6qo philosophical transactions. [anno 1775. 



224° ; or may even pass without injury into air heated to a much greater degree, 

 according to the observations of Duhamel and Tillett, published in the Memoirs 

 of the Acad, of Sciences for 1761. On the other hand, all those bodies which 

 are powerful conductors of fire from air, are influenced in proportion when 

 surrounded with this medium. The bees wax melted from the mere contact of 

 the air in experiment 8 ; and in experiment 6, the albumen ovi was coagulated 

 on the intervention of another body, which is a strong conductor of fire from 

 air. But whether this method of reasoning on the natural cause of these 

 effects be just or not, the final cause is obvious, and is to be resolved into the 

 wise and benevolent appointment of the Almighty. Man is happily so framed, 

 as to possess a power of keeping nearly the same tenor of heat, in all the varia- 

 tions of the temperature of the air in summer and^ in winter, in hot and cold 

 climates ; and consequently changes his situation on the surface of the globe, 

 with much less inconvenience or injury, than he could otherwise have done. 

 The same power likewise happily adapts different animals to their respective 

 destinations. The lizard and the camelion remain cool under the equator, while 

 the whale and porpoise retain a degree of heat above that of the human body, 

 though surrounded with the waters of the coldest Northern Seas, and amidst 

 mountains of ice in the neighbourhood of the Pole. 



XLVI. Calculations in Spherical Trigonometry Abridged. By Israel Lyons. 



p. 470. 

 Since astronomical observations have been made with much greater precision 

 than formerly, it has become requisite that the calculations corresponding to 

 them should likewise be made to much greater degrees of exactness. The 

 ancient astronomers desired only to make their observations and computations 

 agree within a part of a degree ; succeeding ones were satisfied when they cor- 

 responded within a minute ; but no less exactness than seconds will content the 

 moderns. The rules in spherical trigonometry being reduced to operations by 

 logarithms, it is necessary to use such a number of figures in the tables as will 

 produce the required precision ; this is very different in the various parts of the 

 quadrant, insomuch that if the arc is only 1 degree, 4 places of decimals in the 

 logarithm of a sine are sufficient to determine the arc to which it belongs within 

 a second : whereas if the arc is 89°, there is a necessity of using 8 figures for 

 the same purpose : thus, the logarithm sine of 89° O' O" is 9.9999338, the 

 sam'e 7 figures as for the logarithm sine of 89° o' \". From this consideration 

 it follows, that the analogies commonly laid down and used for the solutions of 

 spherical triangles, are not in all cases equally convenient, and I might say, 

 equally accurate ; and that it would be more easy and exact in calculations to 

 find what was required, by means of sines of arcs, which, being small, require 

 the use of only a few places of figures. Now the cases which often occur in 



