97 



the continual repetition of these changes will likewise produce an 

 equilibrium. According to these principles he undertakes to explain 

 all the laws of increasing and decreasing heat ; he supplies us with 

 various examples as to the application of them, and shows how this 

 theory coincides with the general law laid down in the first part of 

 the paper. 



The drift of this treatise will be still further illustrated, if we at- 

 tend to the following recapitulation given us by the author of the 

 leading principles deduced from the various parts of his investigation. 



1. The effect of a constant source of heat upon the thermometer 

 is not proportional to the heat of that source. 



2. We nevertheless possess a method of determining the heat of 

 the source by its effect on the thermometer, because we know the 

 law this effect follows in its successive increments. 



3. This method is the only one that ought to be employed when 

 it is required to compare two sources of heat, according to their effect 

 in a limited time, less than that which is necessary to produce the 

 maximum of the effect. 



4. In the case of transmitted heat, we must distinguish that which 

 is immediately transmitted, from that which is added by the trans- 

 mitting body after it becomes heated. 



5. If we neglect making the distinction, the interception of heat 

 attributed to the intercepting body is only an inferior limit or mini- 

 mum ; so that it remains undetermined whether the interception has 

 not been much greater, or even total. 



6. By applying these principles to Dr. Herschel's experiments, a 

 more exact appreciation may be obtained ; it is, however, governed 

 by some accessory circumstances, which have not yet been deter- 

 mined. 



7. In those experiments the apparent difference between the in- 

 terception of heat and of light by the same substances, does not af- 

 ford any fair conclusion respecting the difference or the identity of 

 light and heat. 



8. The law mentioned in the first part of the paper is not only 

 proved by direct experiments, but also by its agreement with the 

 true theory of the earth. 



Lastly. This theory is established upon various facts, entirely dif- 

 ferent from the above law, and it is the only one which agrees with 

 the general phenomena of nature. 



Of the Rectification of the Conic Sections. By the Rev. John Hellins, 

 B.D. F.R.S. and Vicar of Potter' s-Pury, in Northamptonshire. 

 Read July 8, 1802. [Phil. Trans. 1802, p. 448.] 



This, it is to be observed, is only the first part of a more extensive 

 work, and relates merely to the rectification of the hyperbola. After 

 a few strictures on the necessity of not relaxing in our endeavours to 

 improve the method of fluxions, to which the author asserts few ad- 

 ditions have been made since its first discovery by the immortal 



