288 



shewn, that there is a waste of heat in the steam-engine, which is 

 a necessary consequence of its nature. It can be reduced only by 

 increasing the initial pressure of steam, and the extent of the expan- 

 sive action ; and to both these resources there are practical limits. 



In conclusion of the present paper, the author states, that, from 

 his equations, many additional formulae are deducible, with respect 

 to the specific heat of imperfect gases, to certain questions in meteor- 

 ology, and to the specific heat of liquids ; but from the want of suffi- 

 cient experimental data, he conceives that they are not as yet capa- 

 ble of being usefully applied. 



2. On Probable Inference. By Bishop Terrot. 



The paper commenced with a suggestion, that, as the inferences of 

 ordinary logic admitted no premises but such as were absolutely cer- 

 tain, and as the premises with which we have to deal in the business 

 of life were not certain, but only probable, therefore it was highly de- 

 sirable that we should have a logic, or rules for drawing inferences 

 on the case of probable premises. 



The attention of the Society was then drawn to the 15th section 

 of the article Probabilities, in the Encyelopcedia Metropolitana, and 

 especially to the following passage : " It is an even chance that A is 

 B, and the same that B is C ; and therefore, 1 to 3 from these 

 grounds only that A is C. But other considerations of themselves 

 give an even chance that A is C. What is the resulting degree of 

 evidence that A is C ?" To which query the answer in the Ency- 

 clopcedia is §. 



On this passage it was observed, in the first place, that the asserted 

 ratio of 1 to 3, or the probability ^ in the first syllogism, was true 

 only on the hypothesis that A can be C only through the intervention 

 of the middle terra B. But that when such is not the case, when 

 other ways are conceivable but totally unknown, the probability is 

 not ^ but ^ ; these two fractions representing, the one the probabi- 

 lity of the evidence of a complete proof that A is C, the other the 

 probability that A is C ; and it was observed, that, in practical ques- 

 tions, it is the latter probability alone which we have an interest in 

 determining. 



