274 PROCEEDINGS OF THE AMERICAN ACADEMY. 



very thin transparent rice paper, with vertical guide-lines at certain 

 standard temperatures, which enabled these plots to be accurately ori- 

 ented as far as rotation and horizontal displacement were concerned, 

 but left them free to slide up and down over each other. The sheets 

 were then piled on top of one another on a transparent table lighted 

 from below, each one placed so as to make its piece of curve coincide 

 most satisfactorily with the overlapping pieces already laid down. The 

 exact relative displacements of the sheets were then carefully measured. 

 This process was repeated for each of the three observers' sets of sheets 

 independently, four different times for each set, in two very different 

 orders and in those orders reversed, on different days, all with the ob- 

 ject of avoiding as far as possible any routinizing effects of memory or 

 habit which might disturb the real independence of the four determina- 

 tions. The means of the measured displacements were then used to 

 reduce each of the pieces of curve in any one of the sets to a zero com- 

 mon to all the curves of that set. The results are marked Gy, Gs, and 

 P in Figure 5. They are plotted separately for clearness, but they 

 are simply different experimental determinations of exactly the same 

 real curve. The vertical scale of each is that indicated at the side of 

 the diagram, but the height of each above its true zero is still unknown. 

 Each of the circles represents at least one independent throttling ob- 

 servation, and some of them two or three independent observations 

 that happened to coincide. It will be noticed that no one of the curves 

 is more than a fifth of a scale division, or four tenths of a calorie, wide 

 between centers. Each is, therefore, a self-consistent determination of 

 the true curve within two tenths of a calorie, or about three hundredths 

 of one per cent. 



The next step was to establish a comparison between the three 

 curves. The points of each were first divided into groups, each includ- 

 ing some 20° of temperature range, and the mean point of each group 

 was used to represent the group. This procedure is justified by the 

 fact that so short a section of the total heat curve can be considered 

 straight without serious error. There were eighteen such means, seven 

 representing Grindley's points, five Griessmann's and six Peake's. 

 These means were then plotted on three more sheets of rice paper, the 

 resulting curves were superposed in the way already described, and a 

 determination was made of the corrections necessary to reduce all three 

 sets of means to a common but still arbitrary zero. 



In the meantime successive means from each of the three curves 

 taken separately were used to compute the values of the derivative 

 dH/dt which are plotted with large circles in Figure 6. It is evident 

 that the results from the three sources agree with each other in deter- 



