

 normal. This is a problem by itself, both as to cause and as to method 

 of treatment. Some study of its prevalence in different trees has been 

 made, and it is usually safe to say that where an epoch is shown to have 

 gross rings in one tree, the chances are at least even that the same 

 years will have gross rings in the next tree. Since gross rings may not 

 come oftener than once in several hundred years and last only 10 to 

 15 years, it is evident that we are dealing with something more than 

 mere accident. The phenomenon probably has a climatic character. 

 Yet, gross rings are not universal at any one time, and while one epoch 

 may show gross rings in half the trees of a group it does not show it in 

 the other half, judging by the groups examined. It is considered best 

 to allow the ring values to enter the curves just as they are found, for 

 while the gross rings disturb very greatly the size of a series of 10 to 

 20 rings, they do not seriously disturb the relation in size between a 

 ring and its immediate neighbors. They therefore, as a rule, do not 

 render the rings unidentifiable. It is likely, therefore, that they should 

 be included in the means, and if some better way of handling them is 

 discovered later it will not be difficult to apply it. 



SMOOTHING. 



In general the smoothing of a curve means removing some of the 

 minor variations, so that the larger variations may be perceived. In 

 the early part of the work the use of overlapping means was adopted. 

 At the very start, overlapping means of a considerable number, such 

 as 11 or 9, were used. This was quickly changed to overlapping means 

 of 3. These overlapping means were done by the calculating machine 

 (Brunswiga). On this machine three were added and then contin- 

 uously the one next in sequence was added, while one at the other end 

 of the three was dropped. However, this was changed to Hann's 

 formula, because his formula is normally easier to apply and it gives a 

 little more individuality to each observation. The method of applying 

 Hann's formula consisted in adding to a table two columns consisting 

 of, respectively, first and second intermediate values. This can be done 

 rapidly and without taking too much space. To express the differences 

 between overlapping means and Hann's formula graphically, we only 

 need to say that if we take successive groups of three in any curve, 

 forming a triangle, the center of gravity of the triangle is the value 



