178 Mr. K. H. M. Bosanquet on the 



the most confident reliance may be placed on this Table for 

 finding a vulgar fraction whose value shall very nearly corre- 

 spond to a given value, yet the particular cases must be ex- 

 cepted in which the given value approaches very nearly to one 



of the critical fractions, T , T , &c, ~, s , &c., ^, o> o> & c - 1 an( ^ 

 so for others. * X 2 2 6 6 6 



This is the point to which, as the leading subject of this 

 paper, I wished to invite the reader's attention. But, as 

 regards the practical use of the Table, in every case (including 

 all these excepted cases) the Table may be made available for 

 exhibiting two vulgar fractions whose product will exhibit the 

 required number with great accuracy, and that in many dif- 

 ferent ways. Suppose, for instance, the number to be pro- 

 duced is 2*0098, whose logarithm is 0*30315. The nearest 

 logarithms in the Table are 0*30103 and 0*30544, which are 

 far too wide for any accurate purpose. But (among many 

 equally favourable combinations) there is no difficulty in fixing 



91 

 on the tabular numbers •== whose logarithm is 0*17371, and 



97 



=75 whose logarithm is 0*12944. The sum of these logarithms 



91 97 

 is 0*30315, as was required; and therefore 2*0098 = ^ x =~. 



On performing numerically the product of these vulgar 

 fractions, it is found to be 2*00979. 



Instead of sum of logarithms of vulgar fractions, difference 

 might be used if it were thought desirable. 



Royal Observatory, Greenwich, 

 1881, August 4. 



XXI. Note on the Laboratory at St. John's College^ Oxford. 

 By E. H. M. Bosanquet*. 



IN the paper on Beats recently published, the examination 

 of certain simple forms of Beat was described. The 

 then existing arrangements were not free from disturbing 

 noises (engine, shafting, &c); and it appeared to me to be a 

 waste of time to proceed further with these investigations 

 until some improvement in this respect could be effected. 



A small hydraulic engine was procured and attached to the 

 main supply. The pressure available proved, however, insuffi- 

 cient, as I had anticipated; and the attempt was consequently 

 a failure. 



Under these circumstances I applied to the College for 



* Communicated by the Author, 



